Yassine Ouazene

Lot-sizing in a multi-stage flow line production system with energy consideration

In this paper, a single-item capacitated lot-sizing problem in a flow-shop system with energy consideration is studied. The planning horizon is defined by a set of periods where each one is characterised by a length, an allowed maximal power, an electricity price, a power price and a demand. The objective is to determine the quantities to be produced by each machine at each period while minimising the production cost in terms of electrical, inventory, set-up and power required costs. For medium- and large-scale problems, lot-sizing problems are hard to solve. Therefore, in this study, two heuristics are developed to solve this problem in a reasonable time. To evaluate the performances of these heuristics, computational experiments are presented and numerical results are discussed and analysed.

Fuzzy-metaheuristic methods to solve a hybrid flow shop scheduling problem with pre-assignment

This paper deals with a particular version of the hybrid flow shop scheduling problem inspired from a real application in the automotive industry. Specific constraints such as pre-assigned jobs, non-identical parallel machines and non-compatibility between certain jobs and machines are considered in order to minimise the total tardiness time. A mixed-integer programming model that incorporates these aspects is developed and solved using ILOG Cplex software. Thus, because of the computation time constraint, we propose approximate resolution methods based on genetic and particle swarm optimisation algorithms coupled or not with fuzzy logic control. The effectiveness of these methods is investigated via computational experiments based on theoretical and real case instances. The obtained results show that fuzzy logic control improves the performances of both genetic and particle swarm optimisation algorithms significantly.

Workload balancing in identical parallel machine scheduling using a mathematical programming method

AbstractThis paper addresses the workload balancing problem in identical parallel machines context. The problem consists of assigning n different jobs to m identical parallel machines in order to minimize the workload imbalance among the different machines. This problem is formulated as a linear mixed integer program to minimize the difference between the greatest and smallest workload assigned to each machine. Based on some numerical examples reported in the literature, we establish that the classical formulation which consists of minimizing the greatest machine completion time does not provide the optimal workload repartition. That is why we consider a new mathematical formulation based on the minimization of the difference between the workload of the bottleneck machine and the workload of the fastest machine. The proposed programming method is also used to provide optimal solutions in reasonable computational times for different test problems presented in the literature by Raghavendra and Murthy 10 to ...

Equivalent machine method for approximate evaluation of buffered unreliable production lines

The addressed paper deals with a new analytical formulation called Equivalent Machine Method to evaluate the system throughput of a buffered serial production line. The machines are unreliable and both failure and repair times are assumed to be exponentially distributed. The proposed method is based on the analysis of the different states of each buffer using birth-death Markov processes. Then, each original machine is replaced by an equivalent one taking into account the probabilities of blockage and starvation. The throughput of the production line is defined as the bottleneck between the effective production rates of the equivalent machines. This method considers both homogeneous and non-homogeneous lines and reduces sensibly the state space cardinality of the Markov chain representation of the system and consequently the computational times. A comparative study based on different test instances existing in the literature is presented and discussed. The obtained results prove the effectiveness and the accuracy of the proposed method comparing with both simulation and existing approaches in the literature.

The Joint Load Balancing and Parallel Machine Scheduling Problem

The addressed problem in this paper considers the joint load balancing and parallel machines scheduling problem. Two decisions are taken at once: to build the best schedule of n jobs on m identical parallel machines in order to minimize the total tardiness and to find the equitable distribution of the machine’s time activity. To our knowledge, these two criteria have never been simultaneously studied for the case of parallel machines. The considered problem is NP-hard since the problem with only the total tardiness minimization is NP-hard. We propose an exact and an approached resolution. The first method is based on the mixed integer linear programming method solved by Cplex solver. The second one is an adapted genetic algorithm. The test examples were generated using the schema proposed by Koulamas [3]for the problem of total tardiness minimization. The obtained results are promising.

Machine and production scheduling under electricity time varying prices

This paper presents two new mathematical models to reduce total energy consumption cost of a single machine manufacturing system. The problem consists of optimizing simultaneously the processing of the jobs and utilization of the machine, each machines state has its own energy consumption and the production shift is composed of a fix number of periods with different energy cost. The first model is an improved formulation of Shrouf et al. (2014) problem that considers a predetermined jobs sequence. Whereas, the second model studies production scheduling on machine and job levels, which proposes an optimal sequence for them by minimizing the occurrence number of each machines state, the optimal allocation of these states during the periods with less energy costs and jobs within the processing state. Finally, difference between these models are discussed based on several numerical examples.

Crane scheduling problem with non-interference constraints in a steel coil distribution centre

This article deals with a parallel machine scheduling problem subject to non-interference constraints. This situation often appears at logistic centres, such as depots, warehouses and stockyards. The analyzed scenario is based on a real case at a distribution centre of steel coils, where two cranes using the same rail must load dispatching trucks. We analyze this case by modelling the situation through a parallel machine perspective and considering two mechanisms to deal with the machine interference, . In the first approach, the machine interference is dealt by scheduling whole trucks. In the second one, we schedule the trucks and the coils within. The proposed mathematical models are able to solve small and medium instances, thus, we develop two genetic algorithms to solve real size instances, allowing the analysis of different storage policies. Results show that the genetic approach is able to find near-optimal solutions independently of the policy, with solutions gap ranging from 10 to 2.1%.

Non-linear Programming Method for Buffer Allocation in Unreliable Production Lines

This paper proposes a new algorithm based on a non-linear programming approach to deal with the buffer allocation problem in the case of unreliable production lines. Processing, failure and repair times are assumed to be random variables exponentially distributed. The proposed approach can be used to solve the different versions of the buffer allocation problem: primal, dual and generalized.

Theoretical Analysis of Workload Imbalance Minimization Problem on Identical Parallel Machines

This paper considers the problem of assigning N non-preemptive jobs to M identical parallel machines or processors as equally as possible. This problem is known as workload imbalance minimization problem. First, we establish that this problem can be formulated as the difference between the maximum and minimum workloads. In other words, it is defined as the minimization of the difference between the workload of the bottleneck machine and the workload of the fastest machine.

A Multi-Level Capacitated Lot-Sizing Problem with energy consideration

This paper reports on a new Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) taking into account the energetic aspect. A linear mixed integer programming model is proposed to solve this problem. Since the MLCLSP is NP-hard ([10]), two heuristics, that provide solutions in a reasonable computational time, are developed. In this study, the horizon is split into T periods where each one is characterized by a duration, an electricity cost, a maximum peak power and a demand. To evaluate the performance of the model and the heuristics, computational experiments are presented and numerical results are discussed.