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Slide1: 

Chapter 1 Introduction

INVENTORY: 

INVENTORY Who cares about it? Real economic impact is worse Cause? Mismatch can take one of two forms Rigidity Process analysis

The Economic Consequences of the Supply-Demand Mismatch are Severe: 

The Economic Consequences of the Supply-Demand Mismatch are Severe

What Can OPC (This Course) Do to Help? Step 1: Help Making Operational Trade-Offs: 

Example: Call center of Deutsche Bundesbahn - objective: 80% of incoming calls wait less than 20 seconds - now (early 2003): 30% of incoming calls wait less than 20 seconds - Problem: staffing levels of call centers / impact on efficiency OM helps: Provides tools to balance responsiveness with efficiency What Can OPC (This Course) Do to Help? Step 1: Help Making Operational Trade-Offs

Step 2: Overcome Inefficiencies: 

Responsiveness Low High Eliminate inefficiencies Current frontier In the industry Labor Productivity (e.g. $/call) Low labor productivity High labor productivity Competitor A Competitor C Competitor B Example: Benchmarking shows the pattern above Don’t just manage the current system… Change it! OM helps: Provides tools to identify and eliminate inefficiencies Step 2: Overcome Inefficiencies

Step 3: Evaluate Proposed Redesigns/New Technologies: 

Example: What will happen if we develop / purchase technology X? Better technologies are always (?) nice to have, but will they pay? OM helps: Evaluates system designs before they occur Step 3: Evaluate Proposed Redesigns/New Technologies

Chapter 2 The Process View of the Organization: 

Chapter 2 The Process View of the Organization

Processes: how to describe them?: 

Inputs and Outputs Flow Unit Process flow chart (activities and buffers) Resources Processes: how to describe them?

Inventory, Rate, and Time: 

Inventory Flow Time Flow Rate Inventory, Rate, and Time

Little’s law: It’s more powerful than you think...: 

What it is: Inventory (I) = Flow Rate (R) * Flow Time (T) Implications: Out of the three fundamental performance measures (I,R,T), two can be chosen by management, the other is GIVEN by nature Hold throughput constant: Reducing inventory = reducing flow time Examples: Indirect measurement of flow time Inventory turns: compute right from financial data Rate: 5000kg/week Inventory: 2500kg Rate: 1500 customers/day Inventory: 25 customers Cost of Goods sold: 25,263 mill $/year Inventory: 2,003 mill $ Cost of Goods sold: 20,000 mill $/year Inventory: 391 mill $ Little’s law: It’s more powerful than you think... Burger King: Dell: Compaq:

Inventory Turns in Retailing and Its Link to Inventory Costs: 

Inventory Turns in Retailing and Its Link to Inventory Costs Inventory Cost Computation

5 Reasons to Hold Inventory: 

5 Reasons to Hold Inventory Pipeline Seasonal Cycle Decoupling/Buffer Safety

Slide13: 

Job Shop Batch Process Worker-paced line Machine-paced line Continuous process Low Volume (unique) Medium Volume (high variety) High Volume (lower variety) Very high volume (standardized) Utilization of fixed capital generally too low Unit variable costs generally too high CABG Surgery Exec. Shirt Toshiba Toyota National Cranberry Manzana Insurance Categorizes processes into one of five clusters Similar processes tend to have similar problems There exists a long-term drift from the upper left to the lower right The Product-Process Matrix

Chapter 3 An Introduction to Operations Management : 

Chapter 3 An Introduction to Operations Management

How to Create a Process Flow Diagram: 

How to Create a Process Flow Diagram

How to Create a Process Flow Diagram (ctd.): 

How to Create a Process Flow Diagram (ctd.) ~ 160 m Iron Ore Fines CFB Preheater Inclined Bucket Elevator 1st Stage CFB Reactor 2nd Stage FB Reactor Briquetting Plant HBI Product Process Gas Heat Exchanger Process Gas Compressor Fired Gas Heaters ~ 110 m Electrical Substation& Control Room

How to Create a Process Flow Diagram (ctd.): 

How to Create a Process Flow Diagram (ctd.)

Key-points to remember from Process Analysis: 

Simplify a complex process using a process flow diagram Bottleneck analysis: analyze the process by looking at the bottleneck Bottleneck may depend on the product mix Time to complete X units Starting with a loaded system: Starting with an empty system - For continuous flow processes: (X-1) = X - If capacity constrained, flow rate is dictated by the bottleneck Key-points to remember from Process Analysis

Flow Rate R: Demand vs. Capacity Constrained: 

Flow Rate=Min{Demand, Capacity} Demand Input Bottleneck (Capacity) Excess capacity Flow Rate Demand Input Bottleneck (Capacity) Excess capacity Flow Rate Demand constrained Demand Input Bottleneck (Capacity) Excess capacity Flow Rate Demand Input Bottleneck (Capacity) Excess capacity Flow Rate Capacity constrained Demand constrained Flow Rate R: Demand vs. Capacity Constrained

Process Utilization and Capacity Utilization: 

Process Utilization and Capacity Utilization Utilization: How much is produced relative to what could be produced Can be computed for an entire process and for each resource in a process Maximum values?

How To Conduct a Process Analysis: 

How To Conduct a Process Analysis Use different Colors to mark Flow units Note that capacity levels may differ depending on product type Compute the work - load across all product types Step with highest implied utilization Extensions required For working with Multiple flow units Use different Colors to mark Flow units Note that capacity levels may differ depending on product type Compute the work - load across all product types Step with highest implied utilization

Slide22: 

A finance company receives 1,000 loan applications per 30 day working month and makes accept/reject decisions based upon a thorough review. On average, 20% of all applications receive approval. An internal audit revealed that the company has 500 applications in process at various stages. In response to customer complaints, the company forms an initial review team to pre-process all applications. Each application will be categorized either A (excellent), B (needs more detailed review), or C (reject). On average 25% of the applications are type A and type B, and 50% are type C. 70% of type A and 10% of type B applications are approved on review. Internal audit checks show that 200 applications are with the initial review team, 25 with the type A team, and 150 with the type B team. Has customer service improved?

Slide23: 

A hospital ER is currently organized so that all patients register through an initial check-in process. At his turn, each patient is seen by a doctor and then exits the process, either with a prescription or with admission to the hospital. Currently, 50 people per hour arrive at the ER, 10% of whom are admitted to the hospital. On average, 30 people are waiting to be registered and 40 are registered and waiting to see a doctor. The registration process takes, on average, 2 minutes per patient. Among patients who receive prescriptions, average time spent with a doctor is 5 minutes. Among those admitted to the hospital, average time is 30 minutes. On average, how long does a patient stay in the ER? how many patients are being examined by doctors? how many patients are in the ER?

Chapter 4 Estimating and Reducing Labor Costs: 

Chapter 4 Estimating and Reducing Labor Costs

A Labor Intense Process (Novacruz Case): 

A Labor Intense Process (Novacruz Case) Components Finished Xootrs Activity 1 13 minutes Activity 2 11 minutes Activity 3 8 minutes    

Xootr Task Durations: 

Xootr Task Durations

Labor Content and Idle Time: 

Measures of labor productivity Labor Content and Idle Time

Time to Process X Units Starting Empty: 

Time to Process X Units Starting Empty Initial Xootr calculations for CY 2000…

Lifecycle Demand Trajectory for Xooters: 

Lifecycle Demand Trajectory for Xooters

Scaling Up to Higher Volumes/Increasing Efficiency: 

Scaling Up to Higher Volumes/Increasing Efficiency Line balancing Takt time Line replicating Task specialization Adding workers

Balancing an Assembly Line (Fig 4.5) : 

Balancing an Assembly Line (Fig 4.5) Step 1 Step 2 Step 3 Step 1 Step 2 Step 3 Cycle Time Before Line Balancing Cycle Time After Line Balancing 0 100 200 300 400 500 600 700 800 900 Activity time [seconds] 0 100 200 300 400 500 600 700 800 900 Activity time [seconds] 1: Prepare cable 2: Move cable 3: Assemble washer 4: Apply fork, threading cable end 5: Assemble Socket head screws 6: Steer pin nut 7: Brake shoe, spring, pivot bolt 8: Insert front wheel 9: Insert axle bolt 10: Tighten axle bolt 11: Tighten brake pivot bolt 12: Assemble handle-cap 13: Assemble brake lever + cable 14: Trim and cap cable 15: Place first rib 16: Insert axles and cleats 17: Insert rear wheel 18: Place second rib and deck 19: Apply grip tape 20: Insert deck fasteners 21: Inspect and wipe-off 22: Apply decal and sticker 23: Insert in bag 24: Assemble carton 25: Insert Xootr and manual 26: Seal carton 6 1 2 3 4 5 7 8 9 10 12 13 14 15 16 17 18 19 11 20 22 23 24 26 21 25 6 12 11 13 14 15 17 16 18 19 20 22 23 26 21 25 24

Labor Productivity Measures: 

=Idle Time Overall Performance Measures Labor Productivity Measures

Key-points to remember: Work Methods Design Exercise: 

Where process times / cost estimates quoted by production managers come from How to make labor related decisions pricing hiring Impact of process design on productivity Line balance Idle time Direct labor content Cost of direct labor Calculations: Determining resource requirements to support a volume target. Estimating direct labor content. Calculating direct manufacturing cost Adjusting for idle time The Importance of Process DESIGN Mechanics of a worker-paced line Mechanics of a work cell Key-points to remember: Work Methods Design Exercise

Slide34: 

4.1 Consider a process consisting of three resources in a worker-paced line and a wage rate of $10 per hour. Assume there is unlimited demand for the product. How long does it take to produce 100 units starting with an empty system? What is the average labor content? What is the average labor utilization? What is the cost of direct labor?

