Reference no: EM132803853
A company is considering 4 locations to open warehouses: New York Los Angeles Chicago Atlanta
, , and . Each warehouse can ship up to 100 units per week. The weekly fixed cost of keeping each warehouse open is $400 for NY, $500 for LA, $300 for Chicago, and $150 for Atlanta. The company's customers are spread across three well-defined regions across the country. Region 1 requires 80 units per week, region 2 requires 70 units per week and region 3 requires 40 units per week. The unit transportation costs for each warehouse to a region are shown in the following table:
Table of Unit Transportation Costs
FROM
TO
Region 1
Region 2
Region 3
New York
$20
$40
$50
Los Angeles
48
15
26
Chicago
26
35
18
Atlanta
24
50
35
The company wants to meet weekly demands at minimum cost, subject to the preceding information and he following strategic criteria:
- If the NY warehouse is opened, then the LA warehouse must be opened.
- At mosttwo warehouses can be opened.
- Either the Atlanta or LA warehouse must be opened.
Formulate a mixed integer linear program (MILP) for this problem and solve using POM/QM (Integer and Mixed Integer Programming). Interpret your results: (a) which warehouse locations are selected? (b) What is the transportation schedule and what is the total transportation cost?
Hint: Review Distribution System Design (p. 302-205 of textbook) and related in-class example (week 6 session) before attempting this problem. To model the 3 conditions listed as bullets using binary variables, refer to Section 7.4 (p. 313-314) of textbook.
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