Rachid Benmansour

Minimizing the weighted sum of maximum earliness and maximum tardiness costs on a single machine with periodic preventive maintenance

We consider the problem of scheduling a set of jobs on a single machine against a common and restrictive due date. In particular, we are interested in the problem of minimizing the weighted sum of maximum earliness and maximum tardiness costs. This kind of objective function is related to the just-in-time environment where penalties, such as storage cost and additional charges for late delivery, should be avoided. First we present a mixed integer linear model for the problem without availability constraints and we prove that this model can be reduced to a polynomial-time model. Secondly, we suppose that the machine undergoes a periodic preventive maintenance. We present then a second mixed integer linear model to solve the problem to optimality. Although the latter problem can be solved to optimality for small instances, we show that the problem reduces to the one-dimensional bin packing problem. Computational results show that the proposed algorithm best fit decreasing performs well.

Stochastic single machine scheduling with random common due date

This paper studies the single machine scheduling problem for minimising the expected total weighted deviations of completion times from random common due date. Jobs have exponentially distributed processing times and the common due date is a generalised Erlang distribution. The optimal schedules are shown to be ∧-shaped. Moreover, we give the optimal schedules when the machine is subject to stochastic breakdowns with independent and exponentially distributed uptimes and downtimes.

Simulation‐based approach to joint production and preventive maintenance scheduling on a failure‐prone machine

Purpose – The purpose of this study is to propose and model an integrated production‐maintenance strategy for a failure‐prone machine in a just‐in‐time context.Design/methodology/approach – The proposed integrated policy is defined and a simulation model is developed to investigate it.Findings – The paper focuses on finding simultaneously two decision variables: the period (T) at which preventive maintenance actions have to be performed; and the sequence of jobs (S). These values minimize the maintenance costs (MC) and the expected total earliness and tardiness costs (ETC) away from a common due‐date D.Practical implications – The paper attempts to integrate in a single model the two main aspects of any manufacturing and production systems: production and maintenance. It focuses on a stochastic scheduling problem in which n immediately available jobs are to be scheduled jointly with the preventive maintenance. The effect of the period (T) and the sequence of job (S) on the expected total cost are shown th...

Nested general variable neighborhood search for the periodic maintenance problem

In this paper we study the periodic maintenance problem: given a set of m machines and a horizon of T periods, find indefinitely repeating itself maintenance schedule such that at most one machine can be serviced at each period. In addition, all the machines must be serviced at least once for any cycle. In each period the machine i generates a servicing cost bi or an operating cost which depends on the last period in which i was serviced. The operating cost of each machine i in a period equals ai times the number of periods since the last servicing of that machine. The main objective is to find a cyclic maintenance schedule of a periodicity T that minimizes total cost. To solve this problem we propose a new Mixed Integer programming formulation and a new heuristic method based on general Variable neighborhood search called Nested general variable neighborhood search. The performance of this heuristic is shown through an extensive experimentation on a diverse set of problem instances.

On the single-processor scheduling problem with time restrictions

This paper presents a time-indexed mixed integer programming formulation for the single-processor scheduling problem with time restrictions that has been formulated at first by Braun et al. in [1]. The problem is as follows. A set of n independent jobs are simultaneously available for processing at the beginning of the planning horizon, and their processing times are fixed and known in advance. The jobs have to be processed non-preemptively on a single processor that can handle only one job at a time. Furthermore, during any time period of length α > 0 the number of jobs being executed is less than or equal to a given integer value B ≥ 2. The objective is to minimize the completion time of the last job in the optimal sequence (i.e. the makespan). To our knowledge, this is the first time that a mathematical model is given to solve the single-processor scheduling problem with time restrictions exactly. The performance of the model is tested by running it on randomly generated instances. The computational analysis shows that the proposed model, without any valid cuts, performs considerably well for small instances and a relatively large value of the integer B.

