Question

You are the distribution manager for PROP CHICKENZ, a company that produces and distributes rubber

chickens. The transportation costs between warehouses and customers are shown in the matrix below:

	Customer 1	Customer 2	Customer 3	Customer 4
Warehouse A	8	8	11	5
Warehouse B	10	7	15	7

Set up the transportation problem for each situation independently.

A- Each warehouse has a supply of 26 and each customer has a demand of 13. Demand must be satisfied. The objective is to minimize total shipping cost.

B- All demands are 23 and all supplies are 56. All demands must be met, but not all supplies must be shipped. The objective is to minimize total shipping cost.B-

C- All demands are 23 and all supplies are 36. All demands need not be met but ship as much as possible. The objective is to minimize total shipping cost.

D- All demands are 28 and all supplies are 46. All demands need not be met but each customer must receive at least 5 units. Ship as much as possible. The objective is to minimize total shipping cost.

Answer 1

First we set up the LP for the problem:

The boxes in green, are decision variables
The boxes in blue are constrains
The boxes in orange is the objective function

The formulae used:

		Customer 1	Customer 2	Customer 3	Customer 4
	Warehouse A	8	8	11	5
	Warehouse B	10	7	15	7
Dec Var	How much to send from each WH to each customer	Customer 1	Customer 2	Customer 3	Customer 4
	Warehouse A	7	0	13	6	=SUM(C7:F7)	<=	26
	Warehouse B	6	13	0	7	=SUM(C8:F8)	<=	26
		=SUM(C7:C8)	=SUM(D7:D8)	=SUM(E7:E8)	=SUM(F7:F8)
		>=	>=	>=	>=
		13	13	13	13
	Objective function
	Total shipping cost	=SUMPRODUCT(C3:F4,C7:F8)
		Minimization

The solution:

		Customer 1	Customer 2	Customer 3	Customer 4
	Warehouse A	8	8	11	5
	Warehouse B	10	7	15	7
Dec Var	How much to send from each WH to each customer	Customer 1	Customer 2	Customer 3	Customer 4
	Warehouse A	7	0	13	6	26	<=	26
	Warehouse B	6	13	0	7	26	<=	26
		13	13	13	13
		>=	>=	>=	>=
		13	13	13	13
	Objective function
	Total shipping cost	429
		Minimization

A.

So for A:

		Customer 1	Customer 2	Customer 3	Customer 4
	Warehouse A	8	8	11	5
	Warehouse B	10	7	15	7
Dec Var	How much to send from each WH to each customer	Customer 1	Customer 2	Customer 3	Customer 4
	Warehouse A	7	0	13	6	26	<=	26
	Warehouse B	6	13	0	7	26	<=	26
		13	13	13	13
		>=	>=	>=	>=
		13	13	13	13
	Objective function
	Total shipping cost	429
		Minimization