In this note we describe a local‐search heuristic (LSH) for large non‐unicost set‐covering problems (SCPs). The new heuristic is based on the simulated annealing algorithm and uses an improvement routine designed to provide low‐cost solutions within a reasonable amount of CPU time. The solution costs associated with the LSH compared very favorably to the best previously published solution costs for 20 large SCPs taken from the literature. In particular, the LSH yielded new benchmark solutions for 17 of the 20 test problems. We also report that, for SCPs where column cost is correlated with column coverage, the new heuristic provides solution costs competitive with previously published results for comparable problems. © 1995 John Wiley & Sons, Inc.
This article presents the application of a simulated annealing heuristic to an NP‐complete cyclic staff‐scheduling problem. The new heuristic is compared to branch‐and‐bound integer programming algorithms, as well as construction and linear programming‐based heuristics. It is designed for use in a continuously operating scheduling environment with the objective of minimizing the number of employees necessary to satisfy forecast demand. The results indicate that the simulated annealing‐based method tends to dominate the branch‐and‐bound algorithms and the other heuristics in terms of solution quality. Moreover, the annealing algorithm exhibited rapid convergence to a low‐cost solution. The simulated annealing heuristic is executed in a single program and does not require mathematical programming software. © 1993 John Wiley & Sons, Inc.
This paper presents a compact integer-programming model for large-scale continuous tour scheduling problems that incorporate meal-break window, start-time band, and start-time interval policies. For practical scheduling environments, generalized set-covering formulations (GSCFs) of such problems often contain hundreds of millions of integer decision variables, usually precluding identification of optimal solutions. As an alternative, we present an implicit integer-programming model that frequently has fewer than 1,500 variables and can be formulated and solved using PC-based hardware and software platforms. An empirical study using labor-requirement distributions for customer service representatives at a Motorola, Inc. call center was used to demonstrate the importance of having a model that can evaluate tradeoffs among the various scheduling policies.integer programming, implicit formulation, workforce scheduling
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This study used a factorial experimental design and a new modeling methodology to investigate the impact of a number of labor scheduling flexibility alternatives and labor requirements characteristics on labor utilization within a tour scheduling environment. Break-placement flexibility and shift-length flexibility were found to be extremely effective in improving labor utilization for all labor requirement distributions used. Flexibility with respect to the number of days included in a tour schedule resulted in substantial improvement in labor utilization for all labor requirements distributions exhibiting daily and/or weekly variation. Surprisingly, virtually no improvement in labor utilization was achieved for any labor requirement distribution by the removal of requirements for consecutive days off. In addition, almost no improvement was found by allowing the shift start time to vary across the working days included in tours. High labor requirement amplitude was found to have a strong adverse effect on labor utilization while longer operational days were associated with improved labor utilization for all labor requirement distributions. We discuss the implications of these results for service operations management and provide suggestions for future research.Subject Areas: Mathematical Programming and Production/Operations Management.
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