Slide35: 

4.3 PowerToys produces a small remote-controlled toy truck on a conveyor belt with nine stations. Each station has, under the current process layout, one worker assigned to it. Stations and processing times are summarized as follows: What’s the bottleneck? What’s the capacity? What’s the direct labor cost if workers make $15/hour? What’s the direct labor cost for a work cell arrangement? What’s the utilization in station #2? Rebalance the line with 6 workers & compute capacity

Chapter 5 Batching & Flow Operations Setup Times & EOQ: 

Chapter 5 Batching & Flow Operations Setup Times & EOQ

Slide37: 

Inventory The EOQ Model Setup Cost: K Order Quantity: Q Flow Rate (Demand): R Unit Holding Cost: h

Slide38: 

The Cost Minimizing Order Quantity Q Cost C(Q)

Slide39: 

Flow Rate R Economic Order Quantity Q* Per unit ordering and inventory cost C(Q*)/R Ordering and inventory costs as a percentage of total procurement costs 200 4284 0.14 14.1% 400 6058 0.10 10.4% 600 7420 0.08 8.7% 800 8568 0.07 7.6% 1000 9579 0.06 6.8% Scale Economies of the EOQ

Slide40: 

Batch of 12 Batch of 60 Batch of 120 Batch of 300 Time [minutes] 60 120 180 240 300 Set-up from Ribs to Steer support Set-up from steer support to ribs Produce ribs (1 box corresponds to 24 units = 12 scooters) Produce steer supports (1 box corresponds to 12 units = 12 scooters) Production cycle Production cycle The Impact of Set-ups on Capacity

Process Analysis with Batching : 

Capacity calculation changes: Note: Capacity increases with batch size… … and so does inventory (and thus flow time) Common in low volume manufacturing (including a lot of high-tech) Also: transportation, education / training Creates an inherent mismatch between demand and supply Process Analysis with Batching

Batch Flow Operations Carry a Lot of Inventory: 

Example: Movie theater vs. a room full of DVD players SMED (Single minute exchange of die): reduce set-up times Batch Flow Operations Carry a Lot of Inventory

Slide44: 

5.1 Metal window boxes are manufactured in two process steps: stamping and assembly. Each window box is made of 3 pieces: base A and two side Bs. These parts are fabricated by a stamping machine with a setup time of 2 hours whenever switching between the two part types. Once the machine is set up, the activity time for part A is one minute and for part B is 30 seconds. The current rotation is 360 As to 720 Bs. Completed parts move from stamping to assembly once a batch is complete. At assembly, one A, two Bs and some purchased parts are required per finished unit. Each product requires 27 minutes of labor to assemble; there are 12 workers in assembly; there is sufficient demand to sell every box produced. What’s the capacity at stamping? What should the batch size be?

Slide45: 

5.3 Consider the following batch-flow process consisting of 3 process steps performed by 3 machines. Work is processed in batches at each step. Before a batch is processed at a step, the machine must be set up during which it is unable to produce. Each machine has a dedicated setup operator. What is the capacity of step 1 if the batch size is 35? For what batch sizes is step 1 (2,3) the bottleneck?

Variability and Its Impact on Process Performance: Waiting Time Problems Chapter 6: 

Variability and Its Impact on Process Performance: Waiting Time Problems Chapter 6

A Somewhat Odd Service Process (Chapters 1-5): 

A Somewhat Odd Service Process (Chapters 1-5)

A More Realistic Service Process: 

Time 7:10 7:20 7:30 7:40 7:50 8:00 7:00 Patient 1 Patient 3 Patient 5 Patient 7 Patient 9 Patient 11 Patient 2 Patient 4 Patient 6 Patient 8 Patient 10 Patient 12 0 1 2 3 2 min. 3 min. 4 min. 5 min. 6 min. 7 min. Service times Number of cases A More Realistic Service Process

Variability Leads to Waiting Time: 

7:00 7:10 7:20 7:30 7:40 7:50 Inventory (Patients at lab) 5 4 3 2 1 0 8:00 7:00 7:10 7:20 7:30 7:40 7:50 8:00 Wait time Service time Variability Leads to Waiting Time

Variability: Where does it come from?: 

Input: Unpredicted Volume swings Random arrivals (randomness is the rule, not the exception) Incoming quality Product Mix Resources: Breakdowns / Maintenance Operator absence Set-up times Tasks: Inherent variation Lack of SOPs Quality (scrap / rework) Routes: Variable routing Dedicated machines Buffer Processing Especially relevant in service operations (what is different in service industries?): emergency room air-line check in call center check-outs at cashier Variability: Where does it come from?

An Example of a Simple Queuing System: 

Blocked calls (busy signal) Abandoned calls (tired of waiting) Calls on Hold Sales reps processing calls Answered Calls Incoming calls Call center Financial consequences Lost throughput Holding cost Lost goodwill Lost throughput (abandoned) $$$ Revenue $$$ Cost of capacity Cost per customer At peak, 80% of calls dialed received a busy signal. Customers getting through had to wait on average 10 minutes Extra telephone expense per day for waiting was $25,000. An Example of a Simple Queuing System

The “Memoryless” Exponential Function: 

The “Memoryless” Exponential Function Interarrival times follow an exponential distribution Exponential interarrival times = Poisson arrival process Exponential function Coefficient of Variation (CV )

Proving Your Data are Exponential: 

Proving Your Data are Exponential Stationary Vs Seasonal patterns Tests for Exponential Distribution Four step test (Cachon & Terwiesch) Compute the interarrival times for the n data points Sort interarrival times in increasing order a1 smallest an largest. Plot pair (ai, i/n) Compare with “known exponential data” with a=i/n More Rigorous Tests for Exponential Distribution Lilliefors Test Kolmogorov-Smirnov Test Anderson-Darling Test

The Waiting Time Formula: 

Average flow time T Theoretical Flow Time Utilization 100% Waiting Time Formula Service time factor Utilization factor Variability factor Inflow Outflow Inventory waiting Iq Entry to system Departure Begin Service Time in queue Tq Service Time p Flow Time T=Tq+p Flow rate The Waiting Time Formula

Waiting Time Formula for Multiple, Parallel Resources: 

Waiting Time Formula for Multiple (m) Servers (an approximation (u/m high)) Inflow Outflow Inventory waiting Iq Entry to system Departure Begin Service Time in queue Tq Service Time p Flow Time T=Tq+p Inventory in service Ip Flow rate Waiting Time Formula for Multiple, Parallel Resources

Summary of Queuing Analysis: 

Server Inflow Outflow Inventory waiting Iq Entry to system Departure Begin Service Waiting Time Tq Service Time p Flow Time T=Tq+p Flow unit Inventory in service Ip Utilization (Note: make sure <1) Time related measures Inventory related measures (Flow rate=1/a) Summary of Queuing Analysis

Slide57: 

6.1 Customers send emails to a help desk of an online retailer every 2 minutes, on average, and the standard deviation of the inter-arrival time is also 2 minutes. The online retailer has three employees answering emails. It takes on average 4 minutes to write a response email. The standard deviation of the service times is 2 minutes. Estimate the average customer wait before being served. (b) How many emails would there be -- on average -- that have been submitted to the online retailer, but not yet answered?

Service Levels in Waiting Systems: 

Target Wait Time (TWT) Service Level = Probability{Waiting TimeTWT} Example: Deutsche Bundesbahn Call Center - now (2003): 30% of calls answered within 20 seconds - target: 80% of calls answered within 20 seconds 0 0.2 0.4 0.6 0.8 1 0 50 100 150 200 Waiting time [seconds] Fraction of customers who have to wait x seconds or less Waiting times for those customers who do not get served immediately Fraction of customers who get served without waiting at all 90% of calls had to wait 25 seconds or less Service Levels in Waiting Systems

Managing Waiting Systems: Points to Remember: 

Variability is the norm, not the exception - understand where it comes from and eliminate what you can - accommodate the rest Variability leads to waiting times although utilization<100% Use the Waiting Time Formula to - get a qualitative feeling of the system - analyze specific recommendations / scenarios Adding capacity is expensive, although some safety capacity is necessary Next case: - application to call center - use CV=1 - careful in interpreting March / April call volume Managing Waiting Systems: Points to Remember

Data in Practical Call Center Setting: 

0 20 40 60 80 100 120 140 160 0:15 2:00 3:45 5:30 7:15 9:00 10:45 12:30 14:15 16:00 17:45 19:30 21:15 23:00 Number of customers Per 15 minutes 0 20 40 60 80 100 120 140 160 0:15 2:00 3:45 5:30 7:15 9:00 10:45 12:30 14:15 16:00 17:45 19:30 21:15 23:00 Time Number of customers Per 15 minutes 0 0.2 0.4 0.6 0.8 1 0:00:00 0:00:09 0:00:17 0:00:26 0:00:35 0:00:43 0:00:52 0:01:00 0:01:09 Distribution Function Empirical distribution (individual points) Exponential distribution 0 0.2 0.4 0.6 0.8 1 0:00:00 0:00:09 0:00:17 0:00:26 0:00:35 0:00:43 0:00:52 0:01:00 0:01:09 Distribution Function Empirical distribution (individual points) Exponential distribution Seasonality vs. variability Need to slice-up the data Within a “slice”, exponential distribution (CVa=1) Data in Practical Call Center Setting

The Power of Pooling: 

Independent Resources 2x(m=1) Pooled Resources (m=2) 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 60% 65% m=1 m=2 m=5 m=10 70% 75% 80% 85% 90% 95% Waiting Time Tq Utilization u Implications: + balanced utilization + Shorter waiting time (pooled safety capacity) - Change-overs / set-ups The Power of Pooling

Priority Rules in Waiting Time Systems: 

Service times: A: 9 minutes B: 10 minutes C: 4 minutes D: 8 minutes 9 min. 19 min. 23 min. Total wait time: 9+19+23=51min 4 min. 13 min. 21 min. Total wait time: 4+13+21=38 min SPT FCFS EDD Priority WNIFOARB Priority Rules in Waiting Time Systems

Operator Performance in a Call Center: 

Operator Performance in a Call Center

Balancing Efficiency with Responsiveness: 

Responsiveness Efficiency High Low High per unit costs (low utilization) Low per unit costs (high utilization) Now Responsive process with high costs Low cost process with low responsiveness System improvement (e.g. pooling of resources) Frontier reflecting current process Reduce staff (higher utilization) Increase staff (lower utilization) Balancing Efficiency with Responsiveness

Slide65: 

6.3 The airport branch of a car rental company maintains a fleet of 50 SUVs. The interarrival time between requests for an SUV is 2.4 hours with a standard deviation of 2.4 hours. Assume that , if all SUVs are rented, customers are willing to wait until an SUV is available. An SUV is rented, on average for 3 days, with a standard deviation of 1 day. What is the average number of SUVs in the company lot? What is the average time a customer has to wait to rent an SUV? The company discovers that if it reduces its daily $80 rental price by $25, the average demand would increase to 12 rentals per day and the average rental duration will become 4 days. Should they go for it? How would the waiting time change if the company decides to limit all SUV rentals to exactly 4 days? Assume that if such a restriction is imposed, the average interarrival time will increase to 3 hours as will the std deviation.

