Question

                      Trucks for Us Inc. buys 15 used Trucks at each of two truck auctions each week held at different locations. It then transports the trucks to repair shops it contracts with. When they are restored to Trucks for Us, Inc.’s specifications, it sells 10 each to three different used truck lots. There are costs associated with transportation from each auction to each repair shop. Also there are transportation costs from the repair shops to the used car lots. Trucks for Us is concerned with minimizing its cost given in the table below.

a.	Given the costs below, draw a network representation for this problem.
		Repair Shops				Used Truck Lots
		S1	S2				L1	L2	L3
	Auction 1	55	50			S1	25	30	50
	Auction 2	60	45			S2	35	65	45
b.	Formulate this problem as a transshipment linear programming model.

Answer 1

(a)

(b)

As shown in the above network,

Let AiSj = Units transported from Auction-i to Repair Shop-j for (i,j) = 1,2 and SjLk = Units transported from Repair ship-j to Unsed truck lot-k for j=1,2 and k=1,2,3

Minimize Z = 55 A1S1 + 50 A1S2 + 60 A2S1 + 45 A2S2 + 25 S1L1 + 30 S1L2 + 50 S1L3 + 35 S2L1 + 65 S2L2 + 45 S2L3

Subject to,

A1S1 + A1S2 = 15
A2S1 + A2S2 = 15

A1S1 + A2S1 - S1L1 - S1L2 - S1L3 = 0
A1S2 + A2S2 - S2L1 - S2L2 - S2L3 = 0

S1L1 + S2L1 = 10
S1L2 + S2L2 = 10
S1L3 + S2L3 = 10

AiSj >= 0 for i=1,2 and j=1,2
SjLk >= 0 for j=1,2 and k=1,2,3