Simon Thevenin

Metaheuristics for a scheduling problem with rejection and tardiness penalties

In this paper, we consider a single-machine scheduling problem (P) inspired from manufacturing instances. A release date, a deadline, and a regular (i.e., non-decreasing) cost function are associated with each job. The problem takes into account sequence-dependent setup times and setup costs between jobs of different families. Moreover, the company has the possibility to reject some jobs/orders, in which case a penalty (abandon cost) is incurred. Therefore, the problem at hand can be viewed as an order acceptance and scheduling problem. Order acceptance problems have gained interest among the research community over the last decades, particularly in a make-to-order environment. We propose and compare a constructive heuristic, local search methods, and population-based algorithms. Tests are performed on realistic instances and show that the developed metaheuristics significantly outperform the currently available resolution methods for the same problem.

Order acceptance and scheduling with earliness and tardiness penalties

This paper addresses a production scheduling problem in a single-machine environment, where a job can be either early, on time, late, or rejected. In order acceptance and scheduling contexts, it is assumed that the production capacity of a company is overloaded. The problem is therefore to decide which orders to accept and how to sequence their production. In contrast with the existing literature, the considered problem jointly takes into account the following features: earliness and tardiness penalties (which can be linear or quadratic), sequence-dependent setup times and costs, rejection penalties, and the possibility of having idle times. The practical relevance of this new NP-hard problem is discussed and various solution methods are proposed, ranging from a basic greedy algorithm to refined metaheuristics (e.g., tabu search, the adaptive memory algorithm, population-based approaches loosely inspired on ant algorithms). The methods are compared for instances with various structures containing up to 200 jobs. For small linear instances, the metaheuristics are favorably compared with an exact formulation using CPLEX 12.2. Managerial insights and recommendations are finally given.

Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibility

In this paper, an extension of the graph colouring problem is introduced to model a parallel machine scheduling problem with job incompatibility. To get closer to real-world applications, where the number of machines is limited and jobs have different processing times, each vertex of the graph requires multiple colours and the number of vertices with the same colour is bounded. In addition, several objectives related to scheduling are considered: makespan, number of pre-emptions and summation over the jobs’ throughput times. Different solution methods are proposed, namely, two greedy heuristics, two tabu search methods and an adaptive memory algorithm. The latter uses multiple recombination operators, each one being designed for optimising a subset of objectives. The most appropriate operator is selected dynamically at each iteration, depending on its past performance. Experiments show that the proposed algorithm is effective and robust, while providing high-quality solutions on benchmark instances for the graph multi-colouring problem, a simplification of the considered problem.

Tabu Search for a Preemptive Scheduling Problem with Job Incompatibilities

Abstract In this paper, the problem of scheduling n jobs of different durations on parallel machines is considered. Preemption is allowed and there exist incompatibilities between jobs. Furthermore, a global deadline is set to make it impossible to perform all jobs. The problem is to select the jobs to be performed and to schedule them to maximize the total gain. To generate realistic solutions, a multi-objective approach is used which considers both penalties for preemption and the time spent by the jobs in the production shop. The problem is modeled as an extension of the k -multi-coloring problem. A greedy algorithm and two local search approaches are designed, based on five different neighborhood structures. The results show the efficiency of the tabu search method.

Graph multi-coloring for a job scheduling application

In this paper, we introduce a graph multi-coloring problem where each vertex must be assigned a given number of different colors, represented as integers, and no two adjacent vertices can share a common color. In the variant considered, the number of available colors is such that not all vertices can be colored. Furthermore, there is a bound on the number of vertices which can be assigned the same color. A gain is associated with each vertex and the first objective is to maximize the total gain over all colored vertices. Secondary objectives consider the sequence of colors assigned to each vertex. More precisely, the range and the number of interruptions must be minimized, where the range corresponds to the difference between the largest and smallest colors assigned to a vertex. This variant of the graph multi-coloring problem is of interest because it can model practical job scheduling applications. An integer linear programming formulation is first proposed to address small-size instances. A construction heuristic, as well as local search methods, are then reported to tackle larger instances. The local search methods are based on several neighborhood structures, each one focusing on a specific property of the problem. Different ways to combine these neighborhood structures are also investigated.

All-Terrain Tabu Search Approaches for Production Management Problems

A metaheuristic is a refined solution method able to find a satisfying solution to a difficult problem in a reasonable amount of time. A local search metaheuristic works on a single solution and tries to improve it iteratively. Tabu search is one of the most famous local search, where at each iteration, a neighbor solution is generated from the current solution by performing a specific modification (called a move) on the latter. The goal of this chapter is to present tabu search approaches with enhanced exploration and exploitation mechanisms. For this purpose, the following ingredients are discussed: different neighborhood structures (i.e., different types of moves), guided restarts based on a distance function, and deconstruction/reconstruction techniques. The resulting all-terrain tabu search approaches are illustrated for various production problems: car sequencing, job scheduling, resource allocation, and inventory management.

Model and metaheuristics for a scheduling problem integrating procurement, sale and distribution decisions

This paper presents an integrated approach for short-term supply chain management (SCM) at a fast moving consumer goods production plant. The problem is to determine the production quantities, to provide a detailed production schedule, to trigger the relevant express deliveries of raw material, and to manage the distribution. We propose a linear integer model, which integrates all of these decisions within scheduling. To find high quality solutions in a reasonable amount of time, various solution methods are proposed, such as a greedy constructive heuristic, two tabu search metaheuristics, a basic variable neighborhood search and an enhanced one, which uses a variable shaking operator. Experiments on realistic instances show that the latter method is efficient and robust. This paper is a contribution to the SCM literature (indeed, only few references address the integration of short term decisions) and to the general metaheuristics field (as the variable neighborhood search paradigm is extended).