The Impact of Variability on Process Performance: Throughput Losses Chapter 7: 

The Impact of Variability on Process Performance: Throughput Losses Chapter 7

Buffer or Suffer Principle: 

Buffer or Suffer Principle Table 7.1 Sandwich Vendor Demand and capacity take on values of 0, 1, or 2 within a 5 minute time window

Emergency Room Crowding and Ambulance Diversion: 

Pictures from various Newspapers; put together by L. Green Emergency Room Crowding and Ambulance Diversion

Macro Economic Trends Driving Emergency Room Crowding and Ambulance Diversion: 

Macro Economic Trends Driving Emergency Room Crowding and Ambulance Diversion Data from L. Green; general accounting office 20% of US hospitals are on diversion status for more than 2.4 hours per day Increase in ER visits (14% from 1997 to 2000) 40% of patients admitted through the ER Decrease in number of emergency departments (8.1% decline since 1994) Consequences: Long wait times (see waiting time analysis) Loss of throughput (requires new analysis)

Analyzing Loss Systems: 

Analyzing Loss Systems Trauma center moves to diversion status once all servers are busy incoming patients are directed to other locations Resources 3 trauma bays (m=3) Demand Process One trauma case comes in every 3 hours (a=3 hours) a is the interarrival time Exponential interarrival times Service Process Patient stays in trauma bay for an average of 2 hours (p=2 hours) p is the service time Can have any distribution What is Pm, the probability that all m resources are utilized?

Throughput Loss for a Queue with One Single Resource: 

Throughput Loss for a Queue with One Single Resource Probability of m units in a system Pm depends on two parameters, u and r. Implied utilization u – it is possible to have u>100%; some flow units don’t enter the system and don’t contribute to throughput. Number of resources m

Analyzing Loss Systems: Finding Pm(r): 

Analyzing Loss Systems: Finding Pm(r) Define Example: r= 2 hours/ 3 hours r=0.67 Recall m=3 Use Erlang Loss Table Find that P3 (0.67)=0.0255 Given Pm(r) we can compute: r = p / a m

Erlang Loss Table Appendix B (1st section): 

Probability{all m servers busy}= Erlang Loss Table Appendix B (1st section)

Implied Utilization Vs Probability of Having all Servers Utilized: Pooling Revisited: 

Implied utilization Probability that all servers are utilized m=1 m=2 m=5 m=10 m=20 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 m=3 Implied Utilization Vs Probability of Having all Servers Utilized: Pooling Revisited

Customer Impatience & Throughput Loss: 

Customer Impatience & Throughput Loss Customers wait forever Vs Customers balk at waiting (or are blocked) Intermediate cases Customers join a buffer Customers abandon the queue (renege) Three improvements for the intermediate cases Reduce wait times Increase the maximum number of flow units that can be in the buffer Avoid customers leaving that have already waited.

The Role of Appointment Systems: 

Appointment systems attempt to match supply with demand But: this creates two types of waiting lines (one of them hidden) - currently: 30% of US population cannot get an appointment with MD What to do with emergency cases? - add cases / cancel appointments - reserve capacity for emergencies Advanced Access Model: “Do today’s work today” - based on JIT idea (zero inventory) - ED problem: turns one necessary visit into two (zero waste) - need to forecast demand better (flu, back-to-school) - have more flexible capacity The Role of Appointment Systems

Several Resources with Variability in Sequence: 

Several Resources with Variability in Sequence Blocked resource – can’t release a flow unit due to full buffer downstream Starved resource – can’t work because it and its buffer are empty Matchstick game Unbuffered system Buffered system Horizontal pooling Upstream Downstream R1 R3 R2 B2 B3 B1

Slide78: 

7.1 Flow units arrive at a demand rate of 55 units per hour. It takes, on average, six minutes to serve a flow unit. Service is provided by seven servers. What is the probability that all seven servers are utilized? How many units are served every hour? How many units are lost every hour?

Slide79: 

7.3 A small video store has nine copies of the DVD The Texas Chainsaw Massacre, in its store. There are 15 customers every day who request this movie for their children. If the movie is not on the shelf, they leave and go to a competing store. Customers arrive evenly distributed over 24 hours; the average rental duration is 36 hours. What is the likelihood that a customer going to the video store will find the movie available? Assume each rental is $5. How much revenue does the store make per day from the movie? Assume each child that is not able to obtain the movie will receive a $1 bill. How much money would the store have to give out to children every day? Assume demand for the movie will stay the same for another six months. What would be the payback time (not considering interest rates) for purchasing an additional copy of the movie at $50?

Quality Management and the Toyota Production System Chapter 8: 

Quality Management and the Toyota Production System Chapter 8

The System of Lean Production (Toyota, Citroen, …): 

Zero Inventories Zero Defects Flexibility / Zero set-ups Zero breakdowns Zero handling / non value added Just-in-time Production Kanban Classical Push “Real” Just-in-time Mixed Production Set-up reduction Autonomation Competence and Training Continuous Improvement Quality at the source Organization Methods Principles The System of Lean Production (Toyota, Citroen, …)

Principles of Lean Production: Zero Inventory and Zero Defects: 

Avoid unnecessary inventory To be seen more as an ideal Two types of (bad) inventory: a. resulting from defects / rework b. absence of a smooth process flow Remember the other costs of inventory (capital, flow time) Pictures: Citroen Principles of Lean Production: Zero Inventory and Zero Defects

Principles of Lean Production: Zero Set-ups, Zero NVA and Zero Breakdowns: 

Flexible machines with short set-ups Allows production in small lots Real time with demand Large variety Maximize uptime Without inventory, any breakdown will put production to an end preventive maintenance Avoid Non-value-added activities, specifically rework and set-ups Principles of Lean Production: Zero Set-ups, Zero NVA and Zero Breakdowns

Methods of Lean Production: Just-in-time: 

Push: make to forecast Pull: Synchronized production Pull: Kanban Visual way to implement a pull system Amount of WIP is determined by number of cards Kanban = Sign board Work needs to be authorized by demand Classical MRP way Based on forecasts Push, not pull Still applicable for low cost parts Part produced for specific order (at supplier) shipped right to assembly real-time synchronization for large parts (seat) inspected at source Methods of Lean Production: Just-in-time

Methods of Lean Production: Mixed Production and Set-up reduction: 

Cycle Inventory End of Month Beginning of Month Produce Sedan Produce Station wagon End of Month Beginning of Month Produce Sedan Produce Station wagon End of Month Beginning of Month End of Month Beginning of Month Methods of Lean Production: Mixed Production and Set-up reduction

Organization of Lean Production: Autonomation and Training: 

Automation with a human touch Create local decision making rather than pure focus on execution Use machines / tools, but avoid the lights-off factory Cross training of workers Develop problem solving skills Organization of Lean Production: Autonomation and Training

Organization of Lean Production: Continuous Improvement and Quality-at-the-source: 

Solve the problems where they occur - this is where the knowledge is - this is the cheapest place Traditional: inspect and rework at the end of the process Once problem is detected, send alarm and potentially stop the production Organization of Lean Production: Continuous Improvement and Quality-at-the-source

Betting on Uncertain Demand: The Newsvendor Model Chapter 9: 

Betting on Uncertain Demand: The Newsvendor Model Chapter 9

Hammer 3/2 timeline and economics: 

Hammer 3/2 timeline and economics Economics: Each suit sells for p = $180 TEC charges c = $110 per suit Discounted suits sell for v = $90 The “too much/too little problem”: Order too much and inventory is left over at the end of the season Order too little and sales are lost. Marketing’s forecast for sales is 3200 units.

Newsvendor model implementation steps: 

Newsvendor model implementation steps Gather economic inputs: Selling price, production/procurement cost, salvage value of inventory Generate a demand model: Use empirical demand distribution or choose a standard distribution function to represent demand, e.g. the normal distribution, the Poisson distribution. Choose an objective: e.g. maximize expected profit or satisfy a fill rate constraint. Choose a quantity to order.

Forecasting: 

Forecasting A statement about the future Used to Plan the system Plan the use of the system Our focus will be here

Features of Forecasts: 

Features of Forecasts Wrong! Aggregate forecasts Time horizon The same underlying causal system will continue to exist

Elements of a Good One: 

Elements of a Good One Timely Accurate Reliable Appropriate units Parsimonious Documented

Forecasting Approaches: 

Forecasting Approaches Judgment Time series Associative (regression)

Judgment Forecasts: 

Judgment Forecasts Why use one? Data, time, arena Techniques Executive opinion Salesforce Opinion Consumer Survey Delphi Method Nominal Group Technique

Time Series Forecasts: 

Time Series Forecasts Observations over a fixed interval of time Components of time series Trend Seasonality Cycles Irregular variations Random variation

Notes on Notation: 

Notes on Notation F = Forecast A = Actual (known demand) t+1 = next period, t = current period A bar over something means “average” e.g. X ∑ = repeated addition (summation)

Time Series Techniques: 

Time Series Techniques Naïve Method Moving Average Exponential Smoothing

More Time Series Equations: 

More Time Series Equations Exponential Smoothing (alternate version) Linear Trend

How to Forecast: 

How to Forecast Use subject matter knowledge Use graphical methods Use statistical tests Correct functional specification Constant variance Uncorrelated errors Normally distributed residuals

Slide101: 

#2 Depends, Inc. sells adult diapers. Monthly sales for a seven month period were as follows. Month Sales (000 units) Feb 19 Mar 18 Apr 15 May 20 Jun 18 Jul 22 Aug 20 Plot the data Forecast sales for September using linear trend; 5 month moving average; exponential smoothing with alpha=0.2 assuming a March forecast of 19; naïve approach; weighted average of .60 for Aug, .30 for July, and .10 for June.

