Alice Yalaoui

Reliability allocation problem in a series–parallel system

Abstract In order to improve system reliability, designers may introduce in a system different technologies in parallel. When each technology is composed of components in series, the configuration belongs to the series–parallel systems. This type of system has not been studied as much as the parallel–series architecture. There exist no methods dedicated to the reliability allocation in series–parallel systems with different technologies. We propose in this paper theoretical and practical results for the allocation problem in a series–parallel system. Two resolution approaches are developed. Firstly, a one stage problem is studied and the results are exploited for the multi-stages problem. A theoretical condition for obtaining the optimal allocation is developed. Since this condition is too restrictive, we secondly propose an alternative approach based on an approximated function and the results of the one-stage study. This second approach is applied to numerical examples.

Integrated production planning and preventive maintenance in deteriorating production systems

Abstract The traditional production planning model based upon the famous linear programming formulation has been well documented. However, the integration of preventive maintenance planning in the same model is a recent problem. This paper proposes an extended linear programming model as a hybrid approach for computing the optimum production plan with minimum total cost. The dual objective problem of production planning and maintenance is treated into a mixed integer linear program. This program is not only considering cases of multi-lines, multi-periods and multi-items but also taking into account the deterioration of the lines. This deterioration is represented in the model as a reduction of production lines capacities in function of the time evolution. Maintenance operations are supposed to provide lines in an operational state as good as new, i.e. with a maximum capacity. Through the study of the models limits, it is shown that the proposed approach can deal with a broader range of problems than that of Aghezzaf and Najid (2008) [3]. An optimal relaxation technique based on the polyhedral theory is developed to improve the computational time and expand the limits of the proposed model. Also, a “Fix and Relax heuristic” is developed for complex problems. Their computation time and their difference are computed referring to the same lower bound and the same considerations as those presented by Aghezzaf and Najid. It is proved through more than 880 several simulations for each model with different capacities and different setup costs, that this approach can solve large size problems with moderate computational time and gap.

Efficient immune algorithm for optimal allocations in series-parallel continuous manufacturing systems

This paper uses an immune algorithm (IA) meta-heuristic optimization method to solve the problem of structure optimization of series-parallel production systems. In the considered problem, redundant machines and buffers in process are included in order to attain a desirable level of availability. A procedure which determines the minimal cost system configuration is proposed. In this procedure, multiple choices of producing machines and buffers are allowed from a list of product available in the market. The elements of the system are characterized by their cost, estimated average up and down times, productivity rates and buffers capacities. The availability is defined as the ability to satisfy the consumer demand which is represented as a piecewise cumulative load curve. The proposed meta-heuristic is used as an optimization technique to seek for the optimal design configuration. The advantage of the proposed IA approach is that it allows machines and buffers with different parameters to be allocated.

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.

The bi-objective two-dimensional loading vehicle routing problem with partial conflicts

The two-dimensional loading vehicle routing problem with partial conflicts combines two NP-hard problems: the classical vehicle routing problem and the two-dimensional bin-packing problem with partial conflicts. This new variant of transportation problems is inspired from hazardous materials classification and compatibilities, where some materials can be partially conflicting. In this case, they can be loaded together but an additional constraint on the distance separating them must be respected. We propose in this paper an NSGA-II algorithm to perform a bi-objective study in which the minimization of the total cost of transportation as well as the load balancing between different routes in terms of used area of vehicles are the considered objectives. The first results for this new problem are presented, using benchmarks available in the literature that have been adapted to deal with the problem. Moreover, the adding value of path relinking is proved with different statistical measurements.

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.

Reliability Allocation Problem in Series-Parallel Systems: Ant Colony Optimization

Reliability optimization is an important step in industrial systems design. In order to develop a reliable system, designers may introduce different redundant technologies with the same functionality in parallel. In this paper, each technology is assumed to be composed of series components. The obtained configuration belongs to the series-parallel systems. The presented tool is for the design or the improvement of such systems, in order to minimize the system cost with a reliability constraint. The aim is to find the reliability to allocate to each component in order to minimize the total cost, such that the global system reliability verifies a minimal level constraint. This problem is known to be NP-hard. In this paper, a metaheuristic approach, based on the Ant Colony Optimization technics ACO, is used in order to improve an existing approach. The experimental results, based on randomly generated instances, outperform the one of previous method dedicated to this problem.

The Vehicle Routing Problem with Conflicts

Abstract The Vehicle Routing Problem (VRP) is a classical problem for which several exact and approximation methods were proposed. In real life applications, such as in Hazardous Material transportation, transported items may be incompatible. This paper summarizes the first methods developed for this extension called the Vehicle Routing Problem with Conflicts (VRPC). This study presents a mathematical model, heuristics, metaheuristics (an Iterated Local Search (ILS) and a Greedy Randomized Adaptive Search Procedure – Evolutionary Local Search (GRASP-ELS)). A lower bound is also introduced in this article.

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.