CHAPTER 8 Operations Scheduling McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.

Scheduling Problems in Operations 8-2 Scheduling Problems in Operations Job Shop Scheduling. Personnel Scheduling Facilities Scheduling Vehicle Scheduling and Routing Project Management Dynamic versus Static Scheduling

The Hierarchy of Production Decisions 8-3 The Hierarchy of Production Decisions The logical sequence of operations in factory planning corresponds to the sequencing of chapters in the book. All planning starts with the demand forecast. Demand forecasts are the basis for the top level (aggregate) planning. The Master Production Schedule (MPS) is the result of disaggregating aggregate plans down to the individual item level. Based on the MPS, MRP is used to determine the size and timing of component and subassembly production. Detailed shop floor schedules are required to meet production plans resulting from the MRP.

Hierarchy of Production Decisions 8-4 Hierarchy of Production Decisions

Characteristics of the Job Shop Scheduling Problem 8-5 Characteristics of the Job Shop Scheduling Problem Job Arrival Pattern Number and Variety of Machines Number and skill level of workers Flow Patterns Evaluation of Alternative Rules

Objectives in Job Shop Scheduling 8-6 Objectives in Job Shop Scheduling Meet due dates Minimize work-in-process (WIP) inventory Minimize average flow time Maximize machine/worker utilization Reduce set-up times for changeovers Minimize direct production and labor costs (note: that these objectives can be conflicting)

8-7 Terminology Flow shop: n jobs processed through m machines in the same sequence Job shop: the sequencing of jobs through machines may be different, and there may be multiple operations on some machines. Parallel processing vs. sequential processing: parallel processing means that the machines are identical. Flow time of job i: Time elapsed from initiation of first job until completion of job i. Makespan: Flow time of the job completed last. Tardiness: The positive difference between the completion time and the due date. Lateness: Difference between completion time and due date (may be negative).

Common Sequencing Rules 8-8 Common Sequencing Rules FCFS. First Come First Served. Jobs processed in the order they come to the shop. SPT. Shortest Processing Time. Jobs with the shortest processing time are scheduled first. EDD. Earliest Due Date. Jobs are sequenced according to their due dates. CR. Critical Ratio. Compute the ratio of processing time of the job and remaining time until the due date. Schedule the job with the largest CR value next.

Results for Single Machine Sequencing 8-9 Results for Single Machine Sequencing The rule that minimizes the mean flow time of all jobs is SPT. The following criteria are equivalent: Mean flow time Mean waiting time. Mean lateness Moore’s algorithm minimizes number of tardy jobs Lawler’s algorithm minimizes the maximum flow time subject to precedence constraints.

Results for Multiple Machines 8-10 Results for Multiple Machines The optimal solution for scheduling n jobs on two machines is always a permutation schedule (that is, jobs are done in the same order on both machines). (This is the basis for Johnson’s algorithm.) For three machines, a permutation schedule is still optimal if we restrict attention to total flow time only. Under rare circumstances, the two machine algorithm can be used to solve the three machine case. When scheduling two jobs on m machines, the problem can be solved by graphical means.

Stochastic Scheduling: Static Case 8-11 Stochastic Scheduling: Static Case Single machine case. Suppose that processing times are random variables. If the objective is to minimize average weighted flow time, jobs are sequenced according to expected weighted SPT. That is, if job times are t1, t2, . . ., and the respective weights are u1, u2, . . . then job i precedes job i+1 if E(ti)/ui < E(ti+1)/ui+1.

Stochastic Scheduling: Static Case (continued) 8-12 Stochastic Scheduling: Static Case (continued) Multiple Machines. Requires the assumption that the distribution of job times is exponential, (memoryless property). Assume parallel processing of n jobs on two machines. Then the optimal sequence is to to schedule the jobs according to LEPT (longest expected processing time first). Johnsons algorithm for scheduling n jobs on two machines in the deterministic case has a natural extension to the stochastic case as long as the job times are exponentially distributed.

Stochastic Scheduling: Dynamic Analysis 8-13 Stochastic Scheduling: Dynamic Analysis When jobs arrive to the shop dynamically over time, queueing theory provides a means of analyzing the results. The standard M/M/1 queue applies to the case of purely random arrivals to a single machine with random processing times. If the selection discipline does not depend on the flow times, the mean flow times are the same, but the variance of the flow times will differ. If job times are realized when the job joins the queue rather than when the job enters service, SPT generally results in lowest expected flow time.

Assembly Line Balancing 8-14 Assembly Line Balancing Characteristics of the Assembly Line Balancing problem. A collection of n tasks must be completed on each item Tasks are assigned to stations. Tasks must be sequenced properly, and certain tasks may not be done at the same station. The objective is to assign tasks to stations to minimize the cycle time, C. The general problem is difficult to solve optimally, but effective heuristics are available. (the text discusses one known as the ranked positional weight technique.)

Schematic of a Typical Assembly Line 8-15 Schematic of a Typical Assembly Line