1. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 1 Outline Questions? Quiz Results Exam in this classroom on Thursday New homework Review

2. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 2 Quiz Results

3. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 3 Quiz Results

4. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 4 Production System Schematic Operation or plant DemandSupplyMaster Production Schedule (MPS) MRP explosion Capacity Planning Material Orders Daily Schedule Status Output Closed loop check

5. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 5 Adding up the costs (example) A plant generates 270,000 earned hours per year (established by standards for each of the products produced). 85% efficiency is assumed. The cost of an hour of labor, including benefits, is $30 Indirect labor totals $30M per year Materials cost $70M per year Material overhead costs are $4M per year What is the cost of a product containing 0.8 hours of standard labor and $20 of material? We first calculate the total labor rate as (30,000,000+270,000*30/0.85)/270,000=$146.40/hour

6. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 6 Adding up the costs (example continued) Material overhead = $4M/$70M= 5.7% Direct and indirect labor =0.8* $146.40=$117.12 Material=$20.00 Material Overhead= 0.057*20=$1.14 Total Cost =$138.26 We can separate the direct and indirect labor into: Direct labor = 0.8*30=$24 Indirect=$93.12 And you can see why everyone attacks overhead If you are independent, the profit would add another 10% or so. It is very dependent on the industry and level of investment

7. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 7 Cost Distribution

8. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 8 Access Data Base

9. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 9 Hayes-Wheelwright

10. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 10 Master Production Scheduling (continued) Creating a Master Production Schedule –Select items to be included (levels) –Select planning horizon –Select method for available to promise (ATP) ATP = the uncommitted portion of a company’s inventory or planned production (one method is called “cumulative with lookahead” ) –Combine inventory, orders, forecasts etc.

11. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 11 Capacity Planning Evaluated at MPS level - Rough cut capacity planning (RCCP) MRP level - Capacity requirements planning (CRP) “..capacity planning is somewhat misleading. Both RCCP and CRP are information tools rather than decision making tools. They indicate which capacity constraints are violated, but they do not provide guidance for resolving the conflict… They ignore actual lead times” from Sipper and Bulfin

12. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 12 Inventory

13. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 13 Inventory Safety stock methods Service level % Stockout Cost of a Stockout Inventory Policies (s,Q) (s,S) (R,S) (R,s,S)

14. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 14 Shop Floor Control Many MRP packages include Shop Floor Control modules These are designed to track the progress of products through a factory The best of them, especially when tied to real time data gathering are very good at letting managers now where things are. They are very dependent on timely input of data The newer ones will often include scheduling software as well. It is, however, more common to have the scheduling software in a separate module

15. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 15 Benefits and shortcomings Benefits: Ability to evaluate the feasibility and requirements Material plan Identifying shortages Shortcomings Infinite capacity assumption Uncertainty - deterministic system Lead time discrepancies Yield estimates System nervousness due to rolling horizon Integrity of data

16. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 16 Introduction to Scheduling The general job shop problem All problems are subsets or relaxations of basic assumptions Organized research and study of this area followed W.W.II n jobs {J 1, J 2, ….J n } a job is a task or lot or batch that is to processed as a unit. If it is broken into several jobs, we restart the problem with each part a new job m machines {M 1, M 2, ….M m } a machine is a processor or resource that performs a specific function required by a job

17. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 17 Introduction to Scheduling (continued) Processing of a job on a machine is called an operation nm operations o ij is the i th job on the j th machine Each job passes through each machine once and only once (Real jobs may repeat or skip) Each job has a prescribed order in which it is processed by the machines - This is called its Technological Constraint (TC). Other names are processing order, routing, process plan. General Job Shop - each job has its own processing order Flow Shop - all jobs have the same processing order Permutation Shop - all machines see the jobs in the same order

18. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 18 Introduction to Scheduling (continued) A production line with all machines tied together is an example of a permutation shop If all jobs have the same processing order, but the machines are not tied together, we have a Flow shop, because some machines may not see all jobs in the same order.

19. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 19 Examples J2J1J3J2J1J3 M1 M2 M1 M2 M1 M2 Flow Permutation Flow non-Permutation General J2J1J3 J1 J3J2J1J2 J1 J2 J1

20. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 20 Notations and definitions d i - due date of Job i r i - ready time of Job i a i - allowance = d i - r i s i - slack = d i - remaining operations p ij - the time required to process o ij W ik - the waiting time of Job i preceding its k th operation (not the work on M k ): J 1 ’s time = W 11 +p 11 +W 12 +p 13 +W 13 +p 12 +W 14 +p 1 17, if the TC is M1 to M3 to M2 to M17 We designate the kth operation as o ij(k)

21. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 21 Notations and definitions (continued) C i is the completion time of Job i F i is the flow time of Job i = C i - r i Even though the English words have an identical meaning, we distinguish between Lateness and Tardiness Lateness L i =C i - d i, therefore maybe positive or negative depending on whether we complete a job before or after its due date

22. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 22 Notations and definitions (continued) Tardiness is non- zero only if the job is completed after its due date: T i = max{L i, 0} We also define Earliness as E i = Max{-L i, 0} The weight or importance of a job is indicated either by w i or Some of our definitions refer to instants in time Completion, readiness Others refer to elapsed time Processing, Waiting, Flow

23. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 23 Notations and definitions (continued) Scheduling - the ordering of operations subject to restrictions and providing start and finishing times for each operation Closed Shop - serves customers from inventory (make to stock) Open shops - Jobs are made to order

24. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 24 Measures Optimality or goodness of schedules only makes sense if we define the measure under which we are considering optimality or goodness. There are three broad categories of measures: Completion time Due dates Inventory or utilization We also define a general class of measures called regular measures

25. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 25 Measures (continued) Given two sets of completions times obtained under two schedules generated for the same problem: C and C’ if C i <= C i ’ implies that R(C)<=R(C’) then R is regular

26. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 26 Classification notation All problems can be classified as n/m/A/B where n - number of jobs m - number of machines A - pattern F - Flow Shop P - Permutation G - General Job Shop B - Measure C max, F max etc.

27. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 27 Some further definitions Jobs and ready times fixed = Static Parameters known and fixed = Deterministic Random arrival of jobs= Dynamic Uncertain processing times= stochastic

28. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 28 Kinds of scheduling Taking sequences and placing them in a schedule is called time tabling (creating a Gantt chart) Semiactive - process each job as soon as it can be (slide to the left on the chart) Active - No operation can be started earlier without delaying some other operation Non-delay - no machine is kept idle Non-feasible - does not meet Technological Constraints Number of possible schedules (including non-feasible ones) = (n!) m

29. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 29 Optimality Since for any given problem there are a countable number of possible schedules (as long as we do not allow preemption or unnecessary delays) there must be an optimum (or optima) because we can (theoretically) compare all possible schedules and select the best one If we look at the space that contains our schedules and attempt to locate the optimum we find that:

30. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 30 Optimality (continued) Optimal all possible feasible semi active Active non - delay

31. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 31 Kinds of scheduling Taking sequences and placing them in a schedule is called time tabling (creating a Gantt chart) Semiactive - process each job as soon as it can be (slide to the left on the chart) Active - No operation can be started earlier without delaying some other operation Non-delay - no machine is kept idle Non-feasible - does not meet Technological Constraints Number of possible schedules (including non-feasible ones) = (n!) m

32. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 32 Optimality Since for any given problem there are a countable number of possible schedules (as long as we do not allow preemption or unnecessary delays) there must be an optimum (or optima) because we can (theoretically) compare all possible schedules and select the best one If we look at the space that contains our schedules and attempt to locate the optimum we find that:

33. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 33 Optimality (continued) Non-delay is shown as containing the optimum but this is not always true Optimal all possible feasible semi active Active non - delay

34. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 34 Schedule Generation As a start, we will define a routine that will generate an active schedule A semiactive schedule is one that starts every job as soon as it can, while obeying the technological and scheduling sequences. Also, the set of all semiactive schedules for a problem contains the optimal schedule Fortunately, the set of active schedules also contains the optimum and is a smaller set. We can forget about generating semiactive schedules

35. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 35 Active scheduling For a given problem there will be many active schedules The routine we will use generates only one and we will have to make frequent choices. Were we to follow each of these decision paths, we would generate all the active schedules and find the optimum However, our purpose here is to make those choices as intelligently as possible, even though it is difficult to foresee their eventual consequence An active schedule is one in which no operation could be started earlier without delaying another operation or violating the technological constraints

36. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 36 Definitions First we will define some terminology useful for our routine: Class of problems - n/m/G/B with no restrictions Stage - step in the routine that places an operation into the schedule - there are therefore nm stages t - counter for stages P t - partial schedule at stage t Schedulable operation - an operation with all its predecessors in P t S t - set of schedulable operations at stage t

37. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 37 Definitions (continued) sigma k - the earliest time an operation o k in S t could be started phi k - the earliest time that o k in S t could be finished phi k = sigma k + p k

38. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 38 Routine by Giffler and Thompson 1. t = 1, S 1 is the set of first operations in all jobs 2. Find min{phi k in S t } and designate it phi* Designate M on which phi* occurs as M* (could be arbitrary) 3. Choose o j in S t such that it satisfies these conditions: a. It uses M* b. sigma j < phi* 4. a. Add o j to P t, which now becomes P t+1 b. Delete o j from S t which now becomes S t+1 c. Add the operation that follows o j in the same job to S t+1 d. Increment t by 1

39. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 39 Routine by Giffler and Thompson (continued) 5. If there are operations left to schedule, go to step 2, else stop Note well that at step 3b. sigma j < phi*, we will often have several choices. We always have at least one, namely, phi* These choices are an extensive topic that we will cover later Follow the example I have taken from French Generating these schedules is tedious work, so leave yourselves some extra time for that homework.

40. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 40 Non-delay schedules Non-delay schedules are a smaller set than the active schedules and therefore are a tempting set to explore Unfortunately, they do not always contain the optimum We will not let that deter us, because non-delay schedules have been found to be usually very good, if not optimal A non-delay schedule is one where every operation is started as soon as it can be

41. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 41 Non-delay schedules (continued) We change two steps in the procedure for active schedules to obtain a non-delay procedure: Step 2. instead of phi, we select sigma Find min{sigma k in S t } and designate it sigma* Designate M on which sigma* occurs as M* (could be arbitrary) Step 3 b. sigma j = sigma*

42. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 42 SPT Minimizes Fbar

43. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 43 EDD Minimizes Tmax and Lmax

44. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 44 Moore Minimizes number of tardy jobs

45. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 45 Smith - modified Minimizes Fbar subject to Tmax <=Given Constant

46. Session 13 University of Southern California ISE514 October 6, 2015 Geza P. Bottlik Page 46 Lawler Minimizes the maximum of regular measures that are linearly increasing functions of Completion times