1. DECISION MODELING WITH MICROSOFT EXCEL Chapter 12 Copyright 2001 Prentice Hall Publishers and Ardith E. Baker Multi-Objective Decision Making and Heuristics Part 1

2. INTRODUCTION Sometimes a _________________model may be too complex to be solved with traditional_____________. This situation may occur when: The model is too_______, too nonlinear, or logically too_________. ___________programming was developed to solve these types of models. Simplifying ___________or approximations would destroy too much of the real-world structure of the model.

3. A heuristic _________is one that efficiently provides good approximate ____________to a given model. In the optimization context, with some heuristic algorithms, one can make a statement like “Upon _____________, you can be sure of being within __% of optimality.” An important aspect of a heuristic algorithm, is that it never gives a “______” solution. A _________is an intuitively appealing rule of thumb for dealing with some aspect of a model. A collection of heuristics, or heuristic algorithms, is referred to as a_______________________. Heuristics are used in everyday ___________solving (e.g., choosing the shortest waiting line at the bank).

4. Employed mainly for______________, a heuristic procedure or algorithm can only guarantee its results, if at all, in a ____________manner or within certain margins of uncertainty. From the viewpoint of a manager, a heuristic procedure may be as acceptable as a “___________” algorithm that produces an ___________solution. The dominant considerations should be: the amount of _________and guidance that the model can provide, and the overall net ________as measured by the difference “savings due to the model less cost of producing the model and its solution.”

5. In this chapter, heuristic algorithms will be applied to large _________________optimization models. Combinatorial optimization means there are only a _______number of feasible alternatives, and if all of these are enumerated, the _______one can be found. ________programming will be used to deal with models whose objective is to achieve acceptable levels of certain “__________.” Analytic _________process (AHP) is a tool to help managers choose between many different decision ______________when there are multiple _________ that are used to score the alternatives.

6. FACILITY SCHEDULING (SEQUENCING JOBS) SEQUENCE-DEPENDENT SETUP TIME Consider a single production facility through which numerous jobs must be____________. Typically, the facility may have to shut down after processing one _____in order to set up for the next. Such “__________” is termed _____(or changeover) time. The length of this setup time may depend on the next job to be ___________or the job just completed. A sequence of _______jobs would be interrupted by less setup time than a sequence of __________jobs.

7. A typical managerial problem would be to sequence the jobs in such a way as to ___________total setup time. From a combinatorial point of view, this can be a very ________model. For example, if there are only 3 jobs to be processed, say A, B, and C, then any of the three could be taken_____, with either of the remaining two second and third_____________. The 6 possible sequences are displayed as a ______ with each branch representing one sequence. ABCABCABCABC B CA CA B C BC AB A

8. In general, with n jobs, there are n! = n(n-1)(n-2) … 1 possible ______________or sequences. For example, 10 jobs produces 10! = 10(9)(8)(7)(6)(5)(4)(3)(2)(1) = 3,268,800 different sequences. Complete ______________can be used to solve this minimization problem. However, even though this would provide a _______optimum, it is not practical even for modest values of____.

9. HEURISTIC SOLUTIONS Heuristic ________are often applied to this type of model for they will usually lead quite quickly to a ______________solution. For example, consider a machine operator who has three rather long _______jobs to be run on Monday afternoon. The machine is currently______. ToJobFromJob ABC 0 A B C 272132 3522 4946 4612 For each of these jobs, there is a _______time which includes cleaning the machine from the last job, setting up the individual ___________and other auxiliary equipment for the new job, etc.

10. As you can see above, the optimal (minimum total setup time) sequence is 0 A C B. SEQUENCE SETUP TIME TOTAL (MIN) 0 A B C 27 + 35 + 46 108 0 A C B 27 + 22 + 12 61 0 B C A 21 + 46 + 46 113 0 B A C 21 + 49 + 22 92 0 C A B 32 + 46 + 35 113 0 C B A 32 + 12 + 49 93 Since there are only 3! = 3(2)(1) = 6 possible sequences, they can all be enumerated.

