Mustapha Nourelfath

Tabu search for the redundancy allocation problem of homogenous series–parallel multi-state systems

Abstract This paper develops an efficient tabu search (TS) heuristic to solve the redundancy allocation problem for multi-state series–parallel systems. The system has a range of performance levels from perfect functioning to complete failure. Identical redundant elements are included in order to achieve a desirable level of availability. The elements of the system are characterized by their cost, performance and availability. These elements are chosen from a list of products available in the market. System availability is defined as the ability to satisfy consumer demand, which is represented as a piecewise cumulative load curve. A universal generating function technique is applied to evaluate system availability. The proposed TS heuristic determines the minimal cost system configuration under availability constraints. An originality of our approach is that it proceeds by dividing the search space into a set of disjoint subsets, and then by applying TS to each subset. The design problem, solved in this study, has been previously analyzed using genetic algorithms (GAs). Numerical results for the test problems from previous research are reported, and larger test problems are randomly generated. Comparisons show that the proposed TS out-performs GA solutions, in terms of both the solution quality and the execution time.

Ant system for reliability optimization of a series system with multiple-choice and budget constraints

Many researchers have shown that insect colonies behavior can be seen as a natural model of collective problem solving. The analogy between the way ants look for food and combinatorial optimization problems has given rise to a new computational paradigm, which is called ant system. This paper presents an application of ant system in a reliability optimization problem for a series system with multiple-choice constraints incorporated at each subsystem, to maximize the system reliability subject to the system budget. The problem is formulated as a nonlinear binary integer programming problem and characterized as an NP-hard problem. This problem is solved by developing and demonstrating a problem-specific ant system algorithm. In this algorithm, solutions of the reliability optimization problem are repeatedly constructed by considering the trace factor and the desirability factor. A local search is used to improve the quality of the solutions obtained by each ant. A penalty factor is introduced to deal with the budget constraint. Simulations have shown that the proposed ant system is efficient with respect to the quality of solutions and the computing time.

Coupling ant colony and the degraded ceiling algorithm for the redundancy allocation problem of series–parallel systems

The redundancy allocation problem (RAP) is a well known NP-hard problem which involves the selection of elements and redundancy levels to maximize system reliability given various system-level constraints. As telecommunications and internet protocol networks, manufacturing and power systems are becoming more and more complex, while requiring short developments schedules and very high reliability, it is becoming increasingly important to develop efficient solutions to the RAP. This paper presents an efficient algorithm to solve this reliability optimization problem. The idea of a heuristic approach design is inspired from the ant colony meta-heuristic optimization method and the degraded ceiling local search technique. Our hybridization of the ant colony meta-heuristic with the degraded ceiling performs well and is competitive with the best-known heuristics for redundancy allocation. Numerical results for the 33 test problems from previous research are reported and compared. The solutions found by our approach are all better than or are in par with the well-known best solutions.

Performance evaluation of multi-state degraded systems with minimal repairs and imperfect preventive maintenance

In this paper, we develop a model for evaluating the availability, the production rate and the reliability function of multi-state degraded systems subjected to minimal repairs and imperfect preventive maintenance. The status of the system is considered to degrade with use. These degradations may lead to decrease in the system efficiency. It is assumed that the system can consecutively degrade into several discrete states, which are characterized by different performance rates, ranging from perfect functioning to complete failure. The latter is observed when the degradation level reaches a certain critical threshold such as the system efficiency may decrease to an unacceptable limit. In addition, the system can fail randomly from any operational or acceptable state and can be repaired. This repair action brings the system to its previous operational state without affecting its failure rate (i.e., minimal repair). The used preventive maintenance policy suggests that if the system reaches the last acceptable degraded state, it is brought back to one of the states with higher efficiency. Considering customer demand as constant, the system is modeled as a continuous-time Markov process to assess its instantaneous and stationary performance measures. A numerical example is given to illustrate the proposed model.

Robust production planning in a manufacturing environment with random yield: A case in sawmill production planning

This paper addresses a multi-period, multi-product sawmill production planning problem where the yields of processes are random variables due to non-homogeneous quality of raw materials (logs). In order to determine the production plans with robust customer service level, robust optimization approach is applied. Two robust optimization models with different variability measures are proposed, which can be selected based on the tradeoff between the expected backorder/inventory cost and the decision maker risk aversion level about the variability of customer service level. The implementation results of the proposed approach for a realistic-scale sawmill example highlights the significance of using robust optimization in generating more robust production plans in the uncertain environments compared with stochastic programming.

