Tamara Macewen

Tamara MacEwen IE 416

Problem 2 By: Ms. Tamara MacEwen Good job.

Each day, Sunco manufactures four types of gasoline: lead-free premium (LFP), lead-free regular (LFR), leaded premium (LP), and leaded regular (LR). Because of cleaning and resetting of machinery, the time required to produce a batch of gasoline depends on the type of gasoline last produced. For example, it takes longer to switch between a lead-free gasoline and a leaded gasoline than it does to switch between two lead-free gasolines. The time (in minutes) required to manufacture each day’s gasoline requirements as shown in Table 75.

Table 75: Last- Gas to be Next Produced Produced Gasoline LFR LFP LR LP LFR - 50 120 140 LFP 60 - 140 120 LR 90 130 - 60 LP 130 120 80 -

a) Using Assignment option of WinQSB and creating the branch-and-bound tree similar to page 532 in Winston’s book. Document input and output for each subproblem. Branch on a subtour different from what I used in class.

Subproblem 1:

X12 = X21 = 1 Subtour X34 = X43 = 1 Subtour

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Subproblem 2: branch on X43 Input

Output

X13 -> X34 -> X42 -> X21 Complete tour

Subproblem 3: branch on X34 Input

Output

X12 -> X24 -> X43 -> X31 Complete tour – reverse direction of subproblem 2

Subproblem 1 Z = 250 X = X = X = X = 1 12 21 34 43

X43 = 0 X34 = 0

Subproblem 2 Subproblem 3 Z = 360 Z = 330 X = X = X = X = 1 X = X = X = X = 1 13 34 42 21 12 24 43 31

Subproblem 3 is the optimal solution with the least increase in Z.

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b) Using TSP option of WinQSB. Print input and output results.

Original input

Output

Report to Manager: After reviewing and analyzing the time to produce each of the gasolines, I would recommend the following daily production order. 1) Lead-free regular 2) Lead-free premium 3) Leaded premium 4) Leaded regular By producing in this order, you will produce all four types of gasoline daily at a minimal time of 330 minutes or 5 hours and 30 minutes.