Associative Forecasting: 

Associative Forecasting One item’s value depends on another item’s value Does this equation look familiar? Linear regression

Slide103: 

#23 The following data were collected during a study of consumer buying patterns. Observation X Y Observation X Y 1 15 74 8 18 78 2 25 80 9 14 70 3 40 84 10 15 72 4 32 81 11 22 85 5 51 96 12 24 88 6 47 95 13 33 90 7 30 83 Plot the data. Obtain a regression line. How much variance is explained? Predict Y when X=41.

Accuracy & Control: 

Accuracy & Control MAD = Mean Absolute Deviation MSE = Mean Squared Error Bias = Bias

Historical forecast performance at O’Neill: 

Historical forecast performance at O’Neill Forecasts and actual demand for surf wet-suits from the previous season

Empirical distribution of forecast accuracy: 

Empirical distribution of forecast accuracy

Using historical A/F ratios to choose a Normal distribution for the demand forecast : 

Start with an initial forecast generated from hunches, guesses, etc. O’Neill’s initial forecast for the Hammer 3/2 = 3200 units. Evaluate the A/F ratios of the historical data: Set the mean of the normal distribution to Set the standard deviation of the normal distribution to Using historical A/F ratios to choose a Normal distribution for the demand forecast

O’Neill’s Hammer 3/2 normal distribution forecast: 

O’Neill’s Hammer 3/2 normal distribution forecast O’Neill should choose a normal distribution with mean 3192 and standard deviation 1181 to represent demand for the Hammer 3/2 during the Spring season.

Empirical vs Normal Demand Distribution: 

Empirical vs Normal Demand Distribution Empirical distribution function (diamonds) and normal distribution function with mean 3192 and standard deviation 1181 (solid line)

“Too much” and “Too little” Costs: 

“Too much” and “Too little” Costs Co = overage cost The cost of ordering one more unit than what you would have ordered had you known demand. In other words, suppose you had left over inventory (i.e., you over ordered). Co is the increase in profit you would have enjoyed had you ordered one fewer unit. For the Hammer 3/2 Co = Cost – Salvage value = c – v = 110 – 90 = 20 Cu = underage cost The cost of ordering one fewer unit than what you would have ordered had you known demand. In other words, suppose you had lost sales (i.e., you under ordered). Cu is the increase in profit you would have enjoyed had you ordered one more unit. For the Hammer 3/2 Cu = Price – Cost = p – c = 180 – 110 = 70

Balancing the Risk and Benefit of Ordering a Unit: 

Balancing the Risk and Benefit of Ordering a Unit Ordering one more unit increases the chance of overage … Expected loss on the Qth unit = Co x F(Q) F(Q) = Distribution function of demand = Prob{Demand <= Q) … but the benefit/gain of ordering one more unit is the reduction in the chance of underage: Expected gain on the Qth unit = Cu x (1-F(Q)) As more units are ordered, the expected benefit from ordering one unit decreases while the expected loss of ordering one more unit increases.

Newsvendor Expected Profit Maximizing Order Quantity: 

Newsvendor Expected Profit Maximizing Order Quantity To maximize expected profit order Q units so that the expected loss on the Qth unit equals the expected gain on the Qth unit: Rearrange terms in the above equation -> The ratio Cu / (Co + Cu) is called the critical ratio. Hence, to maximize profit, choose Q such that we don’t have lost sales (i.e., demand is Q or lower) with a probability that equals the critical ratio

Finding the Hammer 3/2’s expected profit maximizing order quantity with the empirical distribution function: 

Finding the Hammer 3/2’s expected profit maximizing order quantity with the empirical distribution function Inputs: Empirical distribution function table; p = 180; c = 110; v = 90; Cu = 180-110 = 70; Co = 110-90 =20 Evaluate the critical ratio: Lookup 0.7778 in the empirical distribution function table If the critical ratio falls between two values in the table, choose the one that leads to the greater order quantity (choose 0.788 which corresponds to A/F ratio 1.3) Convert A/F ratio into the order quantity

Hammer 3/2’s expected profit maximizing order quantity using the normal distribution: 

Hammer 3/2’s expected profit maximizing order quantity using the normal distribution Inputs: p = 180; c = 110; v = 90; Cu = 180-110 = 70; Co = 110-90 =20; critical ratio = 0.7778; mean = m = 3192; standard deviation = s = 1181 Look up critical ratio in the Standard Normal Distribution Function Table: If the critical ratio falls between two values in the table, choose the greater z-statistic Choose z = 0.77 Convert the z-statistic into an order quantity:

Newsvendor Model Performance Measures: 

Newsvendor Model Performance Measures For any order quantity we would like to evaluate the following performance measures: Expected lost sales The average number of units demand exceeds the order quantity Expected sales The average number of units sold. Expected left over inventory The average number of units left over at the end of the season. Expected profit Expected fill rate The fraction of demand that is satisfied immediately In-stock probability Probability all demand is satisfied Stockout probability Probability some demand is lost

Expected lost sales of Hammer 3/2s with Q = 3500: 

Expected lost sales of Hammer 3/2s with Q = 3500 Definition: e.g., if demand is 3800 and Q = 3500, then lost sales is 300 units. e.g., if demand is 3200 and Q = 3500, then lost sales is 0 units. Expected lost sales is the average over all possible demand outcomes. If demand is normally distributed: Step 1: normalize the order quantity to find its z-statistic. Step 2: Look up in the Standard Normal Loss Function Table the expected lost sales for a standard normal distribution with that z-statistic: L(0.26)=0.2824 or, in Excel Step 3: Evaluate lost sales for the actual normal distribution:

Measures that follow expected lost sales : 

Measures that follow expected lost sales Expected sales = m - Expected lost sales = 3192 – 334 = 2858 Expected Left Over Inventory = Q - Expected Sales = 3500 – 2858 = 642 Note: the above equations hold for any demand distribution

Service measures of performance: 

Service measures of performance In-stock probability = F(Q) = F(z) Evaluate the z-statistic for the order quantity : Look up F(z) in the Std. Normal Distribution Function Table, F(0.26) = 60.26% Stockout probability = 1 – F(Q) =1 – In-stock probability = 1 –0.6026 = 39.74% Note: the in-stock probability is not the same as the fill rate

Choose Q subject to a minimum in-stock probability : 

Choose Q subject to a minimum in-stock probability Suppose we wish to find the order quantity for the Hammer 3/2 that minimizes left over inventory while generating at least a 99% in-stock probability. Step 1: Find the z-statistic that yields the target in-stock probability. In the Standard Normal Distribution Function Table we find F(2.32) = 0.9898 and F(2.33) = 0.9901. Choose z = 2.33 to satisfy our in-stock probability constraint. Step 2: Convert the z-statistic into an order quantity for the actual demand distribution. Q = m + z x s = 3192 + 2.33 x 1181 = 5944

Choose Q subject to a minimum fill rate constraint: 

Choose Q subject to a minimum fill rate constraint Suppose we wish to find the order quantity for the Hammer 3/2 that minimizes left over inventory while generating at least a 99% fill rate. Step 1: Find the lost sales with a standard normal distribution that yields the target fill rate. Step 2: Find the z-statistic that yields the lost sales found in step 1. From the Standard Normal Loss Function Table, L(1.53)=0.0274 and L(1.54) = 0.0267 Choose the higher z-statistic, z = 1.54 Step 3: Convert the z-statistic into an order quantity for the actual demand distribution. Q = m + z x s = 3192 + 1.54 x 1181 = 5011

Newsvendor model summary: 

Newsvendor model summary The model can be applied to settings in which … There is a single order/production/replenishment opportunity. Demand is uncertain. There is a “too much-too little” challenge: If demand exceeds the order quantity, sales are lost. If demand is less than the order quantity, there is left over inventory. Firm must have a demand model that includes an expected demand and uncertainty in that demand. With the normal distribution, uncertainty in demand is captured with the standard deviation parameter. At the order quantity that maximizes expected profit the probability that demand is less than the order quantity equals the critical ratio: The expected profit maximizing order quantity balances the “too much-too little” costs.

Slide122: 

Fashionables is a franchisee of The Limited, the well-known retailer of fashionable clothing. Prior to the winter season, The Limited offers Fashionables the choice of 5 different colors of a particular sweater design. The sweaters are knit overseas by hand, and because of the lead times involved, Fashionables will need to order its assortment in advance of the selling season. As per the contracting terms offered by The Limited, Fashionables also will not be able to cancel, modify, or reorder sweaters during the selling season. Demand for each color during the season is normally distributed with a mean of 500 and a standard deviation of 200. Further, you may assume that the demands for each sweater are independent of those for a different color. The Limited offers the sweater to Fashionables at the wholesale price of $40 per sweater, and Fashionables plans to sell each sweater at the retail price of $70 per unit. The Limited delivers orders places by Fashionables in truckloads at a cost of $2,000 per truckload. The transportation cost of $2,000 is borne by Fashionables. Assume unless otherwise specified that all the sweaters ordered by Fashionables will fit into one truckload. Also assume that all other associated costs, such as unpacking and handling are negligible. The Limited does not accept any returns of unsold inventory. However, Fashionables can sell all of the unsold sweaters at the end of the season at the fire-sale price of $20 each. How many units of each type of sweater should Fashionables order? If Fashionable wishes to ensure a 97.5% in-stock probability, what should its order quantity be? If Fashionables wishes to ensure a 97.5% fill rate, what should its order quantity be? Now assume that Fashionables orders 725 of each kind of sweater What is Fashionables’ expected profit? What is Fashionables’ expected fill rate for each type of sweater? What is the stockout probability for each type of sweater? Now suppose that The Limited announces that the unit of truckload capacity is 2,500 units. What now is Fashionables’ optimal order quantity for each sweater?