11. A Greedy Heuristic The heuristic rule to be applied to this model is the_______________, sometimes called a __________algorithm. 1. At step 1, perform the task with ________initial startup time. 2. At each subsequent step, select the _____with least setup time, based on the current state. From the previous table, the task with the least _____setup time is B. Hence, the first step is 0 B. According to the greedy algorithm, given that we have just completed B, the task to be selected is C, since the setup for B C is less than for B A.

12. Thus, since we have 0 B C, then we can only finish with A. Thus, we obtain Greedy heuristic: 0 B C A Total setup time: 21 + 46 + 46 = 113 Although easy to apply, for ____________decision models, the greedy algorithm does not lead to an optimal solution. However,__________, for the above type sequencing model, the rule is not bad and will often produce better _________than could be obtained by a purely random selection of tasks.

13. A Better Heuristic The following _________heuristic gives even better results: 1. Transform the original _______time data by subtracting the __________setup time in each column from all other entries in that column. ABC 0 A B C 27 - 27 49 - 27 46 - 27 21 - 12 35 - 12 12 - 12 32 - 22 22 - 22 46 - 22 ABC 0 A B C 0910 22 230 190 24

14. 2. Apply the greedy algorithm to this set of ____________data. Doing this, we obtain Best first step: 0 A Best second step: A C Third step: C B And thus the modified heuristic produces the sequence 0 A C B, which was already shown to be optimal for this model. Although this modified heuristic will not always give the __________solution, it is easy to implement, and in practice, for large models, it often produces _____ results.

15. Consider the following scheduling model displaying the ______________relationships: SCHEDULING WITH LIMITED RESOURCES (WORKLOAD SMOOTHING) A SIMPLE EXAMPLE BeginEnd I3II2IV1 V2 VII1 III1 IX2 VIII2 VI4 Precedence relationships indicate which _________ must be completed before others can begin.

16. This table shows the __________of each activity (in weeks) and the resources required (number of people) to complete each activity. TIME REQUIRED TO NO. PEOPLE (PER WK) TIME REQUIRED TO NO. PEOPLE (PER WK) ACTIVITY COMPLETE (WKS) REQUIRED TO COMPLETE I36 I36 II23 II23 III13 III13 IV13 IV13 V26 V26 VI 45 VI 45 VII13 VII13 VIII24 VIII24 IX23 IX23

17. The proposed activity _______which will achieve the overall completion time of 9 weeks is given below. Note that this diagram respects _______________ relationships and at the same time shows when each activity should ______and how long it will take. Weeks 1 2 3 4 5 6 7 8 9 I II III IV V VII IX VIII VI

18. Now consider the number of people per week required to _________the proposed schedule as displayed in the personnel _________chart shown below. Weeks Total people scheduled The proposed schedule makes an ________ utilization of personnel. _________ programs can be applied to employ resources more smoothly.

19. _______is the maximum amount of time an activity can be delayed without delaying overall project completion. WORKLOAD SMOOTHING HEURISTIC

20. Weeks 1 2 3 4 5 6 7 8 9 I II III IV V VII IX VIII VI If the _________time of activity V were delayed, then activity VI would also be delayed and the project could not be completed by the end of the _______ week. In contrast, the completion of activity _____could be delayed by 3 weeks without delaying the completion of the project. Activity VIII has a slack of_________.

21. The following heuristic is given to provide a smoother ______________across time: 1. Determine the maximum required ________ in the proposed schedule, say m workers/week. 2. In each week, impose a new __________of m-1 for resource utilization, and, if possible, revise the proposed schedule to satisfy this ____________. a. Beginning with the earliest week ________ the constraint, consider the activities contributing to the __________and move forward the one with most slack as little as possible until it contributes to no overloading, but without ____________the completion of the entire project.

22. Note, do not move any activities with _____ slack. If there are ties, move forward the activity that contributes ____ to the overload (i.e., requires the fewest people). Note, do not move any activities with _____ slack. If there are ties, move forward the activity that contributes ____ to the overload (i.e., requires the fewest people). b. The heuristic __________when the current overload cannot be decreased.

