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IE 323: 

IE 323 Warehouse location problems

Basic idea: 

2 Basic idea Integrated plan for production and distribution: Where should production plants be located? Where should transshipment centers (warehouses) be located? How should goods be transported? Objective is to minimize total operating cost

Ideas should be familiar: 

3 Ideas should be familiar You’ve seen: Transportation and transshipment problems Location problems Now combine these to produce an integrated logistics plan

Huntco example: 

4 Huntco example Determine: Which plants and warehouses to operate How much to ship from each plant to each warehouse How much to ship from each warehouse to each customer Minimize total fixed costs and production and shipping costs

Objective: 

5 Objective Minimize total costs, which include: Fixed costs of operating plants and warehouses Variable production costs at plants Shipping costs from plants to warehouses and from warehouses to customers

Constraints: 

6 Constraints Don’t ship at all from plants that are closed Don’t ship more than capacity from plants that are open Amounts shipped into warehouses must equal amounts shipped out Don’t ship into or out of warehouses that are closed Meet customer requirements

Inputs: 

7 Inputs Unit production/shipping costs from plants to warehouses Unit shipping costs from warehouses to customers Fixed costs of operating plants Fixed costs of operating warehouses Customer requirements

Decision Variables: 

8 Decision Variables Amounts shipped from plants to warehouses 0-1 variables to indicate which plants are operating Amounts shipped from warehouses to customers 0-1 variables to indicate which warehouses are operating

Spreadsheet Model (See “Steps 1-3” sheet of Excel): 

9 Spreadsheet Model (See “Steps 1-3” sheet of Excel) Step 1: Enter all inputs Step 2: Enter any amounts to ship from each plant to each warehouse and from each warehouse to each customer Step 3: Enter any values in the 0-1 changing cells for which plants and warehouses to operate

See “Steps 4,5” sheet of Excel: 

10 See “Steps 4,5” sheet of Excel Step 4: Calculate the amounts shipped out of the plants as row sums Step 5: Using 0-1 variables, calculate the logical upper limits for the sums in step 4: For an operating plant, this is the plant capacity For a closed plant, this is 0

See “Steps 6,7” sheet of Excel: 

11 See “Steps 6,7” sheet of Excel Step 6a: Calculate an upper limit on the amount shipped out of each warehouse Total customer demand Step 6b: Using the 0-1 variables, calculate a logical upper bound on the amount shipped out of each warehouse: Bound from step 6a for an operating warehouse 0 for a closed warehouse

See “Steps 6,7” sheet of Excel: 

12 See “Steps 6,7” sheet of Excel Step 7a: Calculate the amounts shipped out of the warehouses as row sums Step 7b: Transpose these into a row

See “Steps 8,9” sheet of Excel: 

13 See “Steps 8,9” sheet of Excel Step 8: Calculate the amounts received by the warehouses as column sums Step 9: Calculate the amounts received by the customers as column sums

See “Steps 10-12” sheet of Excel: 

14 See “Steps 10-12” sheet of Excel Step 10: Calculate all production and shipping costs with SUMPRODUCT functions Step 11: Calculate all fixed costs with SUMPRODUCT functions Step 12: Calculate the total cost

See “Optimal” sheet of Excel: 

15 See “Optimal” sheet of Excel Click on Tools/Solver Fill in the Solver dialog box: See next slide Don’t forget to check the Assume Linear Model box under Options Click on Solve

Solver Dialog Box: 

16 Solver Dialog Box

Optimal Solution: 

17 Optimal Solution Plants 2, 3, and 5 are operated Warehouses 2 and 3 are operated The plant-warehouse shipments are: P2-W2, P3-W3, P5-W3 All operating plants produce and ship their capacity The warehouse-customer shipments are: W2-C1, W3-C2, W3-C3, W3-C4

Summary: 

18 Summary This model combined: Transportation and transshipment analysis Location analysis It produced an integrated logistics plan for Huntco Next step would probably be to start asking “what-if” questions: Cost variation, etc.

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