Slide123: 

Weekday lunch demand for the spicy black bean burritos at Kiosk, a local snack bar, is approximately Poisson with a mean of 22. The Kiosk charges $4.00 for each burrito, which are all made before the lunch crowd arrives. Virtually all burrito customers also buy a soda that is sold for 60¢. The burritos cost the Kiosk $2.00, while the sodas cost 5¢. Management is very sensitive about the quality of the food they serve. Thus, they maintain a strict “No Old Burrito” policy, so any burrito left at the end of the day is fed to the chickens. The distribution function of a Poisson with a mean of 22 is as follows: Suppose burrito customers buy their snack elsewhere if the Kiosk is out of stock. How many burritos should the Kiosk make for their lunch crowd? Suppose that any customer unable to purchase a burrito settles for a lunch of Pop-Tarts and a soda. Pop-Tarts sell for 75¢ and cost the Kiosk 25¢. (As Pop-Tarts and soda are easily stored, the Kiosk never runs out of these essentials.) How many burritos should Kiosk management prepare?

Chapter 10 Assemble-to-Order, Make-to-Order, and Quick Response with Reactive Capacity: 

Chapter 10 Assemble-to-Order, Make-to-Order, and Quick Response with Reactive Capacity

The demand-supply mismatch cost: 

The demand-supply mismatch cost Definition – the demand supply mismatch cost includes the cost of left over inventory (the “too much” cost) plus the opportunity cost of lost sales (the “too little” cost): For Hammer 3/2: The maximum profit is the profit without any mismatch costs, i.e., every unit is sold and there are no lost sales: The mismatch cost can also be evaluated with For the Hammer 3/2: Mismatch cost = Maximum profit – Expected profit

When is the mismatch cost cost high?: 

When is the mismatch cost cost high? Mismatch cost as a percent of the maximum profit where f(z) = density function of the Normal distribution (In Excel f(z)=normdist(z,0,1,0)) Hammer 3/2’s mismatch cost as a percentage of the maximum profit is The mismatch cost is high when (f(z) / F(z)) and (s / m) are high.

Low critical ratios  high mismatch costs: 

Low critical ratios  high mismatch costs The mismatch cost is high when (f(z) / F(z)) is high … … (f(z) / F(z)) is high when the critical ratio is low:

High demand uncertainty  high mismatch costs: 

High demand uncertainty  high mismatch costs The mismatch cost is high when the coefficient of variation, s/m, is high. The coefficient of variation is the right measure of demand uncertainty: The probability demand is within 20% of the forecast demand depends on the coefficient of variation (COV) and not the standard deviation:

Find your product’s mismatch cost (as % of maximum profit) …: 

Find your product’s mismatch cost (as % of maximum profit) …

Unlimited, but expensive reactive capacity: 

Unlimited, but expensive reactive capacity TEC charges a premium of 20% per unit ($132 vs. $110) in the second order. There are no restrictions imposed on the 2nd order quantity. O’Neill forecast of total season sales is nearly perfect after observing initial season sales. How many units should O’Neill order in October?

Apply Newsvendor logic even with a 2nd order option: 

Apply Newsvendor logic even with a 2nd order option The “too much cost” remains the same: Co = c – v = 110 – 90 =20. The “too little cost” changes: If the 1st order is too low, we cover the difference with the 2nd order. Hence, the 2nd order option prevents lost sales. So the cost of ordering too little per unit is no longer the gross margin, it is the premium we pay for units in the 2nd order. Cu = 132 – 110 = 22 Critical ratio: Corresponding z-statistic F(0.05)=0.5199, F(0.06)=0.5239, so z = 0.06.

Profit improvement due to the 2nd order option: 

Profit improvement due to the 2nd order option With a single ordering opportunity: Optimal order quantity = 4101 units Expected profit = $191,760 Mismatch cost as % of revenue = 4.9% The maximum profit is unchanged = $223,440 With a second order option: Optimal order quantity = 3263 units Reduction in mismatch cost = 38% (19,774 vs. 31,680) Mismatch cost as % of revenue = 3.1%

Limited reactive capacity: 

Limited reactive capacity Units in the 2nd order are no more expensive than in the 1st order But there is limited capacity for a 2nd order

Sample of wetsuits: 

Sample of wetsuits 1st order must be at least 10,200 suits so that there is enough capacity for the 2nd order. What should we produce in the 1st order?

Profit and mismatch with only 1 ordering opportunity: 

Profit and mismatch with only 1 ordering opportunity Use the Newsvendor model to evaluate the optimal order quantity, expected profit, maximum profit and mismatch cost A suits produced in the 1st order earns the Newsvendor profit but a suit produced in the 2nd order earns the maximum profit.

Produce “safer” products early, produce “risky” products with reactive capacity: 

Produce “safer” products early, produce “risky” products with reactive capacity Sort items by their mismatch cost to order quantity ratio. Fill the 1st order up to the minimum quantity (10,200) with the items that have the lowest mismatch – quantity ratio The mismatch cost is reduced by 66%!

Slide137: 

10.11 Office Supply Company has a spare parts warehouse in Alaska to support its office equipment maintenance needs. Once every six months, a major replenishment shipment is received. If the inventory of any given part runs out before the next replenishment, then emergency air shipments are used to resupply the part as needed. Orders are placed on March 17 and September 17, and orders are received on April 17 and October 17 respectively. OSC must determine replenishment quantities for its spare parts. As an example, historical data show that total demand for part 1AA-66 over a six month interval is Poisson with mean 6.5. The cost of inventorying the unneeded part for six months is $5 (which includes both physical and financial holding costs and is charged based on inventory at the end of the six month period.) The variable production cost for 1AA-66 is $37 per part. The cost of a regular, semiannual shipment is $32 per part and the cost of an emergency shipment is $50 per part. It is March 17, and there are currently three aAA-66 parts in inventory. How many parts should arrive on April 17?

Slide138: 

10.3 Flextrola is developing a new product and Solectrics (ref Q9.3) can produce one of the key components for $72 per unit as long as Flextrola submits an order well in advance of the selling season. Flextrola’s demand forecast is ~N(1000,600). Flextrola sells the unit after integrating some software for $121. Leftover units are sold for $50 after the season. Xandova Electronics (XE) wants a piece of this action and is able to offer 100% fill rate and one day delivery no matter when the orders are submitted. Flextrola promises a one-week lead time, so the one day lead from XE would allow Flextrola to operate with make-to-order production. XE’s price is $83.50 per unit. What is Flextrola’s expected profit if they use XE as their sole supplier? How many units should Flextrola buy from each if they use both suppliers? Solectrics comes back to the table and offers an option contract of Q options for $25 each. During the selling season Flextrola can exercise up to the Q options with a one day lead time and the exercise price is $50 per unit. If Flextrola wants more units beyond the options already purchased, Solectrics will provide them at XE’s price of $83.50. How many options should Flextrola purchase? Given your answer to c) what is Flextrola’s profit?

Revenue (Yield) Management Chapter 13: 

Revenue (Yield) Management Chapter 13

Matching supply to demand when supply is fixed: 

Matching supply to demand when supply is fixed Examples of fixed supply: Travel industries (fixed number of seats, rooms, cars, etc). Advertising time (limited number of time slots). Telecommunications bandwidth. Size of the MBA program. Doctor’s availability for appointments. Revenue management is a solution: If adjusting supply is impossible – adjust the demand! Segment customers into high willingness to pay and low willingness to pay. Limit the number of tickets sold at a low price, i.e., control the average price by changing the mix of customers.

Revenue management and margin arithmetic: 

Revenue management and margin arithmetic Small changes in revenue can have a big impact on profit, especially for high gross margin and low net profit % industries:

Environments suitable for revenue management : 

Environments suitable for revenue management The same unit of capacity (e.g., airline seat) can be used to deliver services to different customer segments (e.g., business and leisure customers) at different prices. High gross margins (so that the variable cost of additional sales is low). Perishable capacity (it cannot be stored) and limited capacity (all possible customers cannot always be served). Capacity is sold in advance of demand. There is an opportunity to segment customers (so that different prices can be charged) and different segments are willing to pay different prices. It is not illegal or morally irresponsible to discriminate among customers.

Revenue Management: Booking limits and protection levels: 

Revenue Management: Booking limits and protection levels The Park Hyatt Philadelphia at the Bellevue. 118 King/Queen rooms. Hyatt offers a rL= $159 (low fare) discount fare for a mid-week stay targeting leisure travelers. Regular fare is rH= $225 (high fare) targeting business travelers. Demand for low fare rooms is abundant. Let D be uncertain demand for high fare rooms. Suppose D has Poisson distribution with mean 27.3. Assume most of the high fare (business) demand occurs only within a few days of the actual stay. Objective: Maximize expected revenues by controlling the number of low fare rooms you sell.

Yield management decisions: 

Yield management decisions The booking limit is the number of rooms you are willing to sell in a fare class or lower. The protection level is the number of rooms you reserve for a fare class or higher. Let Q be the protection level for the high fare class. Q is in effect while you sell low fare tickets. Since there are only two fare classes, the booking limit on the low fare class is 118 – Q: You will sell no more than 118-Q low fare tickets because you are protecting (or reserving) Q seats for high fare passengers. 0 118 Q seats protected for high fare passengers Sell no more than the low fare booking limit, 118 - Q

The connection to the newsvendor: 

The connection to the newsvendor A single decision is made before uncertain demand is realized. There is an overage cost: If D < Q then you protected too many rooms (you over protected) ... … so some rooms are empty which could have been sold to a low fare traveler. There is an underage cost: If D > Q then you protected too few rooms (you under protected) … … so some rooms could have been sold at the high fare instead of the low fare. Choose Q to balance the overage and underage costs.

