Linear Programming Lesson in Excel (using solver) or Lindo Transshipment Model This is an extension of the transportation model There are now intermediate transshipment points added between the sources (plants) and destinations (retailers) Items being shipped from a Plant (p i ) must be shipped to a Warehouse (w j ) before being shipped to the Retailer (r k ) Each Plant will have an associated supply (s i ) and each Retailer will have a demand (d k ) The number of plants is n, number of warehouses is q and the number of retailers is m The edges (i,j) from plant (p i )to warehouse (w j ) have costs associated denoted cp(i,j) The edges (j,k) from a warehouse (w j )to a retailer (r k ) have costs associated denoted cw(j,k) The graph below shows the transshipment map for a manufacturer of refrigerators Refrigerators are produced at four plants and then shipped to a warehouse (weekly) before going to the retailer Below are the costs of shipping from a plant to a warehouse and then a warehouse to a retailer If it is impossible to ship between the two locations an X is placed in the table cost W1 W2 W3 P1 $10 $15 X P2 $11 $8 X P3 $13 $8 $9 P4 X $14 8 cost R1 R2 R3 R4 R5 R6 R7 W1 $5 $6 $7 $10 X X X W2 X X $12 $8 $10 $14 X W3 X X X $14 $12 $12 $6 P1 P2 P3 P4 Supply 150 450 250 150 R1 R2 R3 R4 R5 R6 R7 Demand 100 150 100 200 200 150 100 Lesson in Excel (using Solver) or Lindo Part 1 Determine the number of refrigerators to be shipped from the plants to the warehouses and then warehouses to retailers to minimize the cost Formulate the problem as a linear program with an objective function and all constraints Determine the optimal solution for the linear program using any software you want What are the optimal shipping routes and minimum cost Part 2 Due to old infrastructure Warehouse 2 is going to close eliminating all of the associated routes What is the optimal solution for this modified model Is it feasible to ship all the refrigerators to either warehouse 1 or 3 and then to the retailers without using warehouse 2 Why or why not Part 3 Instead of closing Warehouse 2 management has decide to keep a portion of it open but limit shipments to 100 refrigerators per week Is this feasible If so what is the optimal solution when warehouse 2 is limited to 100 refrigerators R1 R2 P1 W1 P2 P3 R5 R6 R7

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Linear Programming: Lesson in Excel (using solver) or Lindo Transshipment Model: This is an extension of the transportation model. There are now intermediate transshipment points

Linear Programming:

Lesson in Excel (using solver) or Lindo

Transshipment Model: This is an extension of the transportation model. There are now intermediate transshipment points added between the sources (plants) and destinations (retailers). Items being shipped from a Plant (p_i) must be shipped to a Warehouse (w_j) before being shipped to the Retailer (r_k). Each Plant will have an associated supply (s_i) and each Retailer will have a demand (d_k). The number of plants is n, number of warehouses is q and the number of retailers is m. The edges (i,j) from plant (p_i)to warehouse (w_j) have costs associated denoted cp(i,j). The edges (j,k) from a warehouse (w_j)to a retailer (r_k) have costs associated denoted cw(j,k). The graph below shows the transshipment map for a manufacturer of refrigerators. Refrigerators are produced at four plants and then shipped to a warehouse (weekly) before going to the retailer.

image text in transcribed

Below are the costs of shipping from a plant to a warehouse and then a warehouse to a retailer. If it is impossible to ship between the two locations an X is placed in the table.

cost	W1	W2	W3
P1	$10	$15	X
P2	$11	$8	X
P3	$13	$8	$9
P4	X	$14	8

cost	R1	R2	R3	R4	R5	R6	R7
W1	$5	$6	$7	$10	X	X	X
W2	X	X	$12	$8	$10	$14	X
W3	X	X	X	$14	$12	$12	$6

	P1	P2	P3	P4
Supply	150	450	250	150

	R1	R2	R3	R4	R5	R6	R7
Demand	100	150	100	200	200	150	100

Lesson in Excel (using Solver) or Lindo

Part 1: Determine the number of refrigerators to be shipped from the plants to the warehouses and then warehouses to retailers to minimize the cost. Formulate the problem as a linear program with an objective function and all constraints. Determine the optimal solution for the linear program using any software you want. What are the optimal shipping routes and minimum cost?

Part 2: Due to old infrastructure Warehouse 2 is going to close eliminating all of the associated routes. What is the optimal solution for this modified model? Is it feasible to ship all the refrigerators to either warehouse 1 or 3 and then to the retailers without using warehouse 2? Why or why not?

Part 3: Instead of closing Warehouse 2 management has decide to keep a portion of it open but limit shipments to 100 refrigerators per week. Is this feasible? If so what is the optimal solution when warehouse 2 is limited to 100 refrigerators?

R1 R2 P1 W1 P2 P3 R5 R6 R7