Single machine scheduling with job-dependent machine deterioration

We consider the single machine scheduling problem with job-dependent machine deterioration. In the problem, we are given a single machine with an initial non-negative maintenance level, and a set of jobs each with a non-preemptive processing time and a machine deterioration. Such a machine deterioration quantifies the decrement in the machine maintenance level after processing the job. To avoid machine breakdown, one should guarantee a non-negative maintenance level at any time point; and whenever necessary, a maintenance activity must be allocated for restoring the machine maintenance level. The goal of the problem is to schedule the jobs and the maintenance activities such that the total completion time of jobs is minimized. There are two variants of maintenance activities: in the partial maintenance case each activity can be allocated to increase the machine maintenance level to any level not exceeding the maximum; in the full maintenance case every activity must be allocated to increase the machine maintenance level to the maximum. In a recent work, the problem in the full maintenance case has been proven NP-hard; several special cases of the problem in the partial maintenance case were shown solvable in polynomial time, but the complexity of the general problem is left open. In this paper we first prove that the problem in the partial maintenance case is NP-hard, thus settling the open problem; we then design a $2$-approximation algorithm.Comment: 15 page

Shop scheduling with availability constraints

Scheduling Theory studies planning and timetabling of various industrial and human activities and, therefore, is of constant scientific interest. Being a branch of Operational Research, Theory of Scheduling mostly deals with problems of practical interest which can be easily (from a mathematical point of view) solved by full enumeration and at the same time usually require enormous time to be solved optimally. Therefore, one attempts to develop algorithms for finding optimal or near optimal solutions of the problems under consideration in reasonable time. If the output of an algorithm is not always an optimal solution then the worst-case analysis of this algorithm is undertaken in order to estimate either a relative error or an absolute error that holds for any given instance of the problem. Scheduling problems which are usually considered in the literature assume that the processing facilities are constantly available throughout the planning period. However, in practice, the processing facility, e.g. a machine, a labour, etc. can become non-available due to various reasons, e.g. breakdowns, lunch breaks, holidays, maintenance work, etc. All these facts stimulate research in the area of scheduling with non-availability constraints. This branch of Scheduling Theory has recently received a lot of attention and a considerable number of research papers have been published. This thesis is fully dedicated to scheduling with non-availability constraints under various assumptions on the structure of the processing system and on the types of non-availability intervals

Parallel machine scheduling subject to machine availability constraints

Cataloged from PDF version of article.Within a planning horizon, machines may become unavailable due to unexpected breakdowns or pre-scheduled activities. A realistic approach in constructing the production schedule should explicitly take into account such periods of unavailability. This study addresses the parallel machine-scheduling problem subject to availability constraints on each machine. The objectives of minimizing the total completion time and minimizing the maximum completion time are studied. The problems with both objectives are known to be NP-hard. We develop an exact branch-and-bound procedure and propose three heuristic algorithms for the total completion time problem. Similarly, we propose exact and approximation algorithms also for the maximum completion time problem. All proposed algorithms are tested through extensive computational experimentation, and several insights are provided based on computational results.Sevindik, KayaM.S

A multi-criteria model for maintenance job scheduling

This paper presents a multi-criteria maintenance job scheduling model, which is formulated using a weighted multi-criteria integer linear programming maintenance scheduling framework. Three criteria, which have direct relationship with the primary objectives of a typical production setting, were used. These criteria are namely minimization of equipment idle time, manpower idle time and lateness of job with unit parity. The mathematical model constrained by available equipment, manpower and job available time within planning horizon was tested with a 10-job, 8-hour time horizon problem with declared equipment and manpower available as against the required. The results, analysis and illustrations justify multi-criteria consideration. Thus, maintenance managers are equipped with a tool for adequate decision making that guides against error in the accumulated data which may lead to wrong decision making. The idea presented is new since it provides an approach that has not been documented previously in the literature

Least space-time first scheduling algorithm : scheduling complex tasks with hard deadline on parallel machines

Both time constraints and logical correctness are essential to real-time systems and failure to specify and observe a time constraint may result in disaster. Two orthogonal issues arise in the design and analysis of real-time systems: one is the specification of the system, and the semantic model describing the properties of real-time programs; the other is the scheduling and allocation of resources that may be shared by real-time program modules. The problem of scheduling tasks with precedence and timing constraints onto a set of processors in a way that minimizes maximum tardiness is here considered. A new scheduling heuristic, Least Space Time First (LSTF), is proposed for this NP-Complete problem. Basic properties of LSTF are explored; for example, it is shown that (1) LSTF dominates Earliest-Deadline-First (EDF) for scheduling a set of tasks on a single processor (i.e., if a set of tasks are schedulable under EDF, they are also schedulable under LSTF); and (2) LSTF is more effective than EDF for scheduling a set of independent simple tasks on multiple processors. Within an idealized framework, theoretical bounds on maximum tardiness for scheduling algorithms in general, and tighter bounds for LSTF in particular, are proven for worst case behavior. Furthermore, simulation benchmarks are developed, comparing the performance of LSTF with other scheduling disciplines for average case behavior. Several techniques are introduced to integrate overhead (for example, scheduler and context switch) and more realistic assumptions (such as inter-processor communication cost) in various execution models. A workload generator and symbolic simulator have been implemented for comparing the performance of LSTF (and a variant -- LSTF+) with that of several standard scheduling algorithms. LSTF\u27s execution model, basic theories, and overhead considerations have been defined and developed. Based upon the evidence, it is proposed that LSTF is a good and practical scheduling algorithm for building predictable, analyzable, and reliable complex real-time systems. There remain some open issues to be explored, such as relaxing some current restrictions, discovering more properties and theorems of LSTF under different models, etc. We strongly believe that LSTF can be a practical scheduling algorithm in the near future

Scheduling on parallel machines with a common server in charge of loading and unloading operations

This paper addresses the scheduling problem on two identical parallel machines with a single server in charge of loading and unloading operations of jobs. Each job has to be loaded by the server before being processed on one of the two machines and unloaded by the same server after its processing. No delay is allowed between loading and processing, and between processing and unloading. The objective function involves the minimization of the makespan. This problem referred to as P2, S1|sj , tj |Cmax generalizes the classical parallel machine scheduling problem with a single server which performs only the loading (i.e., setup) operation of each job. For this NP-hard problem, no solution algorithm was proposed in the literature. Therefore, we present two mixedinteger linear programming (MILP) formulations, one with completion-time variables along with two valid inequalities and one with time-indexed variables. In addition, we propose some polynomial-time solvable cases and a tight theoretical lower bound. In addition, we show that the minimization of the makespan is equivalent to the minimization of the total idle times on the machines. To solve large-sized instances of the problem, an efficient General Variable Neighborhood Search (GVNS) metaheuristic with two mechanisms for finding an initial solution is designed. The GVNS is evaluated by comparing its performance with the results provided by the MILPs and another metaheuristic. The results show that the average percentage deviation from the theoretical lower-bound of GVNS is within 0.642%. Some managerial insights are presented and our results are compared with the related literature.Comment: 40 pages, 4 figures, 16 table