Optimal protection level: 

Optimal protection level Overage cost: If D < Q we protected too many rooms and earn nothing on Q - D rooms. We could have sold those empty rooms at the low fare, so Co = rL. Underage cost: If D > Q we protected too few rooms. D – Q rooms could have been sold at the high fare but were sold instead at the low fare, so Cu = rH - rL Optimal high fare protection level: Optimal low fare booking limit = 118 – Q* Choosing the optimal high fare protection level is a Newsvendor problem with properly chosen underage and overage costs.

Hyatt example: 

Hyatt example Critical ratio: Poisson distribution with mean 27.3: Answer: 24 rooms should be protected for high fare travelers. Similarly, a booking limit of 118-24 = 94 rooms should be applied to low fare reservations.

Related calculations: 

Related calculations How many high-fare travelers will be refused a reservation? Expected lost sales = 4.10. How many high-fare travelers will be accommodated? Expected sales = Expected demand - Lost sales = 27.3 - 4.1 = 23.2 How many seats will remain empty? Expected left over inventory = Q - Expected sales = 24 - 23.2 = 0.8. What is the expected revenue? $225 x Exp. sales + $159 x Booking limit = $20,166. Note: without yield management worst case scenario is $159 x 118 = $18,762.

Revenue management challenges …: 

Revenue management challenges … Demand forecasting. Wealth of information from reservation systems but there is seasonality, special events, changing fares and truncation of demand data. Dynamic decisions. Variable capacity: Different aircrafts, ability to move rental cars around. Group reservations. How to construct good “fences” to differentiate among customers? One-way vs round-trip tickets. Saturday-night stay requirement. Non-refundability. Advanced purchase requirements. Multi-leg passengers/multi-day reservations for cars and hotels: Not all customers using a given piece of capacity (a seat on a flight leg, a room for one night) are equally valuable.

A solution to the multi-leg customer: buckets: 

A solution to the multi-leg customer: buckets With segment control there are only three booking limits for the O’Hare-JFK leg, one for each fare class. But an O’Hare-Heathrow customer may be more valuable, so you could have six booking limits, one for each fare-itinerary combination. But that leads to many booking limits, so group similar fare-itineraries into buckets: O’Hare JFK Heathrow

Another solution to multi-legs: bid prices: 

Another solution to multi-legs: bid prices Assign a bid price to each segment: A fare is accepted if it exceeds the sum of the bid prices on the segments it uses: For example, an O’Hare-JFK fare is accepted if it exceeds $290 A O’Hare-Heathrow fare is accepted if it exceeds $290+$170 = $460 The trick is to choose good bid-prices. O’Hare JFK Heathrow

Ugly reality: cancellations and no-shows: 

Ugly reality: cancellations and no-shows Approximately 50% of reservations get cancelled at some point in time. In many cases (car rentals, hotels, full fare airline passengers) there is no penalty for cancellations. Problem: the company may fail to fill the seat (room, car) if the passenger cancels at the very last minute or does not show up. Solution: sell more seats (rooms, cars) than capacity. Danger: some customers may have to be denied a seat even though they have a confirmed reservation.

Revenue Management: Overbooking at the Hyatt: 

Revenue Management: Overbooking at the Hyatt The forecast for the number of customers that do not show up ( X ) is Poisson with mean 8.5. The cost of denying a room to the customer with a confirmed reservation is $350 in ill-will and penalties. How many rooms ( Y ) should be overbooked (sold in excess of capacity)? Newsvendor setup: Single decision when the number of no-shows in uncertain. Underage cost if X > Y (insufficient number of seats overbooked). Overage cost if X < Y (too many seats overbooked).

Overbooking solution: 

Overbooking solution Underage cost: if X > Y then we could have sold X-Y more rooms… … to be conservative, we could have sold those rooms at the low fare, Cu = rL. Overage cost: if X < Y then we bumped Y - X customers … … and incur an overage cost Co = $350 on each bumped customer. Optimal overbooking level: Critical ratio:

Optimal overbooking level: 

Optimal overbooking level Poisson distribution with mean 8.5 Optimal number of overbooked rooms is Y=7. Hyatt should allow up to 118+7 reservations. There is about F(6)=25.62% chance that Hyatt will find itself turning down travelers with reservations.

Putting things together: booking limits, overbooking and multiple flight legs: 

Putting things together: booking limits, overbooking and multiple flight legs Booking limits/number of overbooked seats change over time.

Revenue management summary: 

Revenue management summary Yield management and overbooking give demand flexibility where supply flexibility is not possible. The Newsvendor model can be used: Single decision in the face of uncertainty. Underage and overage penalties. These are powerful tools to improve revenue: American Airlines estimated a benefit of $1.5B over 3 years. National Car Rental faced liquidation in 1993 but improved via yield management techniques. Delta Airlines credits yield management with $300M in additional revenue annually (about 2% of year 2000 revenue.)

Slide158: 

13.5 On a given Philadelphia-LA flight, there are 200 seats. Suppose the ticket price is $475 on average and the number of passengers who reserve a seat but do not show up for departure is ~N(30,15). You decide to overbook the flight and estimate that the average loss from a passenger who will have to be bumped is $800. What is the maximum number of reservations that should be accepted? Suppose you allow 220 reservations. How much money do you expect to pay out in compensation to bumped passengers? Suppose you allow 220 reservations. What is the probability that you will have to deal with bumped passengers?

Slide159: 

13.7 Consider the example of the Park Hyatt Philly discussed in the text. Recall that the full fare is $225, the expected full-fare demand is ~P(27.3), the discount fare is $159, and there are 118 king/queen rooms. Now suppose the cost of an occupied room is $45 per night. That cost includes the labor associated with prepping and cleaning a room, the additional utilities used and the wear and tear on the furniture and fixtures. Suppose the Park Hyatt wishes to maximize expected profit rather than expected revenue. What is the optimal protection level for the full fare?

Supply Chain Coordination Chapter 14: 

Supply Chain Coordination Chapter 14

Suboptimal supply chain performance due to incentive conflicts : 

Suboptimal supply chain performance due to incentive conflicts Suboptimal supply chain performance occurs because of double marginalization: Each firm makes decisions based on their own margin, not the supply chain’s margin. A sunglass supply chain: Zamatia produces sunglasses for $35 each and sells them to Umbra Visage (UV) for $75, UV retails them for $115 and liquidates them for $25. UV’s critical ratio: Supply chain’s critical ratio: The difference in the critical ratio leads to poor performance:

Aligning incentives…: 

Aligning incentives… Marginal cost pricing: Zamatia charges $35 per sunglass, then UV’s critical ratio equals the supply chain’s critical ratio. But Zamatia makes zero profit. What they need is a method to share inventory risk so that the supply chain’s profit is maximized (coordinated) and both firms are better off. Buy-back contract: Zamatia buys back left over inventory at the end of the season. Coordinates the supply chain and can yield any split of the profit…everyone can be better off.

More on buy-back contracts: 

More on buy-back contracts How do they improve supply chain performance? The retailer’s overage cost is reduced, so the retailer stocks more. With a buy-back the supplier shares with the retailer the risk of left over inventory. Other uses for buy-back contracts: Allow for the redistribution of inventory across the supply chain. Helps to protect the supplier’s brand image by avoiding markdowns. Allows the supplier to signal that significant marketing effort will occur. What are the costs of buy-backs? Administrative costs plus additional shipping and handling costs. Where are they used? books, cosmetics, music CDs, agricultural chemicals, electronics …

Other methods to align incentives: 

Other methods to align incentives Quantity discounts: Used to induce larger downstream order quantities so that downstream service is improved and/or handling and transportation efficiency is improved. Franchise fees: Marginal cost pricing coordinates actions, but leaves the upstream party with no profit. So charge a franchise fee to extra profit from the franchisee. Revenue sharing: Supplier accepts a low upfront wholesale price in exchange for a share of the revenue. Under appropriately chosen parameters, the retailer has an incentive to stock more inventory, thereby generating more revenue for the supply chain.

Options contract: 

Options contract What are they? The buyer purchases the option to buy at a future time. Each option costs po and it costs pe to exercise each option. How can they improve supply chain performance? Provides an intermediate level of risk: Fixed long term contract requires a commitment at a price greater than po. Procuring on the volatile spot market could lead to a price greater than po + pe. Where are they used? Semiconductor industry, energy markets (electric power), commodity chemicals, metals, plastics, apparel retailing, air cargo, …

Summary: 

Summary Coordination failure: Supply chain performance may be less than optimal with decentralized operations (i.e., multiple firms making decisions) even if firms choose individually optimal actions. A reason for coordination failure: The terms of trade do not give firms the proper incentive to choose supply chain optimal actions. Why fix coordination failure: If total supply chain profit increase, the “pie” increases and everyone can be given a bigger piece. How to align incentives: Design terms of trade to restore a firm’s incentive to choose optimal actions.

The Order Up To Inventory Model Chapter 11: 

The Order Up To Inventory Model Chapter 11

Medtronic’s InSync pacemaker supply chain and objectives: 

Medtronic’s InSync pacemaker supply chain and objectives Supply chain: One distribution center (DC) in Mounds View, MN. About 500 sales territories throughout the country. Consider Susan Magnotto’s territory in Madison, Wisconsin. Objective: Because the gross margins are high, develop a system to minimize inventory investment while maintaining a very high service target, e.g., a 99.9% in-stock probability or a 99.9% fill rate.

Timing in the order up-to model: 

Timing in the order up-to model Time is divided into periods of equal length, e.g., one hour, one month. During a period the following sequence of events occurs: A replenishment order can be submitted. Inventory is received. Random demand occurs. Lead times: An order is received after a fixed number of periods, called the lead time. Let l represent the length of the lead time. An example with l = 1

Order up-to model vs. newsvendor model: 

Order up-to model vs. newsvendor model Both models have uncertain future demand, but there are differences… Newsvendor applies to short life cycle products with uncertain demand and the order up-to applies to long life cycle products with uncertain, but stable, demand.