A mixed integer linear programming approach for design space exploration in FPGA-based MPSoC

Heterogeneous Multiprocessor System-on-Chip (Ht-MPSoC) architectures represent a promising approach as they allow a higher performance/energy consumption trade-off. In such systems, the processor instruction set is enhanced by application-specific custom instructions implemented on reconfigurable fabrics, namely FPGA. To increase area utilization and guarantee application constraint respect, we propose a new architecture where Ht-MPSoC hardware accelerators are shared among different processors in an intelligent manner. In this paper, a Mixed Integer Linear Programming (MILP) model is proposed to systematically explore the complex design space of the different configurations.

Design Space Exploration for Customized Asymmetric Heterogeneous MPSoC

Modern FPGA allows the design of very complex System-on-Chips (SoC). To fulfil modern application requirements, in terms of performance/energy consumption ratio, Heterogeneous Multiprocessor System-on-Chip (Ht- MPSoC) architectures represent a promising solution. In such systems, the processor instruction set is enhanced by application-specific custom instructions implemented on reconfigurable fabrics, namely FPGA. To increase area utilization and guarantee application constraint respect, we propose a new Ht-MPSoC architecture where hardware accelerators (HW accelerators) are shared among different processors in an intelligent manner. In this paper, we extend existing Ht-MPSoC architectures by considering asymmetric (AHt-MPSoC). In these architectures, cores have different resources that may share in different manners. Depending on the running applications and their needs in processing, private and shared HW accelerators are attached to the different cores. On a 8-core AHt-MPSoC we obtained a speed of 2.6 with a reduced number of HW accelerators for our benchmarks.

Scheduling preventive railway maintenance activities with resource constraints

Abstract In this paper, we focus on the scheduling of preventive railway maintenance activities. The objective is to keep the railway infrastructure in good operating conditions at low costs, also taking into account the limited available resources in what concerns crew members. Equipments degrade with usage and age and a good preventive maintenance program can greatly reduce their unreliability in the sense that expectable failures can be anticipated. We propose a mixed integer programming formulation for the problem of scheduling preventive railway maintenance activities and a Variable Neighborhood Search (VNS) algorithm to solve large instances of the problem.

Balancing preventive and corrective maintenance of aircraft assets: A cyber-physical systems approach

Many aircraft assets are subjected to both preventive (scheduled) and corrective (un-scheduled) replacement tasks to ensure adequate reliability and availability. The problem under this approach, particularly for assets that exist in high quantities, is that preventive replacement tasks will often require removal of the entire population of assets from the aircraft regardless as to whether any of them were replaced on a corrective basis beforehand. To avoid the costs associated with premature asset removal, this article fosters the use of a Cyber-Physical Systems approach to the management of aircraft assets underpinned by Radio Frequency Identification (RFID) technology. This will allow the identification of assets based on their installation date (whether being due to a corrective or preventive installation), meaning that only the required assets are removed during the preventive replacement task. This allows the preventive replacement task to be performed more efficiently, also allowing the scheduling and planning of the task to be improved. An example in the context of aircraft passenger seat covers is used to illustrate our proposal.

A two-stage flow shop scheduling problem with transportation considerations

This paper considers a two-stage robotic flow shop scheduling problem of which the objective is to minimize the maximum completion time of all the jobs. The problem consists of two dedicated machines at the first stage and a single machine at the second stage. Each job is defined by two operations processed in series on two stages. Depending on the job type, each job is processed on a dedicated machine at the first stage, and is then transported, by a robot or a conveyor, to be processed on a single machine at the second stage. To tackle the problem, a mixed integer programming model is proposed, which is solved by CPLEX. This model is improved using valid inequalities based on three lower bounds. In addition, we establish the complexity of several variations of the problem and we identify special cases that can be solved in polynomial time. Furthermore due to the NP-hardness of the problem, two heuristics are proposed to solve approximately large-sized problems. The results indicate that the solutions obtained are of high quality and the corresponding CPU time is acceptable.