Sensitivity analysis of a fuzzy multiobjective scheduling problem

This paper concerns sensitivity analysis of a class of complex job shop scheduling problems which are characterized by: (1) a large number of jobs and machines, (2) uncertain jobs processing times, and (3) multiple measures of schedule performance including average weighted tardiness, the number of tardy jobs, the total setup times, the total idle time of machines, and the total flow times of jobs. The base schedule is generated by applying a new fuzzy multiobjective genetic algorithm which takes into consideration batching of the jobs of a similar type, jobs’ lots sizing and load balancing of the machines. The aim of the proposed sensitivity analysis of a generated schedule is to investigate the consequences of prolongations of job processing times on the measures of schedule performance. The processing times are described by triangular fuzzy numbers and their prolongation is done by expanding the supports of fuzzy numbers. The sensitivity analysis is performed through a series of numerical experiments. The effects of prolongations of job processing times on the measures of performance of a generated schedule are recorded and analysed. It is shown that the sensitivity analysis is among the primaries in evaluating the quality of a generated schedule. The sensitivity analysis is used in identifying the critical jobs and the critical machines which have the properties that the prolongations of their processing times produce the largest deteriorations of the performance measures and the overall quality of a generated schedule.     

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

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.     

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.     

Decision aid for allocation of transportation funds to guardrails

We address the need for allocation of resources to run-off-road and fixed-object hazards on immense secondary road systems. In Virginia, there are 95,000km of roadway with uncharacterized hazards in need of guardrail upgrade, installation, or related warning signs or other protection. A decision aid is developed to assist the planner in guardrail resource allocation by accounting for the potential crash severities, traffic exposures, costs of treatment, and other factors. A premise is that no single benefit-cost ratio or selection criterion applies across all localities. The decision aid enables the planner to interpret the variety of benefits and costs in their own units, emphasizing the needs and preferences of individual localities. The paper describes: (1) archiving and comparison of protected and unprotected hazards; (2) regional screening of hazardous corridors and (3) multicriteria benefit-cost analyses of guardrail sites. A case study of guardrail selection is presented.