InSync demand and inventory at the DC: 

InSync demand and inventory at the DC Average monthly demand = 349 units Standard deviation of monthly demand = 122.28 Average weekly demand = 349/4.33 = 80.6 Standard deviation of weekly demand = (The evaluations for weekly demand assume 4.33 weeks per month and demand is independent across weeks.) Monthly implants (columns) and end of month inventory (line)

InSync demand and inventory in Susan’s territory: 

InSync demand and inventory in Susan’s territory Total annual demand = 75 units Average daily demand = 0.29 units (75/260), assuming 5 days per week. Poisson demand distribution works better for slow moving items Monthly implants (columns) and end of month inventory (line)

Order up-to model definitions: 

Order up-to model definitions On-order inventory / pipeline inventory = the number of units that have been ordered but have not been received. On-hand inventory = the number of units physically in inventory ready to serve demand. Backorder = the total amount of demand that has has not been satisfied: All backordered demand is eventually filled, i.e., there are no lost sales. Inventory level = On-hand inventory - Backorder. Inventory position = On-order inventory + Inventory level. Order up-to level, S the maximum inventory position we allow. sometimes called the base stock level.

Order up-to model implementation: 

Order up-to model implementation Each period’s order quantity = S – Inventory position Suppose S = 4. If a period begins with an inventory position = 1, then three units are ordered. (4 – 1 = 3 ) If a period begins with an inventory position = -3, then seven units are ordered (4 – (-3) = 7) A period’s order quantity = the previous period’s demand: Suppose S = 4. If demand were 10 in period 1, then the inventory position at the start of period 2 is 4 – 10 = -6, which means 10 units are ordered in period 2. The order up-to model is a pull system because inventory is ordered in response to demand. The order up-to model is sometimes referred to as a 1-for-1 ordering policy.

What determines the inventory level?: 

What determines the inventory level? Short answer: Inventory level at the end of a period = S minus demand over l +1 periods. Explanation via an example with S = 6, l = 3, and 2 units on-hand at the start of period 1 D1 D2 D3 D4 ? Period 1 Time Inventory level at the end of period four = 6 - D1 – D2 – D3 – D4 Keep in mind: At the start of a period the Inventory level + On-order equals S. All inventory on-order at the start of period 1 arrives before the end of period 4 Nothing ordered in periods 2-4 arrives by the end of period 4 All demand is satisfied so there are no lost sales. Period 2 Period 3 Period 4

Expected on-hand inventory and backorder: 

Expected on-hand inventory and backorder This is like a Newsvendor model in which the order quantity is S and the demand distribution is demand over l +1 periods. So … Expected on-hand inventory at the end of a period can be evaluated like Expected left over inventory in the Newsvendor model with Q = S. Expected backorder at the end of a period can be evaluated like Expected lost sales in the Newsvendor model with Q = S. S Period 1 Time … … Period 4 D S – D > 0, so there is on-hand inventory S – D < 0, so there are backorders D = demand over l +1 periods

Stockout and in-stock probabilities, on-order inventory and fill rate: 

Stockout and in-stock probabilities, on-order inventory and fill rate The stockout probability is the probability at least one unit is backordered in a period: The in-stock probability is the probability all demand is filled in a period: Expected on-order inventory = Expected demand over one period x lead time This comes from Little’s Law. Note that it equals the expected demand over l periods, not l +1 periods. The fill rate is the fraction of demand within a period that is NOT backordered:

Demand over l+1 periods: 

Demand over l+1 periods DC: The period length is one week, the replenishment lead time is three weeks, l = 3 Assume demand is normally distributed: Mean weekly demand is 80.6 (from demand data) Standard deviation of weekly demand is 58.81 (from demand data) Expected demand over l +1 weeks is (3 + 1) x 80.6 = 322.4 Standard deviation of demand over l +1 weeks is Susan’s territory: The period length is one day, the replenishment lead time is one day, l =1 Assume demand is Poisson distributed: Mean daily demand is 0.29 (from demand data) Expected demand over l+1 days is 2 x 0.29 = 0.58 Recall, the Poisson is completely defined by its mean (and the standard deviation is always the square root of the mean)

DC’s Expected backorder assuming S = 625: 

DC’s Expected backorder assuming S = 625 Expected backorder is analogous to the Expected lost sales in the Newsvendor model: Suppose S = 625 at the DC Normalize the order up-to level: Lookup L(z) in the Standard Normal Loss Function Table: L(2.57)=0.0016 Convert expected lost sales, L(z), for the standard normal into the expected backorder with the actual normal distribution that represents demand over l+1 periods: Therefore, if S = 625, then on average there are 0.19 backorders at the end of any period at the DC.

Other DC performance measures with S = 625: 

Other DC performance measures with S = 625 So 99.76% of demand is filled immediately (i.e., without being backordered) So on average there are 302.8 units on-hand at the end of a period. So there are 241.8 units on-order at any given time.

Performance measures in Susan’s territory: 

Performance measures in Susan’s territory Look up in the Poisson Loss Function Table expected backorders for a Poisson distribution with a mean equal to expected demand over l+1 periods: Suppose S = 3: Expected backorder = 0.00335 In-stock = 99.702% Fill rate = 1 – 0.00335 / 0.29 = 98.84% Expected on-hand = S – demand over l+1 periods + backorder = 3 – 0.58 + 0.00335 = 2.42 Expected on-order inventory = Demand over the lead time = 0.29

Choose S to hit a target in-stock with normally distributed demand: 

Choose S to hit a target in-stock with normally distributed demand Suppose the target in-stock probability at the DC is 99.9%: From the Standard Normal Distribution Function Table, F(3.08)=0.9990 So we choose z = 3.08 To convert z into an order up-to level: Note that m and s are the parameters of the normal distribution that describes demand over l + 1 periods.

Choose S to hit a target fill rate with normally distributed demand: 

Choose S to hit a target fill rate with normally distributed demand Find the S that yields a 99.9% fill rate for the DC. Step 1: Evaluate the target lost sales Step 2: Find the z that generates that target lost sales in the Standard Normal Loss Function Table: L(2.81) = L(2.82) = L(2.83) = L(2.84) = 0.0007 Choose z = 2.84 to be conservative (higher z means higher fill rate) Step 3: Convert z into the order up-to level:

Choose S to hit a target in-stock with Poisson demand: 

Choose S to hit a target in-stock with Poisson demand Recall: Period length is one day, the replenishment lead time is one day, l = 1 Demand over l + 1 days is Poisson with mean 2 x 0.29 = 0.58 Target in-stock is 99.9% In Susan’s territory, S = 4 minimizes inventory while still generating a 99.9% in-stock: These probabilities can be found in the Poisson distribution function table or evaluated in Excel with the function Poisson(S, 0.58, 1)

Choose S to hit a target fill rate with Poisson demand: 

Choose S to hit a target fill rate with Poisson demand Suppose the target fill rate is 99.9% Recall, So rearrange terms in the above equation to obtain the target expected backorder: In Susan’s territory: From the Poisson Distribution Loss Function Table with a mean of 0.58 we see that L(4) = 0.00037 and L(5) = 0.00004, so choose S = 5

Justifying a service level via cost minimization: 

Justifying a service level via cost minimization Let h equal the holding cost per unit per period e.g. if p is the retail price, the gross margin is 75%, the annual holding cost is 35% and there are 260 days per year, then h = p x (1 -0.75) x 0.35 / 260 = 0.000337 x p Let b equal the penalty per unit backordered e.g., let the penalty equal the 75% gross margin, then b = 0.75 x p “Too much-too little” challenge: If S is too high, then there are holding costs, Co = h If S is too low, then there are backorders, Cu = b Cost minimizing order up-to level satisfies Optimal in-stock probability is 99.96% because

The optimal in-stock probability is usually quite high: 

The optimal in-stock probability is usually quite high Suppose the annual holding cost is 35%, the backorder penalty cost equals the gross margin and inventory is reviewed daily.

Impact of the period length: 

Impact of the period length Increasing the period length leads to larger and less frequent orders: The average order quantity = expected demand in a single period. The frequency of orders approximately equals 1/length of period. Suppose there is a cost to hold inventory and a cost to submit each order (independent of the quantity ordered)… … then there is a tradeoff between carrying little inventory (short period lengths) and reducing ordering costs (long period lengths)

Example with mean demand per week = 100 and standard deviation of weekly demand = 75.: 

Example with mean demand per week = 100 and standard deviation of weekly demand = 75. Inventory over time follows a “saw-tooth” pattern. Period lengths of 1, 2, 4 and 8 weeks result in average inventory of 597, 677, 832 and 1130 respectively:

Tradeoff between inventory holding costs and ordering costs: 

Tradeoff between inventory holding costs and ordering costs Costs: Ordering costs = $275 per order Holding costs = 25% per year Unit cost = $50 Holding cost per unit per year = 25% x $50 = 12.5 Period length of 4 weeks minimizes costs: This implies the average order quantity is 4 x 100 = 400 units EOQ model: Ordering costs Inventory holding costs Total costs

Better service requires more inventory at an increasing rate: 

Better service requires more inventory at an increasing rate More inventory is needed as demand uncertainty increases for any fixed fill rate. The required inventory is more sensitive to the fil rate level as demand uncertainty increases The tradeoff between inventory and fill rate with Normally distributed demand and a mean of 100 over (l+1) periods. The curves differ in the standard deviation of demand over (l+1) periods: 60,50,40,30,20,10 from top to bottom.

Shorten lead times and you will reduce inventory: 

Shorten lead times and you will reduce inventory Reducing the lead time reduces expected inventory, especially as the target fill rate increases The impact of lead time on expected inventory for four fill rate targets, 99.9%, 99.5%, 99.0% and 98%, top curve to bottom curve respectively. Demand in one period is Normally distributed with mean 100 and standard deviation 60.

Do not forget about pipeline inventory: 

Do not forget about pipeline inventory Reducing the lead time reduces expected inventory and pipeline inventory The impact on pipeline inventory can be even more dramatic that the impact on expected inventory Expected inventory (diamonds) and total inventory (squares), which is expected inventory plus pipeline inventory, with a 99.9% fill rate requirement and demand in one period is Normally distributed with mean 100 and standard deviation 60

Order up-to model summary: 

Order up-to model summary The order up-to model is appropriate for products with random demand but many replenishment opportunities. Expected inventory and service are controlled via the order up-to level: The higher the order up-to level the greater the expected inventory and the better the service (either in-stock probability or fill rate). The key factors that determine the amount of inventory needed are… The length of the replenishment lead time. The desired service level (fill rate or in-stock probability). Demand uncertainty. When inventory obsolescence is not an issue, the optimal service level is generally quite high.

