Marie-Laure Espinouse

Minimizing setup costs for parallel multi-purpose machines under load-balancing constraint

This article focuses on the minimization of the setup costs of a workshop modeled with parallel multi-purpose machines. Any admissible workshop configuration has to ensure that a load-balanced production plan meeting a given demand exists. This problem is shown to be NP-hard in the strong sense, and is stated as a mixed integer linear program. It is shown that under some hypotheses, it can be stated as a transportation problem and solved in polynomial time. An upper bound and lower bound are proposed, as well as a performance ratio assessment that is reached only when degenerate optimal solutions to the transportation problem exist.

Minimizing the makespan in the two-machine no-wait flow-shop with limited machine availability

Abstract This paper deals with the two-machine no-wait flow-shop problem with limited machine availability. In this model, we assume that machines may not always be available, for example because of preventive maintenance. We only consider the deterministic case where the unavailable periods are known in advance. The objective function considered is the maximum completion time (C max ). We prove that the problem is NP -Hard even if only one unavailability period occurs on one single machine, and NP -Hard in the strong sense for arbitrary numbers of unavailability periods. We also provide heuristic algorithms with error bounding analysis.

Complexity results and approximation algorithms for the two machine no-wait flow-shop with limited machine availability

The scheduling problems studied in this paper concern a two-machine no-wait flow shop problem with limited machine availability. In this model, we assume that machines may not always be available, for example because of preventive maintenance. We only consider the deterministic case where the unavailable periods are known in advance. The objective function considered is the maximum completion time (Cmax). We prove that the problem is NP-hard even if only one non-availability period occurs on one of machines, and NP-hard in the strong sense for arbitrary numbers of non-availability periods. We also provide heuristic algorithms with error bounding analysis.

Makespan minimisation on parallel batch processing machines with non-identical job sizes and release dates

The problem we study in this paper arises from the washing step of hospital sterilisation services. Washers in the washing step are capable of handling more than one medical device set as long as their capacity is not exceeded. The medical device set sizes and arrival times to the sterilisation service may be different, but they all have the same washing duration. Thus, we model the washing step as a batch scheduling problem where medical device sets are treated as jobs with non-identical sizes and release dates, but equal processing times. The main findings we present in this paper are the following. First, we study two special cases for which polynomial algorithms are presented. We then develop a 2-approximation algorithm for the general problem. Finally, we develop a MILP model and compare it with another MILP model from the literature. Computational results show that our MILP model outperforms the model from the literature.

Characterization and modelling of guillotine constraints

This paper focuses on guillotine cuts which often arise in real-life cutting stock problems. In order to construct a solution verifying guillotine constraints, the first step is to know how to determine whether a given cutting pattern is a guillotine pattern. For this purpose, we first characterize guillotine patterns by proving a necessary and sufficient condition. Then, we propose a polynomial algorithm to check this condition. Based on this mathematical characterization of guillotine patterns, we then show that guillotine constraints can be formulated into linear inequalities. The performance of the algorithm to check guillotine cutting patterns is evaluated by means of computational results.

Parallel-machine scheduling with maintenance: Praising the assignment problem

We consider a general model for scheduling jobs on unrelated parallel-machines with maintenance interventions. The processing times are deteriorating with their position in the production sequence and the goal of the maintenance is to help to restore good processing conditions. The maintenance duration is depending on the time elapsed since the last maintenance intervention.

Building flight planning for an airline company under maintenance constraints

Purpose – The purpose of this paper is to provide some heuristic and meta heuristic tools to aid airline companies in flight planning while taking into account maintenance planning. The objective is to maximize aircraft utilization before the maintenance interventions and to smooth the long‐term flight load of the aircraft so that maintenance checks are regular for all the fleet.Design/methodology/approach – The proposed methods, based on operational research solution technics, build a flight planning for an airline company. The simulation of the proposed methods is observed over 40 weeks and evaluated with different problem instances and maintenance policies.Findings – The longest path based method with increasing priority and the simulated annealing are shown to have the best aircraft utilization results.Research limitations/implications – Further research could propose some methods which build simultaneous maintenance and flight planning.Practical implications – The economic value and legal considerati...

A Two-step Heuristic to Build Flight and Maintenance Planning in a Rolling-horizon

Each aircraft of an airline company has to undergo maintenance checks at the end of a certain amount of flight hours to ensure the security conditions. Given a flight schedule for a specific aircraft fleet, our objective is to search the efficiency of the proposed method on rolling horizon and to compare different types of maintenance policies. The proposed method maximizes the aircraft utilization before the maintenance interventions and smooths the flight load of the aircrafts so that the maintenance checks are regular for all the fleet. The flight planning of ten weeks is prepared on a rolling horizon. The sliding time window is one week. We propose a two-step approach to solve this optimization problem. The first sub-problem concerns only the critical aircrafts which must undergo a maintenance check in the planning week. The second sub-problem concerns non-critical aircraft load smoothing. We show that, for different weekly flight loads, different maintenance policies can be more advantageous while some other policies led company disabilities to insure the flights

Synchronization Between Human Resources in Home Health Care Context

This paper deals with the scheduling and routing problem in a Home Health Care structure, when synchronization is needed between two types of human resources, and time windows are considered for patients and caregivers. Our objective is to minimize the total waiting time of caregivers between patients. We give a mathematical formulation of this problem as a mixed integer linear program. We present some experiments in order to analyze the execution time and test the capability of the MILP to solve the problem in real cases, within reasonable execution times, to measure the impact of the proportion of synchronized visits, and to analyze the average workload of an operator.

Optimizing the makespan of washing operations of medical devices in hospital sterilization services

In this paper, we deal with the problem of minimizing the makespan of washing operations in hospitals sterilization services. After use in operating blocs, reusable medical devices (RMD) are sent to the sterilization service which is composed of various processes. In the washing step, different sets of RMD, used for different operations, may be washed together without exceeding washer capacity. An RMD set must be washed in one cycle and so, we are not allowed to split RMD sets. In this case, we consider a batch scheduling problem where RMD sets may have different sizes and different release dates for washing. Note that if all release dates are equal, the problem is reduced to a bin packing problem. We provide a mixed integer linear programming model which aims at minimizing the makespan of washing operations. We provide and also experiment some heuristics based on classical bin packing algorithms.