23. Consider the following proposed plan. The activity label appears _____each arrow while the number of people required each week appears _____the arrow. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel New limit 12 9 6 15 13 9 5 5 5 6I 3II 3III 6V5VI 3IV 3VII 3IX 4VIII The maximum required __________is 15 in period 4, so impose a new upper limit of 14 in each week.

24. Applying the Heuristic Now, move forward only those activities with _________slack. The movable activities contributing to the _________are IV, VIII, and IX. IV has the most slack. 3IV 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel New limit 12 9 6 15 13 9 5 5 5 14 14 14 14 14 14 14 14 14 6I 3II 3III 6V5VI 3VII 3IX 4VIII

25. Applying the Heuristic Now, move forward only those _________with positive slack. The movable activities contributing to the overload are IV, VIII, and IX. IV has the most_________. 3IV 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel New limit 12 9 6 15 13 9 5 5 5 6I 3II 3III 6V5VI 3VII 3IX 4VIII

26. Applying the Heuristic Now, move forward only those activities with __________slack. The movable activities contributing to the overload are IV, VIII, and IX. IV has the most slack. 3IV 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel New limit 12 9 6 15 13 9 5 5 5 6I 3II 3III 6V5VI 3VII 3IX 4VIII

27. Applying the Heuristic Now, move forward only those activities with positive slack. The movable ___________contributing to the overload are IV, VIII, and IX. IV has the most slack. 3IV 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel New limit 12 9 6 12 13 12 5 5 5 6I 3II 3III 6V5VI 3VII 3IX 4VIII 12 12 12 12 12 12 12 12 12 The new upper limit is now 12 in each week.

28. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel New limit 12 9 6 12 13 12 5 5 5 6I 3II 3III 6V5VI 3IV 3VII 3IX 4VIII Now the only overload based on a limit of 12 is caused by activities VIII and IX in week 5.

29. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel New limit 12 9 6 9 10 12 8 8 5 6I 3II 3III 6V5VI 3IV 3VII 3IX 4VIII Activity IX has the most slack, and it must be advanced 3 weeks to begin in week 7. 11 11 11 11 11 11 11 11 11 The new upper limit is now 11 in each week.

30. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel New limit 12 9 6 9 10 12 8 8 5 6I 3II 3III 6V5VI 3IV 3VII 3IX 4VIII 11 11 11 11 11 11 11 11 11 Now there are ______________in weeks 1 and 6. According to the algorithm, first move activity III forward 2 weeks and then activity IV forward 1 week.

31. 3III 3IV 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel New limit 9 9 9 9 10 9 11 8 5 9 9 9 9 10 9 11 8 5 6I 3II 6V5VI 3VII 3IX 4VIII Now there are violations in weeks 1 and 6. According to the____________, first move activity III forward 2 weeks and then activity IV forward 1 week. The new upper limit is now 10 in each week. 10 10 10 10 10 10 10 10 10

32. Now the only violation is in week 7. So, move activity IV forward 2 weeks. 10 10 10 10 10 10 10 10 10 3III 3IV 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel New limit 9 9 9 9 10 9 11 8 5 9 9 9 9 10 9 11 8 5 6I 3II 6V5VI 3VII 3IX 4VIII

33. Heuristic Terminates The algorithm is unable to ________beyond the fifth proposal. Hence, this schedule is the _________solution. The maximum __________is now 10 weeks and the minimum is 8. 3III 3IV 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel New limit 9 9 9 9 10 9 8 8 8 9 9 9 9 10 9 8 8 8 6I 3II 6V5VI 3VII 3IX 4VIII

34. For this model, an optimal solution is one that ___________the maximum utilization of personnel. The optimal schedule according to this __________ criteria is shown below. 3III 3IV 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9Week Total personnel 9 9 9 9 9 9 9 8 8 9 9 9 9 9 9 9 8 8 6I 3II 6V5VI 3VII 3IX 4VIII

35. End of Part 1 Please continue to Part 2