Batch scheduling and common due-date assignment on a single machine

We consider the problem of scheduling n groups of jobs on a single machine where three types of decisions are combined: scheduling, batching and due-date assignment. Each group includes identical jobs and may be split into batches; jobs within each batch are processed jointly. A sequence independent machine set-up time is needed between each two consecutively scheduled batches of different groups. A due-date common to all jobs has to be assigned. A schedule specifies the size of each batch, i.e. the number of jobs it contains, and a processing order for the batches. The objective is to determine a value for the common due-date and a schedule so as to minimize the sum of the due date assignment penalty and the weighted number of tardy jobs. Several special cases of this problem are shown to be ordinary NP-hard. Some cases are solved in O(n log n) time. Two pseudopolynomial dynamic programming algorithms are presented for the general problem, as well as a fully polynomial approximation scheme.     

Due-date assignment and maintenance activity scheduling problem

In the scheduling problem addressed in this note we have to determine: (i) the job sequence, (ii) the (common) due-date, and (iii) the location of a rate modifying (maintenance) activity. Jobs scheduled before (after) the due-date are penalized according to their earliness (tardiness) value. The processing time of a job scheduled after the maintenance activity decreases by a job-dependent factor. The objective is minimum total earliness, tardiness and due-date cost. We introduce a polynomial (O(n⁴)) solution for the problem.     

Due-date assignment on uniform machines

The classical weighted minsum scheduling and due-date assignment problem (with earliness, tardiness and due-date costs) was shown to be polynomially solvable on a single machine, more than two decades ago. Later, it was shown to have a polynomial time solution in the case of identical processing time jobs and parallel identical machines. We extend the latter setting to parallel uniform machines. We show that the two-machine case is solved in constant time. Furthermore, the problem remains polynomially solvable for a given (fixed) number of machines.     

A first passage time problem for spectrally positive Lévy processes and its application to a dynamic priority queue

We study a first passage time problem for a class of spectrally positive Lévy processes. By considering the special case where the Lévy process is a compound Poisson process with negative drift, we obtain the Laplace–Stieltjes transform of the steady-state waiting time distribution of low-priority customers in a two-class M/GI/1$M/GI/1$ queue operating under a dynamic non-preemptive priority discipline. This allows us to observe how the waiting time of customers is affected as the policy parameter varies.     

A due-date assignment problem with learning effect and deteriorating jobs

In this paper we consider a single-machine scheduling problem with the effects of learning and deterioration. In this model, job processing times are defined by functions of their starting times and positions in the sequence. The problem is to determine an optimal combination of the due-date and schedule so as to minimize the sum of earliness, tardiness and due-date. We show that the problem remains polynomially solvable under the proposed model.     

Improving delivery reliability by a new due-date setting rule

We study the dynamic due-date setting problem where the objective is to improve delivery performance. Since the problem is NP-hard, we propose a simple, new, general, heuristic due-date setting procedure called the SL rule. For the classical M/M/1 queuing model, we analytically determine the optimum parameter for the proposed rule to achieve best due-date performance. We then show that the optimized SL rule outperforms the work-content-based TWK rule in terms of fraction tardy, mean tardiness, and mean earliness. Additional numerical and simulation analysis for a range of conditions, covering different shop workload levels and priority regimes, confirms that the proposed rule produces best due-date performance, compared to the work-content-based rule, under most of the conditions studied.     

Minimizing due date related measures for a single machine scheduling problem with outsourcing allowed

This paper considers two single-machine scheduling problems with outsourcing allowed where each job can be either processed on an in-house single-machine or outsourced. They include the problem of minimizing maximum lateness and outsourcing costs, and that of minimizing total tardiness and outsourcing costs. Outsourcing is commonly required as a way to improve productivity in various companies including electronics industries and motor industries. The objective is to minimize the weighted sum of the outsourcing cost and the scheduling measure represented by either one of maximum lateness and total tardiness, subject to outsourcing budget. It is proved that the problem is NP-hard. Some solution properties are characterized to derive heuristic algorithms, and also a branch-and-bound algorithm. Numerical experiments are conducted to evaluate performance of the derived algorithms.     

Minimizing earliness and tardiness costs in stochastic scheduling

We address the single-machine stochastic scheduling problem with an objective of minimizing total expected earliness and tardiness costs, assuming that processing times follow normal distributions and due dates are decisions. We develop a branch and bound algorithm to find optimal solutions to this problem and report the results of computational experiments. We also test some heuristic procedures and find that surprisingly good performance can be achieved by a list schedule followed by an adjacent pairwise interchange procedure.     

A note on optimal assignment of slack due-dates in single-machine scheduling

This paper extends T.C.E. Cheng's approach for optimal assignment of slack due-dates and sequencing in the single-machine shop to the case when preemption is allowed and there are precedence constraints and ready times of jobs. It is shown that under special conditions the presented algorithm may be used when preemption is not allowed.     

Safe scheduling: Setting due dates in single-machine problems

We consider single-machine stochastic scheduling models with due dates as decisions. In addition to showing how to satisfy given service-level requirements, we examine variations of a model in which the tightness of due-dates conflicts with the desire to minimize tardiness. We show that a general form of the trade-off includes the stochastic E/T model and gives rise to a challenging scheduling problem. We present heuristic solution methods based on static and dynamic sorting procedures. Our computational evidence identifies a static heuristic that routinely produces good solutions and a dynamic rule that is nearly always optimal. The dynamic sorting procedure is also asymptotically optimal, meaning that it can be recommended for problems of any size.