Single-machine scheduling

About: Single-machine scheduling is a research topic. Over the lifetime, 2473 publications have been published within this topic receiving 56288 citations.

Job Shop Scheduling under a Non-Renewable Resource Constraint

Abstract: In this paper we consider the job shop scheduling problem under a discrete non-renewable resource constraint. We assume that jobs have arbitrary processing times and resource requirements and there is a unit supply of the resource at each time period. We develop an approximation algorithm for this problem and empirically test its effectiveness in finding the minimum makespan schedules. Most of the research done in the area of scheduling deals with the allocation of a single scarce resource over time to perform a collection of tasks. In this study, the scheduling environment is extended to include an additional non-renewable resource. The term non-renewable implies that the resource is actually being consumed by the jobs competing for it. Financial constraints are typical examples of such constraints and for this reason non-renewable resource constraints are often called financial constraints1. Materials shared by different products can also be regarded as a non-renewable resource in manufacturing environments. Considering these constraints explicitly is likely to yield more realistic schedules. A limited amount of research has been done in the area of non-renewable resource constrained scheduling. There are some polynomially bounded solution algorithms for precedence constrained scheduling problems2 and for pre-emptive scheduling of independent jobs on parallel machines1. In the case of arbitrary resource requirements and availabilities, Slowinski' states that Carlier has shown that even the non-preemptive single machine scheduling problem is NP-complete if job processing times are different from unity. In Toker et al.3, it is shown that when the amount of resource available at each time period is constant, the single machine non-renewable resource constrained problem is equivalent to a resource- free, two-machine flowshop problem. Hence it is solvable in polynomial time. They also extended their results to the m-machine case and showed how to transform different types of resource constrained problems into equivalent, unconstrained problems. The scheduling environment we consider is a job shop. A single non-renewable resource becomes available over time in equal quantities (say unity) and there is a set of jobs to be processed. Each operation requires an arbitrary amount of the non-renewable resource which must be available at the start of that operation and which is consumed during its processing. We used makespan as the performance measure. Optimization algorithms for the general job shop scheduling problem are restricted to implicit enumeration techniques, such as branch-and-bound based procedures4-7. On the other hand, approximation algorithms usually use a dispatching rule to give priorities to operations to be scheduled8. The non-renewable resource constrained job shop scheduling problem is NP-complete as, when all resource requirements are zero, it reduces to the unconstrained job shop problem which is NP-complete9. This complexity result serves as a formal justification to use approximation algorithms for the constrained problem. We first describe the approximation algorithm developed and then introduce two lower bounds for the n-job, m-machine resource-constrained job shop scheduling problem. Next, we discuss the computational results. Finally, we present our conclusions.

Minimizing the sum of maximum earliness and maximum tardiness in the single-machine scheduling problem with sequence-dependent setup time

Abstract: This paper considers the problem of scheduling a given number of jobs on a single machine to minimize the sum of maximum earliness and maximum tardiness when sequence-dependent setup times exist (1∣STsd∣ETmax). In this paper, an optimal branch-and-bound algorithm is developed that involves the implementation of lower and upper bounding procedures as well as three dominance rules. For solving problems containing large numbers of jobs, a polynomial time-bounded heuristic algorithm is also proposed. Computational experiments demonstrate the effectiveness of the bounding and dominance rules in achieving optimal solutions in more than 97% of the instances.

Single-machine scheduling with proportionally deteriorating jobs subject to availability constraints

Abstract: We address the nonresumable version of the scheduling problem with proportionally deteriorating jobs on a single machine subject to availability constraints. The objective is to minimize the total weighted completion time. We show that there exists no polynomial-time algorithm with a constant worst-case ratio for the problem with two nonavailability intervals unless . Furthermore, we propose a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme for the problem with a single nonavailability interval.

A Genetic Approach for Dynamic Job-Shop Scheduling Problems

Abstract: Due to their dynamic nature, real scheduling problems have an additional complexity in relation to static ones. In many situations these problems, even for apparently simple situations, are hard to solve, i.e. the time required to compute an optimal solution increases exponentially with the size of the problem [1]. GAs have been extensively used in the context of Job-Shop Scheduling Problems (JSSP). If all jobs are known before processing starts the JSSP is called static, while if job release times are not fixed at a single point in time, i.e. jobs arrive to the system at different times, the problem is called dynamic. Scheduling problems can also be classified as deterministic, when processing times and all other parameters are known and fixed, and stochastic, when some or all parameters are uncertain [7]. The proposed approach deals with these two cases of dynamic scheduling: deterministic and stochastic. For such class of problems, the goal is no longer to find a single optimum, but rather to continuously adapt the solution to the changing environment. The purpose of this paper is to describe an approach based on GA for solving dynamic scheduling problems, where the products (jobs) to be processed have due dates. This paper starts by presenting a scheduling system, based on Genetic Algorithms for the resolution of the dynamic version of Single Machine Scheduling Problem (SMSP). The approach used adapts the resolution of the static problem to the dynamic one in which changes may occur continually. This takes into account dynamic occurrences in a system and adapts the current population to a new regenerated population. Then, it is proposed an approach for the resolution of the Job-Shop Scheduling Problem (JSSP) in dynamic environments. The paper is structured as follows: section 2 provides a description of the considered scheduling problem. Section 3 summarises an approach for the resolution of the Dynamic Single Machine Scheduling Problem. The proposed approach for dynamic scheduling is presented in section 4. Finally, the paper concludes with a summary and some ideas for future work.