Hamilton Emmons

Scheduling to a common due date on parallel uniform processors

We consider scheduling a set of jobs on parallel processors, when all jobs have a common due date and earliness and lateness are penalized at different cost rates. For identical processors, the secondary criteria of minimizing makespan and machine occupancy are addressed. The extension to different, uniform processors is also solved.

Scheduling families of jobs with setup times

Abstract We review the current state of scheduling theory concerning the processing of several families of jobs on single or parallel facilities, where a setup time may be incurred whenever there is a switch from processing a job in one family to a job in another family. We also consider cases with the group technology assumption that the jobs must be scheduled contiguously. Using available results from the literature, we classify the different problems as NP-hard, efficiently solvable or open. We refine some old results and present several new ones. In particular, we show that under the group technology assumption, even with sequence-independent setup times, minimizing the number of late jobs on a single machine is NP-hard. We investigate the complexity of single machine scheduling with interfamily setup times, when we seek to minimize the maximal cost, where the cost for each job is a nondecreasing function of its completion time. We also prove that, when scheduling on parallel machines under the group technology assumption with sequence-independent setup times, minimizing total completion times is NP-hard unless all families contain the same number of jobs.

Interval Scheduling on identical machines

Interval Scheduling problems (IS) address the situation where jobs with fixed start and fixed end times are to be processed on parallel identical machines. The optimization criteria of interest are the maximization of the number of jobs completed and, in case weights are associated with jobs, the subset of jobs with maximal total weight. We present polynomial solutions to several IS problems and study computational complexity issues in the situation where bounds are imposed on the total operating time of the machines. With this constraint, we show that tractability is achieved again when job preemption is allowed.

Off-day scheduling with hierarchical worker categories

A work force includes workers of m types. The worker categories are ordered, with type-1 workers the most highly qualified, type-2 the next, and so on. If the need arises, a type-k worker is able to substitute for a worker of any type j greater than k (k = 1, ..., m - 1). For 7-day-a-week operation, daily requirements are for at least Dk workers of type-k or better, of which at least dk must be precisely type-k. Formulas are given to find the smallest number and most economical mix of workers, assuming that each worker must have 2 off-days per week and a given fraction of weekends off. Algorithms are presented which generate a feasible schedule, and provide work stretches between 2 and 5 days, and consecutive weekdays off when on duty for 2 weekends in a row, without additional staff.

Work-Force Scheduling with Cyclic Requirements and Constraints on Days Off, Weekends Off, and Work Stretch

Abstract A generalization of cyclical work-force scheduling is presented. We compute the minimal number of workers needed for a seven-days-a-week operation to satisfy cyclic demand for D workers every weekday and E workers every weekend day, while giving each worker two days off per week, including A out of B weekends off, for any A and B (A < B). Using this workforce, the generalized cyclical scheduling procedure produces a feasible “master rotation” schedule, which additionally maintains all work stretches between two and four days (unless a worker gets two successive weekends off, in which case he works Monday through Friday), and which gives adjacent weekdays off, as often as possible, to any worker who must work on successive weekends. It is shown that the latter condition can be satisfied for all workers in almost all instances.

Scheduling stochastic jobs with due dates on parallel machines

Abstract Jobs with random processing times, random due dates, and weights are to be scheduled on parallel machines so as to minimize the expected total weight of tardy jobs. Under various assumptions, optimal policies are presented both for static lists and dynamic schedules, preemptive and nonpreemptive.

Scheduling Production on One Machine with Changeover Costs

Abstract A single machine is used to produce several products so as to satisfy known demands over a fixed number of periods. Each time switches are made between products, there are changeover costs as described by a matrix C=[cij ], where cij is the cost of switching from product i to product j. The problem is to find a schedule of production that minimizes the total changeover penalty while meeting the due dates of all customer orders. The function used in a forward-time dynamic program is shown to have a monotonicity property that can be used to advantage when seeking an optimal solution to the problem. This monotonicity property is applied in developing an efficient backward-time search procedure for solving the problem.

Inspection allocation for multistage deteriorating production systems

The paper deals with the layout and operation of an inspection system used for detecting malfunctioning processors in a multistage production system. This problem involves three inter-related decisions: (i) the overall inspection capacity; (ii) the assignment of inspection tasks to inspectors; and (iii) the scheduling of the inspectors tasks. These decisions require a trade-off between the cost of inspectors and the loss associated with non-conforming products. A hierarchical heuristic solution procedure is proposed to support these three related decisions. Numerical experiments demonstrate the performance of the heuristic, showing that solution criteria are very close to their lower bounds. Although we use production terminology, the results might be applicable to any organization, which inspects and maintains a variety of characteristics of its branches or activities.

Optimal and heuristic inspection schedules for multistage production systems

Consider a single inspection facility that can be quickly switched among multiple inspection tasks. It can be used (for example) for detecting malfunction (or down state) production stages in a multistage production system. We assume that a properly working (or up state) production stage moves to a down state in any period with fixed probability. The stage then stays down until it is inspected and immediately restored back to an up state. Our purpose is to schedule inspections among the different production stages so as to maximize the fraction of good items produced. An optimal inspection schedule for a two stage production system is provided. For the general case of more than two stages, four heuristics are compared. We conclude that the proposed dynamic schedule is easy to derive, always feasible, and outperforms the static schedules.

MULTIPLE-SHIFT WORKFORCE SCHEDULING UNDER THE 3-4 COMPRESSED WORKWEEK WITH A HIERARCHICAL WORKFORCE

This paper provides efficient optimal workforce scheduling algorithms for 7-days-a-week operations, not necessarily 24 hours a day, under a compressed workweek arrangement called the 3-4 workweek. The model incorporates both the possibilities of shift rotation and downward worker substitutability. The model is readily usable in many 7-days-a-week operations (e.g., hospitals and utilities).