Production Concepts and Math Model Week 3-2 and 4-1

Ch 3 Manufacturing Models and Metrics:

Ch 3 Manufacturing Models and Metrics Sections: Mathematical Models of Production Performance Manufacturing Costs

Production Concepts and Mathematical Models:

Production Concepts and Mathematical Models Production rate R p Production capacity PC Utilization U Availability A Manufacturing lead time MLT Work-in-progress WIP

Operation Cycle Time:

Operation Cycle Time Typical cycle time for a production operation: T c = T o + T h + T th where T c = cycle time, T o = processing time for the operation, T h = handling time (e.g., loading and unloading the production machine), and T th = tool handling time (e.g., time to change tools)

Production Rate:

Production Rate Batch production: batch time T b = T su + QT c Average production time per work unit T p = T b / Q Production rate (minutely rate) R p = 1/ T p ( hourly rate) R p = 60/ T p Job shop production: For Q = 1, T p = T su + T c For quantity high production (mass production): R p = R c = 60/ T c since T su / Q  0 For flow line production T c = T r + Max T o and R c = 60/ T c

Production Capacity:

Production Capacity Plant capacity for facility in which parts are made in one operation ( n o = 1): PC w = n S w H s R p where PC w = weekly plant capacity, units/wk. Ex) the turret lathe section has six machines, all devoted to the production of the same part. The section operates 10 shift/wk. The number of hours per shift average 8.0. Average production rate of each machine is 17 unit/hr. determine the weekly production capacity of the turret lather section.

Production Capacity:

Production Capacity Plant capacity for facility in which parts require multiple operations ( n o > 1): PC w = where n o = number of operations in the routing

PCw = n Sw Hs Rp:

PC w = n S w H s R p Changes that can be made to increase or decrease plant capacity over the 1) SHORT TERM, The number of shifts per week (S) The number of hours worked per shift (H) 2) The INTERMEDIATE or LONGER TERM, to increase Increase the number of work center, n, in the shop (n) Increase the production rate (R p ) Reduce the number of operations n o

Class Exercise 1:

Class Exercise 1 The ABC Company is planning a new product line and will build a new plant to manufacture the parts for a new product line. The product line will include 50 different models. Annual production of each model is expected to be 1000 units. Each product will be assembled of 400 components. All processing of parts will be accomplished in one factory. There are an average of 6 processing steps required to produce each component, and each processing step takes 1.0 minute (includes an allowance for setup time and part handling). All processing operations are performed at workstations, each of which includes a production machine and a human worker. If each workstation requires a floor space of 250 ft2, and the factory operates one shift (2000 hr/yr), determine (a) how many production operations, (b) how much floorspace, and (c) how many workers will be required in the plant.

Class Exercise 2:

Class Exercise 2 The XYZ Company is planning to introduce a new product line and will build a new factory to produce the parts and assembly the final products for the product line. The new product line will include 100 different models. Annual production of each model is expected to be 1000 units. Each product will be assembled of 600 components. All processing of parts and assembly of products will be accomplished in one factory. There are an average of 10 processing steps required to produce each component, and each processing step takes 30 sec. (includes an allowance for setup time and part handling). Each final unit of product takes 3.0 hours to assemble. All processing operations are performed at work cells that each includes a production machine and a human worker. Products are assembled on single workstations consisting of two workers each. If each work cell and each workstation require 200 ft2, and the factory operates one shift (2000 hr/yr), determine: (a) how many production operations, (b) how much floorspace, and (c) how many workers will be required in the plant.

Utilization and Availability:

Utilization and Availability Utilization: U = where U = utilization of the facility, Q = actual quantity produced by the facility during a given time period (i.e. pc/wk), PC = production capacity for the same period (pc/wk) Ex) A production machine operates 80 hr/wk (two shifts, 5 days) at full capacity. Its production rate is 20 unit/hr. During a certain week, the machine produced 1000 parts and was idle the remaining time. (a) Determine the production capacity of the machine. (b) what was the utilization of the machine during the week under consideration?

