IE 514 Production Scheduling

1. IE 514 Production Scheduling Introduction IE 514

2. Contact Information • Siggi Olafsson • 3018 Black Engineering • 294-8908 • olafsson@iastate.edu • http://www.public.iastate.edu/~olafsson • OH: MW 10:30-12:00 IE 514

3. Administration (Syllabus) • Text • Prerequisites • Assignments • Homework 35% • Project 40% • Final Exam 35% • Computing IE 514

4. What is Scheduling About? • Applied operations research • Models • Algorithms • Solution using computers • Implement algorithms • Draw on common databases • Integration with other systems IE 514

5. Application Areas • Procurement and production • Transportation and distribution • Information processing and communications IE 514

6. Manufacturing Scheduling • Short product life-cycles • Quick-response manufacturing • Manufacture-to-order • More complex operations must be scheduled in shorter amount of time with less room for errors! IE 514

7. Scope of Course • Levels of planning and scheduling • Long-range planning (several years), • middle-range planning (1-2 years), • short-range planning (few months), • scheduling (few weeks), and • reactive scheduling (now) • These functions are now often integrated IE 514

8. Scheduling Systems • Enterprise Resource Planning (ERP) • Common for larger businesses • Materials Requirement Planning (MRP) • Very common for manufacturing companies • Advanced Planning and Scheduling (APS) • Most recent trend • Considered “advanced feature” of ERP IE 514

9. Scheduling Problem • Allocate scarce resources to tasks • Combinatorial optimization problem Maximize profit Subject to constraints • Mathematical techniques and heuristics IE 514

10. Our Approach Scheduling Problem Problem Formulation Model Solve with Computer Algorithms Conclusions IE 514

11. Scheduling Models • Project scheduling • Job shop scheduling • Flexible assembly systems • Lot sizing and scheduling • Interval scheduling, reservation, timetabling • Workforce scheduling IE 514

12. General Solution Techniques • Mathematical programming • Linear, non-linear, and integer programming • Enumerative methods • Branch-and-bound • Beam search • Local search • Simulated annealing/genetic algorithms/tabu search/neural networks. IE 514

13. Scheduling System Design Order master file Shop floor data collection • Databases • Schedule generation • User interfaces Database Management Automatic Schedule Generator Performance Evaluation Schedule Editor Graphical Interface User IE 514

14. LEKIN • On disk with book • Generic job shop scheduling system • User friendly windows environment • C++ object oriented design • Can add own routines IE 514

15. Advanced Topics • Uncertainty, robustness, and reactive scheduling • Multiple objectives • Internet scheduling IE 514

16. Topic 1 Setting up the Scheduling Problem IE 514

17. Modeling • Three components to any model: • Decision variables • This is what we can change to affect the system, that is, the variables we can decide upon • Objective function • E.g, cost to be minimized, quality measure to be maximized • Constraints • Which values the decision variables can be set to IE 514

18. Decision “Variables” • Three basic types of solutions: • A sequence: a permutation of the jobs • A schedule: allocation of the jobs in a more complicated setting of the environment • A scheduling policy: determines the next job given the current state of the system IE 514

19. Model Characteristics • Multiple factors: • Number of machine and resources, • configuration and layout, • level of automation, etc. • Our terminology: Resource = machine (m) Entity requiring the resource = job (n) IE 514

20. Notation • Static data: • Processing time (pij) • Release date (rj) • Due date (dj) • Weight (wj) • Dynamic data: • Completion time (Cij) IE 514

21. Machine Configuration • Standard machine configurations: • Single machine models • Parallel machine models • Flow shop models • Job shop models • Real world always more complicated. IE 514

22. Constraints • Precedence constraints • Routing constraints • Material-handling constraints • Storage/waiting constraints • Machine eligibility • Tooling/resource constraints • Personnel scheduling constraints IE 514

23. Other Characteristics • Sequence dependent setup • Preemptions • preemptive resume • preemptive repeat • Make-to-stock versus make-to-order IE 514

24. Objectives and Performance Measures • Throughput (TP) and makespan (Cmax) • Due date related objectives • Work-in-process (WIP), lead time (response time), finished inventory • Others IE 514

25. Throughput and Makespan • Throughput • Defined by bottleneck machines • Makespan • Minimizing makespan tends to maximize throughput and balance load IE 514

