A faster branch-and-bound algorithm for the earliness-tardiness scheduling problem

This paper addresses the one-machine scheduling problem with earliness-tardiness penalties. We propose a new branch-and-bound algorithm that can solve instances with up to 50 jobs and that can solve problems with even more general non-convex cost functions. The algorithm is based on the combination of a Lagrangean relaxation of resource constraints and new dominance rules.     

Minimizing weighted earliness–tardiness on parallel machines using hybrid metaheuristics

We consider the problem of scheduling a set of jobs on a set of identical parallel machines where the objective is to minimize the total weighted earliness and tardiness penalties with respect to a common due date. We propose a hybrid heuristic algorithm for constructing good solutions, combining priority rules for assigning jobs to machines and a local search with exact procedures for solving the one-machine subproblems. These solutions are then used in two metaheuristic frameworks, Path Relinking and Scatter Search, to obtain high quality solutions for the problem.The algorithms are tested on a large number of test instances to assess the efficiency of the proposed strategies.The results show that our algorithms consistently outperform the best reported results for this problem.     

Multiple machine JIT scheduling: a tabu search approach

This paper presents an approach to solving the multiple machine, non-preemptive, earliness-tardiness scheduling problem with unequal due dates in a flow shop with machine tiers (FMT). In this variant of the flow shop problem, machines are arranged in tiers or groups, and the jobs must visit one machine in each tier. The processing times, machine assignments, and due dates are deterministic and known in advance. The objective is to find a permutation schedule that minimizes the total deviation of each job from its due date. A tabu search (TS) meta-heuristic combined with an LP evaluation function is applied to solve this problem and results are compared to optimal permutation solutions for small problems and the earliest due date schedule for large problems. Several neighborhood generation methods and two diversification strategies are examined to determine their effect on solution quality. Results show that the TS method works well for this problem. TS found the optimal solution in all but one of the small problem instances and improved the earliest due date solutions for larger instances where no optimal solutions could be found.     

Parallel machine scheduling with earliness-tardiness penalties and space limits

In order to maximize an availability of machine and utilization of space, the parallel machines scheduling problem with space limit is frequently discussed in the industrial field. In this paper, we consider the parallel machine scheduling problem in which n jobs having different release times, due dates, and space limits are to be scheduled on m parallel machines. The objective function is to minimize the weighted sum of earliness and tardiness. To solve this problem, a heuristic is developed which is divided into three modules hierarchically: job selection, machine selection and job sequencing, and solution improvement. To illustrate its effectiveness, a proposed heuristic is compared with genetic algorithm (GA), hybrid genetic algorithm (HGA), and tabu search (TS), which are well-known meta-heuristics in a large number of randomly generated test problems based on the field situation. Also, we determine the job selection rule that is suitable to the problem situation considered in this paper and show the effectiveness of our heuristic method.     

Scheduling with a common due-window: Polynomially solvable cases

The single machine scheduling problem to minimize maximum weighted absolute deviations of job completion times from a common due-date, is known to be NP-hard. However, two special cases have been shown to have polynomial time solutions: the case of unit processing time jobs, and the case of due-date assignment for a given job sequence. We extend both cases to a setting of a common due-window. We show that the unit-job problem includes 12 different sub-cases, depending on the size and location of the (given) due-window. Scheduling and due-window assignment for a given job sequence is solved for a single machine, for parallel identical machines and for flow-shops. For each of the above cases, an appropriate special-structured linear program is presented.     

Minimization of squared deviation of completion times about a common due date

We discuss a non-preemptive single-machine job sequencing problem where the objective is to minimize the sum of squared deviation of completion times of jobs from a common due date. There are three versions of the problem—tightly restricted, restricted and unrestricted. Separate dynamic programming formulations have already been suggested for each of these versions, but no unified approach is available. We have proposed a pseudo-polynomial DP solution and a polynomial heuristic for general instance. Computational results show that tightly restricted instances of up to 600 jobs can be solved in less than 6 s. General instances of up to 80 jobs take less than 2 s.Statement of scope and purposeIn this paper, we have considered an NP-complete single-machine scheduling problem arising in JIT environment, a field of great importance in manufacturing industry. The objective of the problem is to schedule a set of given jobs to minimize the sum of squared deviation of their completion times from a common due date. This paper presents a number of precedence rules, a polynomial heuristic and more importantly a unified pseudo-polynomial dynamic programming formulation. Empirical results show that the dynamic programming formulation performs better than the existing approaches.     

Lagrangian bounds for just-in-time job-shop scheduling

We study the job-shop scheduling problem with earliness and tardiness penalties. We describe two Lagrangian relaxations of the problem. The first one is based on the relaxation of precedence constraints while the second one is based on the relaxation of machine constraints. We introduce dedicated algorithms to solve the corresponding dual problems. The second one is solved by a simple dynamic programming algorithm while the first one requires the resolution of an NP-hard problem by branch and bound. In both cases, the relaxations allow us to derive lower bounds as well as heuristic solutions. We finally introduce a simple local search algorithm to improve the best solution found. Computational results are reported.     

Scheduling job classes on uniform machines

We study a scheduling problem with job classes on parallel uniform machines. All the jobs of a given class share a common due-date. General, non-decreasing and class-dependent earliness and tardiness cost functions are assumed. Two objectives are considered: (i) minmax, where the scheduler is required to minimize the maximum earliness/tardiness cost among all the jobs and (ii) minmax-minsum, where the scheduler minimizes the sum of the maximum earliness/tardiness cost in all job classes. The problem is easily shown to be NP-hard, and we focus here on the introduction of simple heuristics. We introduce LPT (Largest Processing Time first)-based heuristics for the allocation of jobs to machines within each class, followed by a solution of an appropriate non-linear program, which produces for this job allocation an optimal schedule of the classes. We also propose a lower bound, based on balancing the load on the machines. Our numerical tests indicate that the heuristics result in very small optimality gaps.