A multi-stage stochastic programming approach for production planning with uncertainty in the quality of raw materials and demand

Motivated by the challenges encountered in sawmill production planning, we study a multi-product, multi-period production planning problem with uncertainty in the quality of raw materials and consequently in processes yields, as well as uncertainty in products demands. As the demand and yield own different uncertain natures, they are modelled separately and then integrated. Demand uncertainty is considered as a dynamic stochastic data process during the planning horizon, which is modelled as a scenario tree. Each stage in the demand scenario tree corresponds to a cluster of time periods, for which the demand has a stationary behaviour. The uncertain yield is modelled as scenarios with stationary probability distributions during the planning horizon. Yield scenarios are then integrated in each node of the demand scenario tree, constituting a hybrid scenario tree. Based on the hybrid scenario tree for the uncertain yield and demand, a multi-stage stochastic programming (MSP) model is proposed which is full recourse for demand scenarios and simple recourse for yield scenarios. We conduct a case study with respect to a realistic scale sawmill. Numerical results indicate that the solution to the multi-stage stochastic model is far superior to the optimal solution to the mean-value deterministic and the two-stage stochastic models.

An Integrated Model for Production and Preventive Maintenance Planning in Multi-State Systems

This paper integrates preventive maintenance with tactical production planning in multi-state systems. The proposed model coordinates the production with the maintenance decisions, so that the total expected cost is minimized. We are given a set of products that must be produced in lots on a multi-state production system during a specified finite planning horizon. Planned preventive maintenance, and unplanned corrective maintenance can be performed on each component of the multi-state system. The maintenance policy suggests cyclical preventive replacements of components, and a minimal repair on failed components. The objective is to determine an integrated lot-sizing and preventive maintenance strategy of the system that will minimize the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs, and production costs, while satisfying the demand for all products over the entire horizon. We model the production system as a multi-state system with binary-states, and s-independent components. A method is proposed to evaluate the times and the costs of preventive maintenance and minimal repair, and the average production system capacity in each period. We show how the formulated problem can be solved by comparing the results of several multi-product capacitated lot-sizing problems. For large-size problems, a genetic algorithm is developed to deal with the preventive maintenance selection task in the integrated planning model.

Optimization of series–parallel multi-state systems under maintenance policies

Abstract In the redundancy optimization problem, the design goal is achieved by discrete choices made from components available in the market. In this paper, the problem is to find, under reliability constraints, the minimal cost configuration of a multi-state series–parallel system, which is subject to a specified maintenance policy. The number of maintenance teams is less than the number of repairable components, and a maintenance policy specifies the priorities between the system components. To take into account the dependencies resulting from the sharing of maintenance teams, the universal generating function approach is coupled with a Markov model. The resulting optimization approach has the advantage of being mainly analytical.

Integrating noncyclical preventive maintenance scheduling and production planning for multi-state systems

This paper integrates noncyclical preventive maintenance with tactical production planning in multi-state systems. The maintenance policy suggests noncyclical preventive replacements of components, and minimal repair on failed components. The model gives simultaneously the appropriate instants for preventive maintenance, and production planning decisions. It determines an integrated lot-sizing and preventive maintenance strategy of the system that will minimize the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs, and production costs, while satisfying the demand for all products over the entire horizon. The model is first solved by comparing the results of several multi-products capacitated lot-sizing problems. Then, for large-size problems, a simulated annealing algorithm is developed and illustrated through numerical experiments.

Integrating production, inventory and maintenance planning for a parallel system with dependent components

Abstract This paper deals with the problem of integrating preventive maintenance and tactical production planning, for a production system composed of a set of parallel components, in the presence of economic dependence and common cause failures. Economic dependence means that performing maintenance on several components jointly costs less money and time than on each component separately. Common cause failures correspond to events that lead to simultaneous failure of multiple components due to a common cause. We use the β-factor model to represent common cause failures. This means that we assume two possible causes for system failure: the independent failure of single components, and the simultaneous common cause failure of all components. The suggested preventive maintenance is a T-age group maintenance policy in which components are cyclically renewed all together. Furthermore, between the periodic group replacements, minimal repairs are performed on failed components. We are given a set of products that must be produced by this parallel system in lots during a specified finite planning horizon. The objective is to determine an integrated lot-sizing and preventive maintenance strategy of the system that will minimize the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the entire horizon. Numerical examples are used to illustrate the proposed approach.