# DIS 300. Quantitative Analysis in Operations Management. Instructions for DIS 300-Transportation

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1 Instructions for -Transportation 1. Set up the column and row headings for the transportation table: Before we can use Excel Solver to find a solution to C&A s location decision problem, we need to set up three tables: the transportation table, the candidate solution table, and the cost calculation table. Let us show you how to use the worksheet called Answer (1) to set up the column and row headings of the transportation table. Double click on the Sheet1 tab and rename it to Answer (1) We will label the sources of demand, which are customers 1, 2, 3, and 4 as the four column headings of the transportation table in cells B1 to E1. Then the label for the sources of supply, which are warehouses A, B, and C/D as the three row headings of the transportation table in cells A2 to A4. The remaining labels are From/To in cell A1, Supply in cell F1, and Demand in cell A5. 1

2 Next, we will fill in the demand of each customer in cells B5 to E5. Enter 400 in cell B5 showing customer 1 s demand. Enter 900 in cell C5 indicating that s customer 2 s demand. Enter 200 in cell D5 which is customer 3 s demand. Enter 500 in cell E5 which is customer 4 s demand. 2

3 We then fill in the available product supply at warehouse A and B in cells F2 and F3. Enter 500 in cell F2 showing warehouse A s supply. Enter 700 in cell F3 showing warehouse B s supply. Question 1 asks us about the amount of unmet supply which is the amount to be entered in cell F4. We can compute that by subtracting the total supply from warehouses A and B from the total demand of customers 1, 2, 3 and 4. Enter the formula =sum(b5:e5) sum(f2:f3) in cell F4. Thus, the minimum amount to be supplied from the new warehouse is 800 units 3

4 2. Set up the transportation table for Location C: Let us copy the transportation table in worksheet Answer (1) to a new worksheet called Answer (C). To do so, select Edit and then Move or Copy Sheet from the Excel Menu. Make sure the Create a copy option is checked in the Move or Copy window. Click OK. Double Click the worksheet tab and rename it to Answer (C). 4

5 Change the row heading in cell A4 to Warehouse C. Fill in the cells of the transportation table with the cost of supplying a unit of the product to each customer from each warehouse. Enter 12 in cell B2, showing that it costs \$12 to ship a unit of product from warehouse A to customer 1. Enter 13 in cell C2, showing that the unit cost of supply from warehouse A to customer 1 is \$13. Enter 4 in cell D2, 6 in cell E2 and so on to complete the set up of the transportation table. 5

6 3. Set up the solution table: Next we will do the set up for the solution table. Enter Solution in cell A7. The headings for this table are the same as the transportation table so you can copy them from the previous table if you like. The cells in B8:E10 will be filled in by Excel to show us the optimal shipping schedule so we will leave them empty. The shipping schedule given by Excel needs to satisfy each customer s demand without exceeding each warehouse s supply. To do so, Enter =sum(b8:b10) in cell B11. Copy the formula to cells C11 to E11. Enter =sum(b8:d8) in cell F8. Copy this formula to cells F9 and F10. 6

7 4. Set up the cost table: Finally, we will set up the cost table. Enter Cost in cell A13. Enter the labels for our customers in cells B13 to E13. Enter the labels for our three warehouses in cells A14 to A16. Enter Total Cost in cell E17. The cells in B14 to E16 will be filled in by Excel to show us the detailed shipping cost based on the shipping schedule shown in cells B8 to E10. Enter =B8*B2 in cell B14. Recall that cell B2 contains the unit cost of supplying customer 1 from warehouse A. Cell B8 contains the amount to be supplied from warehouse A to customer 1. Thus, we will multiply the contents of these two cells to give the total cost of supplying customer 1 from warehouse A. Copy the formula from cell B14 to cells C14 to E14, then to cells B15 to E16. Enter =sum(b14:e16) in cell F17 to compute the total transportation costs of the entire shipping schedule with C being the new warehouse. 7

8 5. Use Excel Solver to find a solution that minimizes costs: After these tables are set up, we can then start Excel Solver. Select Tools and then Solver from the Excel menu. 8

10 The Solver Parameters window will pop up. Click on the Set Target Cell: parameter and select cell F17 from the worksheet. This means that we want Excel to find the total transportation cost if C is the location for C&A s new warehouse. Since we are given the per unit cost of supplying each customer from each warehouse, we will ask Excel to find the minimum total transportation cost. Click on the Min option of the Equal To: parameter. The By Changing Cells: parameter is the location of the shipping schedule in the solution table. Thus, enter B8:E10 for this parameter. 10

11 Finally, we will add to constraints in the Subject to the Constraints: parameter. The first constraint indicates that the total demand from the cost table (i.e., B11 to E11) has to be exactly equal to each customer s demand (i.e., B5 to E5). This demand constraint is entered by clicking the Add button to open the Add Constraint window. The Cell Reference: parameters are set by selecting cells B11 to E11. Change the logical operator parameter to =. Set the Constraint: parameter to cells B5: E5. Then click OK. The second constraint requires that the total supply from the cost table (i.e., F8 to F10) cannot exceed the available supply at each warehouse (i.e., F2 to F4). This supply constraint is entered by clicking the Add button to open the Add Constraint window. The Cell Reference: parameters are set by selecting cells F8 to F10. Change the logical operator parameter to <=. Set the Constraint: parameter to cells F8:F10. Then click OK. 11

12 Next we need to specify two assumptions for this problem. Click the Options button to open the Solver Options window. Check the Assume Linear Model and the Assume Non-Negative options. Then Click OK to return to the Solver Parameters window 12

13 Now we are ready to click the Solve button from the Solve Parameters window. Make sure the Keep Solver Solution option is checked before clicking the OK button. Notice that the shipping schedule is shown in the solution table in cells B8 to D10 indicating that 300 units of the product is transported from warehouse A to customer 1, 100 units from warehouse C to customer 1 and so on. The total transportation cost using C as the new warehouse is given in cell F17 and is \$12,

14 6. Modify the setups of Location C for Location D: Let us copy the worksheet Answer (C) to a new worksheet called Answer (D). Replace C in cells A4, A10, and A16 with D. Replace C s unit shipping costs with those of warehouse D, i.e., enter 20 in cell B4, 8 in cell C4, 6 in cell D4, and 15 in cell E4. 14

15 Since the solution and cost tables can remain unchanged, we are now ready to start Solver to find a solution to this transportation problem. The total transportation cost using D as the new warehouse is shown in cell F17 and is \$12,600. Recall that it costs a total of \$12,000 using C as the new warehouse. Thus, C is a better location as it will save C&A \$600. This will be the answer to Question 2. 15

16 7. Use Excel Solver to find a solution that maximizes profit: To answer question 3, we will make a copy of Answer(C) and Answer (D). Change the label in cell E17 from Total Cost to Total Profit in both Answer (C) (2) and Answer (D) (2) worksheets. Start Solver to find an answer to Answer (C) (2). Since the numbers in cells B2 to E4 represent unit profits, we should ask Excel to find a solution that will maximize total profit. To do so, open the Solver Parameters window, make sure the Max option of the Equal To: parameter is checked before clicking the Solve button. The total profit using C as the new warehouse is shown in cell F17 and is \$21,

17 Repeat the same process for Answer (D) (2). The total profit using D as the new warehouse is \$25,200. Thus, D should be added as the new warehouse for C&A as it will provide \$3600 more in profit. This will be the answer to Question 3. 17

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