Your firm needs to decide how much to ship along each route AND which of the...

 

Transcribed Image Text:

Your firm needs to decide how much to ship along each route AND which of the new stores to open. Opening Gamma incurs a fixed cost of $225. Opening Omega incurs a fixed cost of $200. The relevant supply, demand, and unit shipping cost information are given in the table for this problem. Set up and solve the transshipment model as a mixed-integer linear program (MILP) to minimize total shipping plus fixed costs. a) Define the decision variables the mathematical symbol you use as well as the interpretation and units. b) Write down the objective function. Indicate variable vs fixed costs. What are the constraints? In particular, what are the net flow con- straints for Gamma and Omega, and what are the integer constraints? d) Which of the new store(s) should you open, if any? e) What is the minimum total cost of selling all of your supply from A,B, and C (shipping cost PLUS fixed cost)? From J K L Plant Supply Store 400 X 500 Y 350 Z A B C A B C Demand 400 325 400 Gamma 200 Omega 100 From J K L Gamma $4 $7 $5 $100 $8 $5 $4 $100 $5 $6 $7 $10 Omega $10 $100 $100 X Y Z J K L Gamma $6 $4 $8 $6 $5 $5 $3 $6 $7 $6 $7 $2 $4 $5 $5 $7 $8 $4 Omega $6 $3 $4 Your firm needs to decide how much to ship along each route AND which of the new stores to open. Opening Gamma incurs a fixed cost of $225. Opening Omega incurs a fixed cost of $200. The relevant supply, demand, and unit shipping cost information are given in the table for this problem. Set up and solve the transshipment model as a mixed-integer linear program (MILP) to minimize total shipping plus fixed costs. a) Define the decision variables the mathematical symbol you use as well as the interpretation and units. b) Write down the objective function. Indicate variable vs fixed costs. What are the constraints? In particular, what are the net flow con- straints for Gamma and Omega, and what are the integer constraints? d) Which of the new store(s) should you open, if any? e) What is the minimum total cost of selling all of your supply from A,B, and C (shipping cost PLUS fixed cost)? From J K L Plant Supply Store 400 X 500 Y 350 Z A B C A B C Demand 400 325 400 Gamma 200 Omega 100 From J K L Gamma $4 $7 $5 $100 $8 $5 $4 $100 $5 $6 $7 $10 Omega $10 $100 $100 X Y Z J K L Gamma $6 $4 $8 $6 $5 $5 $3 $6 $7 $6 $7 $2 $4 $5 $5 $7 $8 $4 Omega $6 $3 $4