26. Due Date Related Objectives • Lateness • Minimize maximum lateness (Lmax) • Tardiness • Minimize the weighted tardiness IE 514

27. Due Date Penalties Tardiness Lateness Late or Not In practice IE 514

28. WIP and Lead Time • Work-in-Process (WIP) inventory cost • Minimizing WIP also minimizes average lead time (throughput time) • Minimizing lead time tends to minimize the average number of jobs in system • Equivalently, we can minimize sum of the completion times: IE 514

29. Other Costs • Setup cost • Personnel cost • Robustness • Finished goods inventory cost IE 514

30. Topic 2 Solving Scheduling Problems IE 514

31. Classic Scheduling Theory • Look at a specific machine environment with a specific objective • Analyze to prove an optimal policy or to show that no simple optimal policy exists • Thousands of problems have been studied in detail with mathematical proofs! IE 514

32. Example: single machine • Lets say we have • Single machine (1), where • the total weighted completion time should be minimized (SwjCj) • We denote this problem as IE 514

33. Optimal Solution • Theorem: Weighted Shortest Processing time first - called the WSPT rule - is optimal for • Note: The SPT rule starts with the job that has the shortest processing time, moves on the job with the second shortest processing time, etc. IE 514

34. Proof (by contradiction) • Suppose it is not true and schedule S is optimal • Then there are two adjacent jobs, say job j followed by job k such that • Do a pairwise interchange to get schedule S ’ j k k j IE 514

35. Proof (continued) The weighted completion time of the two jobs under S is The weighted completion time of the two jobs under S ‘ is Now: Contradicting that S is optimal. IE 514

36. Complexity Theory • Classic scheduling theory draws heavily on complexity theory • The complexity of an algorithm is its running time in terms of the input parameters (e.g., number of jobs and number of machines) • Big-Oh notation, e.g., O(n2m) IE 514

37. Polynomial versus NP-Hard IE 514

38. Scheduling in Practice • Practical scheduling problems cannot be solved this easily! • Need: • Heuristic algorithms • Knowledge-based systems • Integration with other enterprise functions • However, classic scheduling results are useful as a building block IE 514

39. General Purpose Scheduling Procedures • Some scheduling problems are easy • Simple priority rules • Complexity: polynomial time • However, most scheduling problems are hard • Complexity: NP-hard, strongly NP-hard • Finding an optimal solution is infeasible in practice  heuristic methods IE 514

40. Types of Heuristics • Simple Dispatching Rules • Composite Dispatching Rules • Branch and Bound • Beam Search • Simulated Annealing • Tabu Search • Genetic Algorithms Construction Methods Improvement Methods IE 514

41. Topic 3 Dispatching Rules IE 514

42. Dispatching Rules • Prioritize all waiting jobs • job attributes • machine attributes • current time • Whenever a machine becomes free: select the job with the highest priority • Static or dynamic IE 514

43. Release/Due Date Related • Earliest release date first (ERD) rule • variance in throughput times • Earliest due date first (EDD) rule • maximum lateness • Minimum slack first (MS) rule • maximum lateness Current Time Processing Time Deadline IE 514

44. Processing Time Related • Longest Processing Time first (LPT) rule • balance load on parallel machines • makespan • Shortest Processing Time first (SPT) rule • sum of completion times • WIP • Weighted Shortest Processing Time first (WSPT) rule IE 514

45. Processing Time Related • Critical Path (CP) rule • precedence constraints • makespan • Largest Number of Successors (LNS) rule • precedence constraints • makespan IE 514

46. Other Dispatching Rules • Service in Random Order (SIRO) rule • Shortest Setup Time first (SST) rule • makespan and throughput • Least Flexible Job first (LFJ) rule • makespan and throughput • Shortest Queue at the Next Operation (SQNO) rule • machine idleness IE 514

47. Discussion • Very simple to implement • Optimal for special cases • Only focus on one objective • Limited use in practice • Combine several dispatching rules Composite Dispatching Rules IE 514

48. Example Single Machine with Weighted Total Tardiness IE 514

49. Setup • Problem: • No efficient algorithm (NP-Hard) • Branch and bound can only solve very small problems (<30 jobs) • Are there any special cases we can solve? IE 514

50. Case 1: Tight Deadlines • Assume dj=0 • Then • We know that WSPT is optimal for this problem! IE 514