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.

Although the supply chain management literature is extensive, the benefits and challenges of coordinated decision making within supply chain scheduling 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 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.

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.