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Unformatted text preview: Lecture Suggestions  Supplement to Chapter 8 Example 1: Transportation Method 1. Select the Example 1 worksheet a. b. c. d. e. 2. Delete the current solution 3. Manually find a solution. enter values in these cells. Also note that as you enter values in D16:H20, the satisfied demand is totaled in D21:H21 and the used capacity is totaled in I16:I20. To find a manual solution, you want to enter values in D16:H20 to satisfy all demand without exceeding any capacity. For example the following procedure will lead to the “northwest corner solution": a. b. c. d. e. f. This procedure results in a feasible solution (all demand is satisfied and no capacity is exceeded) with a total cost of 2460. 4. Manually improve this solution. units out of G17 and into G16. To make the solution feasible, you must balance this shift by shifting 10 units out of E16 (leaving 10 units) and moving them to E18 (resulting in 80 units) which results in an additional savings of 4 per unit. The resulting solution is feasible and has a lower cost of 2350. This is the “stepping stone” method, and you would have to repeat this process, maybe several times, to achieve the optimal solution. 5. Use Solver to find the optimal solution. solution with a cost of 2300. Actually there are two alternate optimal solutions, shifting 80 units between A16, A18, D18, andD16. 6. You may also demonstrate that solved (e.g. enter 200 in I5 and press Solve). But unbalanced problems with demand exceeding supply will require the addition of a "Dummy" supply. All you really need to do for a “Dummy” supply is enter the necessary capacity, leaving the rest of the row blank. For example, if the demand in A is 300, (i.e. enter 300 in D10), add enough capacity in cell I8 to balance total supply to the total demand and you can solve the problem. Lecture Suggestions  Supplement to Chapter 8 xample 1: Transportation Method Select the Example 1 worksheet, note that the following data has been entered: The name of each source (1, 2, 3) The capacity of each source (100, 200, 150) The name of each destination (A, B, C, D) The demand at each destination (80, 90, 120, 160) The cost of shipping from each source to each destination (4, 7, 7, etc.) Note that total supply and demand are computed in K12:K13 Delete the current solution by selecting cells D16:H20 and pressing delete. Manually find a solution. Note that even though cells D16:H20 are not shaded you may manually enter values in these cells. Also note that as you enter values in D16:H20, the satisfied demand is totaled in D21:H21 and the used capacity is totaled in I16:I20. To find a manual solution, you want to enter values in D16:H20 to satisfy all demand without exceeding any capacity. For example the following procedure will lead to the “northwest corner solution": Enter 80 in D16 Enter 20 in E16 Enter 70 in E17 Enter 120 in F17 Enter 10 in G17 Enter 150 in G18 This procedure results in a feasible solution (all demand is satisfied and no capacity is exceeded) with a total cost of 2460. Manually improve this solution. For example, you could save 7 per unit by shifting the 10 units out of G17 and into G16. To make the solution feasible, you must balance this shift by shifting 10 units out of E16 (leaving 10 units) and moving them to E18 (resulting in 80 units) which results in an additional savings of 4 per unit. The resulting solution is feasible and has a lower cost of 2350. This is the “stepping stone” method, and you would have to repeat this process, maybe several times, to achieve the optimal solution. Use Solver to find the optimal solution. Just press the Solve button  this results in the optimal solution with a cost of 2300. Actually there are two alternate optimal solutions, shifting 80 units between A16, A18, D18, andD16. You may also demonstrate that unbalanced problems with supply exceeding demand may be solved (e.g. enter 200 in I5 and press Solve). But unbalanced problems with demand exceeding supply will require the addition of a "Dummy" supply. All you really need to do for a “Dummy” supply is enter the necessary capacity, leaving the rest of the row blank. For example, if the demand in A is 300, (i.e. enter 300 in D10), add enough capacity in cell I8 to balance total supply to the total demand and you can solve the problem. ...
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 Spring '11
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