AN EXPOSITION OF MULTIPLE CONSTRAINT SCHEDULING AS IMPLEMENTED IN THE GOAL SYSTEM (FORMERLY DISASTERTM)

Since Eli Goldratt first appeared on the scene in the late 1970s, his ideas concerning production management have generated a huge amount of interest, controversy, and misunderstanding. These ideas have been proliferated under several names such as optimized production technology (OPT), drum-buffer-rope (DBR), synchronized manufacturing (SM), and theory of constraints (TOC). Although there seems to be general agreement on the importance of how capacity-constrained resources are scheduled, research aimed at advancing the state of the art for the specific problem addressed by DBR continues to be limited by prior misunderstandings and the lack of a rigorous examination by the academic community. This paper seeks “to advance the state of research on constraint scheduling in several ways. First, it presents a concise history of the evolution of DBR. It then explains the use of rods in constraint scheduling. Next, it presents in detail the solution algorithm incorporated by the Goldratt Institute in their production software and, finally, relates that algorithm to alternative methods. In the process of these activities, several lingering misconceptions are resolved.     

MINIMIZING TOTAL WEIGHTED COMPLETION TIME ON A SINGLE BATCH PROCESSING MACHINE

We study the problem of scheduling jobs on a single batch processing machine to minimize the total weighted completion time. A batch processing machine is one that can process a number of jobs simultaneously as a batch. The processing time of a batch is given by the processing time of the longest job in the batch. We present a branch and bound algorithm to obtain optimal solutions and develop lower bounds and dominance conditions. We also develop a number of heuristics and evaluate their performance through extensive computational experiments. Results show that two of the heuristics consistently generate high-quality solutions in modest CPU times.     

TECHNICAL NOTE: A SIMPLE MODEL FOR OPTIMIZING THE SINGLE MACHINE EARLY/TARDY PROBLEM WITH SEQUENCE-DEPENDENT SETUPS

A simple mixed integer programming model for the N job/single machine scheduling problem with possibly sequence-dependent setup times, differing earliness/tardiness cost penalties, and variable due dates is proposed and evaluated for computational efficiency. Results indicated that the computational effort required to reach optimality rose with the number of jobs to be scheduled and with decreased variance in due dates. Though computational effort was significant for the largest problems solved, the model remained viable for optimizing research scale problems.     

OUTPATIENT SCHEDULING IN HEALTH CARE: A REVIEW OF LITERATURE

This paper provides a comprehensive survey of research on appointment scheduling in outpatient services. Effective scheduling systems have the goal of matching demand with capacity so that resources are better utilized and patient waiting times are minimized. Our goal is to present general problem formulation and modeling considerations, and to provide taxonomy of methodologies used in previous literature. Current literature fails to develop generally applicable guidelines to design appointment systems, as most studies have suggested highly situation‐specific solutions. We identify future research directions that provide opportunities to expand existing knowledge and close the gap between theory and practice.     

AN EXPERIMENTAL MODEL FOR INVESTIGATING THE SENSITIVITY OF JOB SHOP PERFORMANCE TO JOB RELEASE TIME DISTRIBUTION PARAMETERS

Work flows in a job shop are influenced by the load per release and time interval between release factors. We focus on the latter factor, job release times. Building on Elvers' work, this study evaluates the impact of different job release time distributions on shop performance. Using a computer simulation of a random job shop and a full factorial experimental design, we demonstrate that the type of distribution does affect performance–a finding consistent with results from job shops characterized by good shop floor control practices. These findings are explained by examining the shape and variance traits of the underlying job release time distributions.     

A NOTE ON “COMMON DUE WINDOW SCHEDULING”

Kramer and Lee recently addressed a common due window scheduling problem with earliness and tardiness penalties, where earliness and tardiness penalty factors are constant and the common window size is given. They showed that the problem is polynomial when the location of the due window is a decision variable. For the case where the location of the due window is given, the problem is also polynomial when the latest due date is greater than or equal to the makespan, and they proposed a pseudopolynomial dynamic programming algorithm to find an optimal schedule when the latest due date is less than the makespan. In this note we address the problem for the case where the location of the due window is given. Specifically, we show that the problem is polynomial if the window location is unrestricted, and present a more efficient dynamic program algorithm to optimally solve the problem if the window location is restricted. The concepts of unrestricted and restricted window locations are defined in this note.     

COMMON DUE-WINDOW SCHEDULING

In this paper, we solve common due-window scheduling problems within the just-in-time window concept, i.e., scheduling problems including both earliness and tardiness penalties. We assume that jobs share the same due window and incur no penalty as long as they are completed within the due window. We further assume that the earliness and tardiness penalty factors are constant and that the size of the window is a given parameter. For cases where the location of the due window is a decision variable, we provide a polynomial algorithm with complexity O(n * log (n)) to solve the problem. For cases where the location of the due window is a given parameter, we use dynamic programming with pseudopolynomial complexity to solve the problem.     

EVALUATING THE TRADE-OFFS BETWEEN IDLING AND SHUTTING DOWN PRODUCTION LINES IN PROCESS INDUSTRIES

The costs of starting-up and shutting down production lines (and plants) in a process industry are often quite high. Therefore, when a plant's capacity significantly exceeds its forecast demand over an annual planning horizon, a manufacturer must either plan temporary production line shutdowns during the year, or plan to temporarily idle production lines without formally shutting line(s) down. The trade-offs between these two strategies can be complex. In this paper, we propose a methodology to evaluate the impact of both strategies on a plant's production costs by developing an analytical model based on the authors' experience with several process industries.     

A DECISION THEORY APPROACH TO PRIORITY DISPATCHING FOR JOB SHOP SCHEDULING

Recent developments in the design of job shop scheduling systems have inspired a new approach to priority dispatching. The basis for the approach is in elementary decision theory: at each decision juncture define the alternative courses of action, evaluate the consequences of each alternative according to a given criterion, and choose the best alternative. The experimental results of a simulated single machine queueing system reinforce earlier findings that a decision theory approach represents a significant advance over conventional priority dispatching.     

A COMPARISON OF ORDER-RELEASE AND DISPATCH RULES FOR THE DYNAMIC WEIGHTED EARLY/TARDY PROBLEM

The early/tardy problem is one of the most vexing pieces of the complex production scheduling decision process. So far most of the research has been on single-machine environments. Hence, we considered the weighted early/tardy scheduling problem in a simulated dynamic multimachine job shop. We analyzed controlled job-release and dispatch rules using time and cost information at a variety of stationary and nonstationary utilization rates, due-date allowances, and early/tardy cost levels. We found a newly developed method for controlling the release for all job operations using early/tardy cost information, superior to other release mechanisms overall in both our stationary and nonstationary analyses. We found immediate release useful at many high utilization conditions and a gateway-only release method best in many low utilization conditions. A modified version of a single-machine early/tardy dispatch method was clearly superior to the dispatch rules for almost all the simulated shop conditions.