Utilization and Availability:

Utilization and Availability Availability: A = where MTBF = mean time between failures, and MTTR = mean time to repair

Availability Example:

Availability Example the turret lathe section has six machines, all devoted to the production of the same part. The section operates 10 shift/wk. The number of hours per shift average 8.0. Average production rate of each machine is 17 unit/hr. determine the weekly production capacity of the turret lather section. Availability of the machines A =90%, and the utilization of the machines U =80%. Given this additional data, compute the expected plant output.

Manufacturing Lead time:

Manufacturing Lead time Total time required to manufacture an item, including order preparation time, queue time, setup time, run time, move time, inspection time, and put-away time. For make-to-order products, it is the time taken from release of an order to production and shipment. For make-to-stock products, it is the time taken from the release of an order to production and receipt into finished goods inventory.

Manufacturing Lead Time (batch production):

Manufacturing Lead Time (batch production) MLT = n o ( T su + QT c + T no ) where MLT = manufacturing lead time, n o = number of operations, T su = setup time, Q = batch quantity, T c the operation cycle time at a given machine (per part), T no = non-operation time

MLT :

MLT Ex) A certain part is produced in a batch size of 100 units. The batch must be routed through five operations to complete the processing of the parts. Average setup time is 3 hr/operation, and average operation time is 6 min (0.1 hr). Average non-operation time due to handling, delays, inspections, etc., is 7 hours for each operation. Determine how many days it will take to complete the batch, assuming the plant runs one 8-hr shift/day.

MLT for Job Shop and Mass Production:

MLT for Job Shop and Mass Production For job shop, the batch size is one (Q=1), MLT = n o ( T su + T c + T no ) For mass production Quantity type mass production ( n o = 1) in which a large number of units are made on a single machine MLT = T c Flow line mass production, the entire production line is set up in advance. Also, the non-operation time between processing steps is simply the transfer time T r . MLT = n o ( T r + Max T 0 ) = n o T c

Work-In-Process:

Work-In-Process WIP = Where, WIP = work-in-process in the facility, pc; A = availability, U = utilization, PC = plant capacity, pc/wk; MLT = manufacturing lead time, hr; S w = shifts per week, H sh = hours per shift, hr/shift

Class Exercise:

Class Exercise A certain part is routed through six machines in a batch production plant. The setup and operation times for each machine are given in the table below. The batch size is 100 and the average nonoperation time per machine is 12 hours. Determine (a) manufacturing lead time and (b) production rate for operation 3. Machine Setup time (hr.) Operation time (min.) 1 4 5 2 2 3.5 3 8 10 4 3 1.9 5 3 4.1 6 4 2.5

Class Exercise 2:

Class Exercise 2 Suppose the part in the previous problem is made in very large quantities on a production line in which an automated work handling system is used to transfer parts between machines. Transfer time between stations = 15 s. The total time required to set up the entire line is 150 hours. Assume that the operation times at the individual machines remain the same. Determine (a) manufacturing lead time for a part coming off the line, (b) production rate for operation 3, (c) theoretical production rate for the entire production line? Based on the data in the problem and your answers to that problem, determine the average level of work‑in‑process (number of parts‑in‑process) in the plant.

Class Exercise:

Class Exercise The average part produced in a certain batch manufacturing plant must be processed sequentially through six machines on average. Twenty (20) new batches of parts are launched each week. Average operation time = 6 min., average setup time = 5 hours, average batch size = 25 parts, and average nonoperation time per batch = 10 hr/machine. There are 18 machines in the plant working in parallel. Each of the machines can be set up for any type of job processed in the plant. The plant operates an average of 70 production hours per week. Scrap rate is negligible. Determine (a) manufacturing lead time for an average part, (b) plant capacity, (c) plant utilization

Costs of Manufacturing Operations:

Costs of Manufacturing Operations Two major categories of manufacturing costs: Fixed costs - remain constant for any output level Variable costs - vary in proportion to production output level Adding fixed and variable costs TC = FC + VC ( Q ) where TC = total costs, FC = fixed costs (e.g., building, equipment, taxes), VC = variable costs (e.g., labor, materials, utilities), Q = output level.

