Nicholas G. Hall

A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process

An important class of machine scheduling problems is characterized by a no-wait or blocking production environment, where there is no intermediate buffer between machines. In a no-wait environment, a job must be processed from start to completion, without any interruption either on or between machines. Blocking occurs when a job, having completed processing on a machine, remains on the machine until a downstream machine becomes available for processing. A no-wait or blocking production environment typically arises from characteristics of the processing technology itself, or from the absence of storage capacity between operations of a job. In this review paper, we describe several well-documented applications of no-wait and blocking scheduling models and illustrate some ways in which the increasing use of modern manufacturing methods gives rise to other applications. We review the computational complexity of a wide variety of no-wait and blocking scheduling problems and describe several problems which remain open as to complexity. We study several deterministic flowshop, jobshop, and openshop problems and describe efficient and enumerative algorithms, as well as heuristics and results about their performance. The literature on stochastic no-wait and blocking scheduling problems is also reviewed. Finally, we provide some suggestions for future research directions.

Supply chain scheduling: Batching and delivery

Although the supply chain management literature is extensive, the benefits and challenges of coordinated decision making within supply chainscheduling models have not been studied. We consider a variety of scheduling, batching, and delivery problems that arise in an arborescent supply chain where a supplier makes deliveries to several manufacturers, who also make deliveries to customers. The objective is to minimize the overall scheduling and delivery cost, using several classical scheduling objectives. This is achieved by scheduling the jobs and forming them into batches, each of which is delivered to the next downstream stage as a single shipment. For each problem, we either derive an efficient dynamic programming algorithm that minimizes the total cost of the supplier or that of the manufacturer, or we demonstrate that this problem is intractable. The total system cost minimization problem of a supplier and manufacturer who make cooperative decisions is also considered. We demonstrate that cooperation between a supplier and a manufacturer may reduce the total system cost by at least 20%, or 25%, or by up to 100%, depending upon the scheduling objective. Finally, we identify incentives and mechanisms for this cooperation, thereby demonstrating that our work has practical implications for improving the efficiency of supply chains.

Earliness-Tardiness Scheduling Problems, I: Weighted Deviation of Completion Times About a Common Due Date

This paper and its companion Part II concern the scheduling of jobs with cost penalties for both early and late completion. In Part I, we consider the problem of minimizing the weighted sum of earliness and tardiness of jobs scheduled on a single processor around a common due date, d. We assume that d is not early enough to constrain the scheduling decision. The weight of a job does not depend on whether the job is early or late, but weights may vary between jobs. We prove that the recognition version of this problem is NP-complete in the ordinary sense. We describe optimality conditions, and present a computationally efficient dynamic programming algorithm. When the weights are bounded by a polynomial function of the number of jobs, a fully polynomial approximation scheme is given. We also describe four special cases for which the problem is polynomially solvable. Part II provides similar results for the unweighted version of this problem, where d is arbitrary.

Earliness-tardiness scheduling problems: II. Derivation of completion times about a restrictive common due date

A companion paper Part I considers the problem of minimizing the weighted earliness and tardiness of jobs scheduled on a single machine around a common due date, d, which is unrestrictively late. This paper Part II considers the problem of minimizing the unweighted earliness and tardiness of jobs, allowing the possibility that d is early enough to constrain the scheduling decision. We describe several optimality conditions. The recognition version of the problem is shown to be NP-complete in the ordinary sense, confirming a well known conjecture. Moreover, this complexity definition is precise, since we describe a dynamic programming algorithm which runs in pseudopolynomial time. This algorithm is also extremely efficient computationally, providing an improvement over earlier procedures, of almost two orders of magnitude in the size of instance that can be solved. Finally, we describe a special case of the problem which is polynomially solvable.

Generating Experimental Data for Computational Testing with Machine Scheduling Applications

The operations research literature provides little guidance about how data should be generated for the computational testing of algorithms or heuristic procedures. We discuss several widely used data generation schemes, and demonstrate that they may introduce biases into computational results. Moreover, such schemes are often not representative of the way data arises in practical situations. We address these deficiencies by describing several principles for data generation and several properties that are desirable in a generation scheme. This enables us to provide specific proposals for the generation of a variety of machine scheduling problems. We present a generation scheme for precedence constraints that achieves a target density which is uniform in the precedence constraint graph. We also present a generation scheme that explicitly considers the correlation of routings in a job shop. We identify several related issues that may influence the design of a data generation scheme. Finally, two case studies illustrate, for specific scheduling problems, how our proposals can be implemented to design a data generation scheme.

