Marino Widmer

Guidelines for the use of meta-heuristics in combinatorial optimization

Abstract The 18th EURO Summer/Winter Institute (ESWI XVIII) took place during the spring 2000 in Switzerland. The topic of ESWI XVIII, “Meta-heuristics in Combinatorial Optimization”, was selected due to its great current scientific interest: indeed, in recent years, several meta-heuristics have proved to be highly efficient for the solution of difficult combinatorial optimization problems. The Institute was focused more particularly on the development and the use of local search and population search algorithms. Applications of these meta-heuristics on academic or real life problems were also discussed. This special issue of EJOR contains papers written by the participants to ESWI XVIII. These papers have benefited from fruitful discussions among the participants, the organizers and the invited speakers. We have tried to summarize here below some guidelines that should help in the design of successful adaptations of meta-heuristics to difficult combinatorial optimization problems.

A case study of single shift planning and scheduling under annualized hours: A simple three-step approach

Abstract In the current economic and industrial conditions, with demand ever fluctuating, designing a timetable to define a work schedule for each employee is not an easy task. Moreover due to legal and cost constraints, it is not always possible to engage and dismiss the employees according to the production requirement. In this paper, a three-step method is presented assigning the daily work for full-time employees working on one shift. It takes into account a set of legal constraints (such as holiday arrangements) and it guarantees that the defined workforce is minimal, assuming that employees are able to perform their tasks.

Mixed Integer Programming to Schedule a Single-Shift Workforce under Annualized Hours

Nowadays flexibility is a strategic concept for firms. Indeed workload has to follow, as close as possible, the development of demand throughout the year. However, firms cannot engage and dismiss employees according to production requirements. Thus, workforce scheduling becomes a delicate task. In this paper, four mixed integer programming models are developed to solve the workforce schedule problem for a single-shift. The annualized hour scenario is considered with respect to a set of Swiss legal constrains. Furthermore, the minimal required workforce is guaranteed and it is assumed that each employee is able to perform each task within the team. All employees are full-time workers.

An improved tabu search approach for solving the job shop scheduling problem with tooling constraints

Flexible manufacturing systems (FMSs) are nowadays installed in the mechanical industry. In such systems. many different part types are produced simultaneously and it is necessary to take tooling constraints into account for finding an optimal schedule. A heuristic method is presented for solving the m-machine, n-job shop scheduling problem with tooling constraints. This method. named TOMATO, is based on an adaptation of tabu search techniques and is an improvement on the JEST algorithm proposed by Widmcr in 1991. Keq’Mords: Flexible manufacturing system; Job shop scheduling: Tooling constraints: Tabu search

A flexible MILP model for multiple-shift workforce planning under annualized hours

Flexibility in workforce planning is one of the best ways to respond to fluctuations of the demand. This paper proposes a flexible mixed integer linear programming (MILP) model to solve a multiple-shift workforce planning problem under annualized working hours. The model takes into account laws and collective agreements that impose constraints on overtime and holidays. We consider possible gradual hiring of full time and partial time workers. Several objectives are pursued such as balancing the workload of the employees or minimizing the workforce size. Computational experiments on a real life problem demonstrate the effectiveness of the model.

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.

FUN: A dynamic method for scheduling problems

Abstract Real time control is an important part of scheduling problems, which have become a prime area of interest in the last years. New concepts have emerged in the field of control of the scheduling of parts and tools. Methods to collect information in real time have also been developed, using the shop network, to allow quick reactions and to handle dynamic and reactive shops. The approach described here is based on a fuzzy rules controller which can be dynamically adapted following the perturbations which could arise in a shop. This neuro-fuzzy method gives an efficient dynamic approach for solving scheduling problems in real time.

Integer linear programming models for a cement delivery problem

We consider a cement delivery problem with an heterogeneous fleet of vehicles and several depots. The demands of the customers are typically larger than the capacity of the vehicles which means that most customers are visited several times. This is a split delivery vehicle routing problem with additional constraints. We first propose a two phase solution method that assigns deliveries to the vehicles, and then builds vehicle routes. Both subproblems are formulated as integer linear programming problems. We then show how to combine the two phases in a single integer linear program. Experiments on real life instances are performed to compare the performance of the two solution methods.

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.

Stochastic optimization of the scheduling of a radiotherapy center

Cancer treatment facilities can improve their efficiency for radiation therapy by optimizing the utilization of the linear accelerators (linacs). We propose a method to schedule patients on such machines taking into account their priority for treatment, the maximum waiting time before the first treatment, the treatment duration, and the preparation of this treatment (dosimetry). At each arrival of a patient, the future workloads of the linacs and the dosimetry are inferred. We propose a genetic algorithm, which schedules future tasks in dosimetry and a constraint programming formulation to verify the feasibility of a planning of dosimetry. This approach ensures the beginning of the treatment on time and thus avoids the cancellation of treatment sessions on linacs. Preliminary results indicate the improvements of this new procedure.