Fixed and Variable Costs:

Fixed and Variable Costs

Manufacturing Costs:

Manufacturing Costs Alternative classification of manufacturing costs: Direct labor - wages and benefits paid to workers Materials - costs of raw materials Overhead - all of the other expenses associated with running the manufacturing firm Factory overhead Corporate overhead

Slide 24:

Factory Overhead Expenses Corporate Overhead Expenses Plant supervision Corporate executives Line foreman Sales and marketing Maintenance crew Accounting department Custodial services Finance department Security personnel Legal counsel Tool crib attendant Engineering Material handling Research and development Shipping and receiving Other support personnel Applicable taxes Applicable taxes Insurance Cost of office space Heat and air conditioning Security personnel Light Heat and air conditioning Power Light Factory depreciation Insurance Equipment depreciation Fringe benefits Fringe benefits Other office costs

Typical Manufacturing Costs:

Typical Manufacturing Costs

Overhead Rates:

Overhead Rates Factory overhead rate: FOHR = Corporate overhead rate: COHR = where DLC = direct labor costs

Example:

Example Suppose that all costs have been compiled for a certain manufacturing firm for last year. The summary is shown in the table below. The company operates two different manufacturing plants plus a corporate headquarters. Determine: (a) the factory overhead rate for each plant. (b) the corporate overhead rate. Expense Category Plant 1 ($) Plant 2($) Corporate Headquarters ($) Direct labor 800,000 400,000 1,200,000 Materials 2,500,000 1,500,000 4,000,000 Factory expense 2,000,000 1,100,000 3,100,000 Corporate expense 7,200,000 7,200,000 0 Total 5,300,000 3,000,000 7,200,000 15,500,000

Establishing Selling Price:

Establishing Selling Price A customer order of 50 parts is to be processed through plant 1 of the previous example. Raw materials and tooling are supplied by the customer. The total time for processing the parts (including setup and other direct labor) is 100 hr. Direct labor cost is $10.00/hr. the factory overhead rate is 250% and the corporate overhead rate is 600%. Compute the cost of the job.

Class Exercise 1:

Class Exercise 1 Costs have been compiled for a certain manufacturing company for the most recent year. The summary is shown in the table below. The company operates two different manufacturing plants, plus a corporate headquarters. Determine (a) the factory overhead rate for each plant, and (b) the corporate overhead rate. The firm will use these rates in the following year. Expense Category Plant 1 ($) Plant 2($) Corporate Headquarters ($) Direct labor 1,000,000 1,750,000 Materials 3,500,000 4,000,000 Factory expense 1,300,000 2,300,000 Corporate expense 5,000,000

Class Exercise 2:

Class Exercise 2 Theoretically, any given production plant has an optimum output level. Suppose a certain production plant has annual fixed costs FC = $2,000,000. Variable cost VC is functionally related to annual output Q in a manner that can be described by the function VC = $12 + $0.005 Q . Total annual cost is given by TC = FC + VC x Q . The unit sales price for one production unit P = $250. (a) Determine the value of Q that minimizes unit cost UC , where UC = TC / Q ; and compute the annual profit earned by the plant at this quantity. (b) Determine the value of Q that maximizes the annual profit earned by the plant; and compute the annual profit earned by the plant at this quantity.

Cost of Equipment Usage:

Cost of Equipment Usage Hourly cost of worker-machine system: C o = C L (1 + FOHR L ) + C m (1 + FOHR m ) where C o = hourly rate, $/hr; C L = labor rate, $/hr; FOHR L = labor factory overhead rate, C m = machine rate, $/hr; FOHR m = machine factory overhead rate