Question

Please submit your solutions as ONE single workbook with the sheets clearly labelled to indicate the corresponding problem numbers as indicated on this test.

• For each problem, you are required to use a textbox to show the definition of your decision variables. You may include this textbox only with part a) of the problem if the following parts do not require additional variables to reformulate.

• If a problem requires sensitivity analysis, re-order the worksheets so that they appear in the order of the questions.

• Answers to the questions should be clearly described in a separate textbox of the corresponding labelled worksheets. Since you will only be credited with problems that have correct answers, please check carefully your report textbox.

• For each problem formulation, please highlight the decision variables in Yellow, the constriants (Left Hand Side) in Blue, and the Objective function in Red.

3) ​The A&B Supermarkets have 3 warehouses A, B, and C, that ships supplies to their 3 stores. Their costs of shipping per unit are given below:

​

	1	2	3
A	14	12	9
B	11	8	12
C	13	10	12

​The capacities of A, B, and C are 240, 360, and 200 units, respectively, while the demands of stores 1, 2, and 3 are 400, 250, and 150, respectively. [Notice that the supplies = demands!]

a) Formulate the transportation problem to minimize total cost for shipping. Please provide the actual shipping schedule derived from Solver.

b) If the shipping routes can be changed so that the supplies can be transshipped from warehouse to warehouse, market to market, and even market to warehouse, would you recommend a new set of shipping routes given the following per unit cost shipping data:

	A	B	C	1	2	3
A	0	1	5	14	12	9
B	1	0	2	11	8	12
C	5	2	0	13	10	12
1	14	11	13	0	4	3
2	12	8	10	4	0	2
3	9	12	12	3	2	0

​

​​

c)​What would be the new shipping routes and quantities? How are these different from those of a)?

Answer 1

a)

Create spreadsheet model as follows:

EXCEL FORMULAS:

	Optimal shipping plan
From / To	1	2	3	Sent
A	90	0	150	=SUM(B10:D10)
B	110	250	0	=SUM(B11:D11)
C	200	0	0	=SUM(B12:D12)
Received	=SUM(B10:B12)	=SUM(C10:C12)	=SUM(D10:D12)
Total Cost	=SUMPRODUCT(B10:D12,B3:D5)

[there are no formulas in the cost of Shipping table. In that table, all the numbers are manually entered]

Enter Solver Parameters as follows:

Click Solve to generate the solution:

b)

Create spreadsheet model as follows:

EXCEL FORMULAS:

	Optimal shipping plan
From / To	A	B	C	1	2	3	Row Total	Net Supply
A							=SUM(B13:G13)	=H13-B19
B							=SUM(B14:G14)	=H14-C19
C							=SUM(B15:G15)	=H15-D19
1							=SUM(B16:G16)
2							=SUM(B17:G17)
3							=SUM(B18:G18)
Column Total	=SUM(B13:B18)	=SUM(C13:C18)	=SUM(D13:D18)	=SUM(E13:E18)	=SUM(F13:F18)	=SUM(G13:G18)
			Net Received	=E19-H16	=F19-H17	=G19-H18
Total Cost	=SUMPRODUCT(B13:G18,B3:G8)

[there are no formulas in the cost of Shipping table. In that table, all the numbers are manually entered]

Enter Solver Parameters as follows:

Click Solve to generate the solution:

The new shipping routes and quantities are shown in optimal shipping plan

This new shipping plan is different from (a) in the sense that in this plan, 90 units are shipped from A to B . This increased the total capacity of B from 360 to 450

This new plan resulted in a cost reduction of = 8420 - 8240

= 180