Risk pooling strategies to reduce and hedge uncertainty : 

Risk pooling strategies to reduce and hedge uncertainty

Risk pooling strategies: 

Risk pooling strategies Redesign of the: supply chain production process product to reduce uncertainty or to hedge uncertainty Four versions of risking pooling: location product lead time delayed differentiation consolidated distribution capacity

Location pooling at Medtronic: 

Location pooling at Medtronic Current operations: Each sales representative has her own inventory to serve demand in her own territory. Lead time is 1 day from Mounds View DC e.g., 3 territories, 3 stockpiles of inventory The location pooling strategy: A single location stores inventory used by several sales reps. Sales reps no longer hold their own inventory, they must pull inventory from the pooled location. Inventory is automatically replenished at the pooled location as depleted by demand. Lead time to pooled location is still 1 day from Mounds View DC. e.g., 3 pooled territories, 1 stockpile of inventory DC Territory 1 Territory 2 Territory 3 DC Territory 1 Territory 2 Territory 3

The impact of location pooling on inventory: 

The impact of location pooling on inventory Suppose each territory’s expected daily demand is 0.29, the required in-stock probability is 99.9% and the lead time is 1 day with individual territories or pooled territories. Pooling 8 territories reduces expected inventory from 11.7 days-of-demand down to 3.6. But pooling has no impact on pipeline inventory.

Location pooling & the inventory-service curve: 

Location pooling & the inventory-service curve Location pooling shifts the inventory-service tradeoff curve For a single product, location pooling decreases inventory with service constant increases service with holding cost constant a combination of inventory reduction and service increase. Location pooling can be used to broaden the product line. Inventory-service tradeoff curve for different levels of location pooling. The curves represent, from highest to lowest, individual territories, two pooled territories, four pooled territories, and eight pooled territories. Daily demand in each territory is Poisson with mean 0.29 and the lead time is one day.

Why does location pooling work?: 

Why does location pooling work? Location pooling reduces demand uncertainty (measured by CV) Reduced demand uncertainty reduces the inventory (with constant service level) But there are declining marginal returns to risk pooling! The relationship between expected inventory (diamonds) and the coefficient of variation (squares) as territories are pooled. Daily demand in each territory is Poisson with mean 0.29 units, the target in-stock probability is 99% and the lead time is one day.

Location pooling pros, cons and alternatives: 

Location pooling pros, cons and alternatives Pros: Reduces demand uncertainty Cons: Location pooling moves inventory away from customers: Alternatives: Virtual pooling: Drop shipping:

Product pooling – universal design: 

Product pooling – universal design O’Neill sells two Hammer 3/2 wetsuits that are identical except for the logo silk screened on the chest. Instead of having two Hammer 3/2 suits, O’Neill could consolidate its product line into a single Hammer 3/2 suit, i.e., a universal design, which we will call the “Universal Hammer”. Surf Hammer 3/2 logo Dive Hammer 3/2 logo

Product pooling analysis assumptions: 

Product pooling analysis assumptions Demand for the Surf Hammer is Normally distributed with mean 3192 and standard deviation 1181. Demand for the Dive Hammer has the same distribution as the Surf Hammer. Surf and Dive demands are independent then the Universal Hammer’s demand has mean 2 x 3192 = 6384 and std deviation = sqrt(2) x 1181 = 1670. Price, cost and salvage value for the Universal Hammer are the same as for the other two: Hence, Co is 110 – 90 = 20, Cu = 180-110 = 70 Same critical ratio = 70 /(20 + 70) = 0.7778 Same optimal z statistic, 0.77

Product pooling analysis results: 

Product pooling analysis results Performance of the two suits (Surf and Dive) Total order quantity = 2 x 4101 = 8202 Total profit = 2 x $191,760 = $383,520 Universal Hammer Order quantity: Profit: Reduces inventory investment by (8202-7670)/8202 = 6.5% Increase profit by (402116-383520)/383520 = 4.85% The profit increase of 4.85% = 1.45% of revenue

Demand correlation: 

Demand correlation Random demand for two products (x-axis is product 1, y-axis is product 2). Correlations are -0.9, 0.0, and +0.9 In all scenarios demand is ~N(10,3).

Key driver of product pooling: 

Key driver of product pooling Most effective if the CVUniversal < CVindividual The correlation between surf and dive demand for the Hammer 3/2 and the expected profit of the universal Hammer wetsuit (decreasing curve) and the coefficient of variation of total demand (increasing curve) CVindividual = 1181/2192 = 0.37 CVUniversal = 1670/6384 = 0.26 Negative correlation in demand for the individual products is best for reducing CV

Limitations of product pooling/universal design: 

Limitations of product pooling/universal design May not provide key functionality to consumers with special needs May be more expensive to produce because additional functionality may require additional components. May be less expensive to produce/procure because each component is needed in a larger volume. May eliminate brand/price segmentation opportunities

Lead time pooling – consolidated distribution: 

Lead time pooling – consolidated distribution Consider the following two systems: In each case weekly demand at each store is ~P(0.5) and the target in-stock probability at each store is 99.5% DC demand is ~N(50,15) If demands were independent across stores, then DC demand would have a standard deviation of sqrt(50) = 7.07

Consolidated distribution results: 

Consolidated distribution results Consolidated distribution … reduces retail inventory by more than 50%! not as effectively as location pooling… … but consolidated distribution keeps inventory near demand, reduces inventory even though the total lead time increases from 8 to 9 weeks!

Consolidated distribution summary: 

Consolidated distribution summary Reduces inventory in a supply chain via lead time risk pooling Decide the total quantity to ship from the supplier, not a total quantity and its allocation across locations. Most effective if demands are negatively correlated across locations. Most effective if the supplier lead time is long and the DC to store lead time is short. Increases distance traveled & lead time from supplier to stores. Other benefits of consolidated distribution: Easier to obtain quantity discounts in purchasing. Easier to obtain economies of scale in transportation:

Lead time risk pooling – delayed differentiation: 

Lead time risk pooling – delayed differentiation A Universal Hammer 3/2 increases O’Neill’s profit, but does not allow O’Neill to differentiate between the Surf and the Dive markets. Delayed differentiation is an alternative to the Universal Hammer: O’Neill stocks “generic” Hammers with no logo. When demand occurs O’Neill quickly silk screens on the appropriate logo, This generates the same profit as the Universal Hammer! Wheee! When does delayed differentiation make sense? Customers demand variety. There is less uncertainty with total demand than demand for individual versions. Variety is created late in the production process. Variety can be added quickly and cheaply. Component needed for variety is inexpensive relative to the generic component.

Other examples of delayed differentiation: 

Other examples of delayed differentiation Retail paint HP printer Private label canned goods manufacturer Black and Decker Nokia

Capacity pooling with flexible manufacturing: 

Capacity pooling with flexible manufacturing Consider the following stylized situation faced by GM … 10 production facilities 10 vehicle models Each plant is capable of producing 100 units/day Demand for each product is ~N(100,40) Each plant can be configured to produce up to 10 products But flexibility is expensive. GM must decide which plants can produce which products before demand is realized. After demand is realized, GM can allocate its capacity to satisfy demand. If demand exceeds capacity, sales are lost.

Four possible capacity configurations: no flexibility to total flexibility: 

Four possible capacity configurations: no flexibility to total flexibility The more links in the configuration, the more flexibility constructed In the 16 link configuration plant 4 is flexible enough to produce 4 products but plant 5 has no flexibility (it produces a single product).

How is flexibility used: 

How is flexibility used Flexibility allows production shifts to avoid lost sales. Two plant, two product example If demand turns out to be 75 for product A, 115 for product B then..

The value of flexibility : 

The value of flexibility Adding flexibility increases capacity utilization and expected sales: Note: 20 links can provide nearly the same performance as total flexibility! These data are collected via simulation

Chaining: how to add flexibility: 

Chaining: how to add flexibility A chain is a group of plants and products connected via links. Flexibility is most effective if it is added to create long chains. A configuration with 20 links can produce nearly the results of total flexibility as long as it constructs one large chain: Hence, a little bit of flexibility is very useful as long as it is designed correctly

When is flexibility valuable?: 

When is flexibility valuable? Flexibility is most valuable when capacity approximately equals expected demand. Flexibility is least valuable when capacity is very high or very low. A 20 link (1 chain) configuration with 1000 units of capacity produces the same expected sales as 1250 units of capacity with no flexibility. If flexibility is cheap relative to capacity, add flexibility. But if flexibility is expensive relative to capacity, add capacity. C = total capacity of all ten plants

One way to make money with capacity pooling: contract manufacturing : 

One way to make money with capacity pooling: contract manufacturing A fast growing industry: But one with low margins: Total revenue of six leading contract manufacturers by fiscal year: Solectron Corp, Flextronics International Ltd, Sanmina-SCI, Jabil Circuit Inc, Celestica Inc and Plexus Corp.

Risk pooling summary: 

Risk pooling summary Risk pooling strategies are most effective when total demand uncertainty is lower than the uncertainty for individual products/locations. A little bit of risk pooling goes a long way: With location pooling the biggest bang is from pooling a few locations With capacity pooling a little bit of well designed flexibility is very effective. Risk pooling strategies do not help reduce pipeline inventory. Risk pooling allows a firm to “have its cake and eat it too” It is possible to lower inventory and increase service simultaneously.

Standard Normal Loss Table Part 1: 

Standard Normal Loss Table Part 1

Standard Normal Loss Table Part 2: 

Standard Normal Loss Table Part 2

Standard Normal Table Part 1: 

Standard Normal Table Part 1

Standard Normal Table Part 2: 

Standard Normal Table Part 2

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