Design and operational issues in AGV-served manufacturing systems

Automated Guided Vehicle (AGV) systems are already in widespread use and their importance for material handling is expected to grow rapidly. The advantages that such systems can offer include increased flexibility, better space utilization, improved factory floor safety, reduction in overall operating cost, and easier interface with other automated systems. This survey paper focuses on design and operational issues that arise in AGV systems. The objectives of the paper are to unify various lines of research related to AGVs and to suggest directions for future study. We consider problems arising in flowpath design, fleet sizing, job and vehicle scheduling, dispatching and conflict-free routing. Flowpath design problems address computationally intractable issues in the physical layout of a single loop and complex networks. Transportation and related models, waiting line analysis and simulation approaches are used to address fleet sizing questions. Scheduling issues focus on three flowpath layouts. In line layouts, the most important issues include finding an efficient job sequencing algorithm and identifying optimal AGV launch times. In loop layouts, issues such as joint scheduling of the job and AGV schedules, interface with a larger manufacturing system, dynamic job arrivals, and the location of the AGV parking area, are important. For complex network layouts, joint scheduling, heuristic dispatching rules, and conflict-free routing of AGVs, are considered. We identify the inefficiencies that result from addressing these issues in isolation, suggesting the need for integration. We also provide a summary of the most important open research issues related to all the above topics.

Scheduling in Robotic Cells: Classification, Two and Three Machine Cells

This paper considers the scheduling of operations in a manufacturing cell that repetitively produces a family of similar parts on two or three machines served by a robot. We provide a classification scheme for scheduling problems in robotic cells. We discuss finding the robot move cycle and the part sequence that jointly minimize the production cycle time, or equivalently maximize the throughput rate. For multiple part-type problems in a two-machine cell, we provide an efficient algorithm that simultaneously optimizes the robot move and part sequencing problems. This algorithm is tested computationally. For a three-machine cell with general data and identical parts, we address an important conjecture about the optimality of repeating one-unit cycles, and show that such a procedure dominates more complicated cycles producing two units. For a three-machine cell producing multiple part-types, we prove that four out of the six potentially optimal robot move cycles for producing one unit allow efficient identification of the optimal part sequence. Several efficiently solvable special cases with practical relevance are identified, since the general problem of minimizing cycle time is intractable. Finally, we discuss ways in which a robotic cell converges to a steady state.

Rescheduling for New Orders

This paper considers scheduling problems where a set of original jobs has already been scheduled to minimize some cost objective, when a new set of jobs arrives and creates a disruption. The decision maker needs to insert the new jobs into the existing schedule without excessively disrupting it. Two classes of models are considered. First, we minimize the scheduling cost of all the jobs, subject to a limit on the disruption caused to the original schedule, where this disruption is measured in various ways. In the second class, a total cost objective, which includes both the original cost measure and the cost of disruption, is minimized. For both classes and various costs based on classical scheduling objectives, and for almost all problems, we provide either an efficient algorithm or a proof that such an algorithm is unlikely to exist. We also show how to extend both classes of models to deal with multiple disruptions in the form of repeated arrivals of new jobs. Our work refocuses the extensive literature on scheduling problems towards issues of rescheduling, which are important because of the frequency with which disruptions occur in manufacturing practice.

Parallel machine scheduling with a common server

This paper considers the nonpreemptive scheduling of a given set of jobs on several identical, parallel machines. Each job must be processed on one of the machines. Prior to processing, a job must be loaded (setup) by a single server onto the relevant machine. The paper considers a number of classical scheduling objectives in this environment, under a variety of assumptions about setup and processing times. For each problem considered, the intention is to provide either a polynomial- or pseudo-polynomial-time algorithm, or a proof of binary or unary NP-completeness. The results provide a mapping of the computational complexity of these problems.

Scheduling in robotic cells: Complexity and steady state analysis

Abstract This paper considers the scheduling of operations in a manufacturing cell that repetitively produces a family of similar parts on several machines served by a robot. The decisions to be made include finding the robot move cycle and the part sequence that jointly minimize the production cycle time, or equivalently maximize the throughput rate. We focus on complexity issues and steady state performance. In a three machine cell producing multiple part-types, we prove that in two out of the six potentially optimal robot move cycles for producing one unit, the recognition version of the part sequencing problem is unary NP -complete. The other four cycles have earlier been shown to define efficiently solvable part sequencing problems. The general part sequencing problem not restricted to any robot move cycle in a three machine cell is shown to be unary NP -complete. Finally, we discuss the ways in which a robotic cell converges to a steady state.