A single machine scheduling problem with availability constraints and sequence-dependent setup costs

Abstract

a b s t r a c tWe study a single machine scheduling problem with availability constraints and sequencedependent setup costs, with the aim of minimizing the makespan. To the authors' knowledge, this problem has not been treated as such in the operations research literature. We derive in this paper a mixed integer programming model to deal with such scheduling problem. Computational tests showed that commercial solvers are capable of solving only small instances of the problem. Therefore, we propose two ways for reducing the execution time, namely a valid inequality that strengthen the linear relaxation and an efficient heuristic procedure that provides a starting feasible solution to the solver. A substantial gain is achieved both in terms of the linear programming relaxation bound and in terms of the time to obtain an integer optimum when we use the enhanced model in conjunction with providing to the solver the solution obtained by the proposed heuristic.

Improved Approaches to Minimize the Makespan on Single-Machine Scheduling with Periodic Preventive Maintenance Activities

“…Objective 11is to minimize the makespan, which is inspired by the bin-packing problem addressed in the studies of Ji et al [9] and Perez-Gonzalez and Framinan [13]. at is, the optimal solution is in the form of having a minimum number of batches plus the lowest load.…”

“…Mathematical Problems in Engineering (13) are the same as constraints (3) and (2). Constraint (14) enforces that jobs be assigned in the preceding available batches, which minimizes the number of batches.…”

“…Preventive maintenance (PM) is one of the factors causing machines to be unavailable for processing jobs, and it can significantly affect the performance of job scheduling. e majority of the studies in the literature assumed that each maintenance activity is either assigned in advance, i.e., its starting and completion times are known, [4][5][6][7][8][9][10][11][12][13][14][15][16] or maintenance activities and jobs are jointly scheduled in the planning horizon [12,[17][18][19][20][21][22][23][24][25][26]. In the abovementioned studies, they assumed that the maintenance time (maintenance duration) is a constant; however, in some maintenance activities such as cleaning, refilling, and recharging, the maintenance time is a nondecreasing function of its starting time, i.e., the later the maintenance activity begins, the longer its duration.…”

A variable neighborhood search algorithm for solving the single machine scheduling problem with periodic maintenance

“…They proposed a mathematical model and a variable neighborhood search algorithm to solve the problem. For problems with setup-times, Angel-Bello et al [1] proposed a mixed integer programming model for solving the single machine scheduling problem with availability constraints and sequence-dependent setup costs. Later, Luo et al [27] investigated a single-machine scheduling problem with workload-dependent maintenance duration with the aim of minimizing the total weighted completion time.…”

Simultaneous Considering of Machine Availability Constraint, Sequence Dependent Setup Time and Ready Time in a No-wait Hybrid Flow Shop Scheduling Problem to Minimize Mean Tardiness

“…One of the most common assumptions in the scheduling literature is that the machines or processors are always available for their use, when actually they may be stopped by several reasons, like failures and maintenances [27]. The other characteristic of this research is related to setup time.…”