Larry W. Jacobs

Note: A local-search heuristic for large set-covering problems

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.

A simulated annealing approach to the cyclic staff‐scheduling problem

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.

A morphing procedure to supplement a simulated annealing heuristic for cost‐ andcoverage‐correlated set‐covering problems

We report on the use of a morphing procedure in a simulated annealing (SA) heuristicdeveloped for set‐covering problems (SCPs). Morphing enables the replacement of columnsin solution with similar but more effective columns (morphs). We developed this procedureto solve minimum cardinality set‐covering problems (MCSCPs) containing columns whichexhibit high degrees of coverage correlation, and weighted set‐covering problems (WSCPs)that exhibit high degrees of both cost correlation and coverage correlation. Such correlationstructures are contained in a wide variety of real‐world problems including many scheduling,design, and location applications. In a large computational study, we found that the morphingprocedure does not degrade the performance of an SA heuristic for SCPs with low degreesof cost and coverage correlation (given a reasonable amount of computation time), and thatit improves the performance of an SA heuristic for problems with high degrees of suchcorrelations.

Cost analysis of alternative formulations for personnel scheduling in continuously operating organizations

Personnel-scheduling problems for continuously operating organizations have proven to be difficult to solve optimally. As a consequence, a number of alternative approaches have been devised for solving these problems. We provide computational results of a study of the staffing costs obtained using a prominent alternative formulation approach. The results demonstrate that excess staffing costs may result from the use of this approach. We subsequently develop a new local-search heuristic based on the simulated annealing algorithm to generate feasible integer personnel schedules in continuously operating organizations. The solution costs and computational effort associated with the new heuristic are shown to be generally superior to those of branch-and-bound integer programming.

Planning Home Assistance for Aids Patients in the City of Rome, Italy

In allocating resources to health-care services, the main difficulties derive from uncertainty concerning the number of patients who need the service and the level of care required by each patient who is entitled to receive it. I deal with the problem of allocating resources to the home-care service provided to AIDS patients in the city of Rome, Italy, which include medical assistance provided by nurses and doctors and social assistance and accompaniment of patients provided by social workers. A simple linear programming model solves the problem for single organizations, which provide assistance within a given budget, and for public-health authorities, which have to evaluate the results of tentative budgets assigned to home care.

The equivalence of general set-covering and implicit integer programming formulations for shift scheduling

In a recent article we demonstrated that implicit optimal modeling for shift scheduling (P2) has inherent size and execution time advantages over the general set-covering formulation for shift scheduling (P1) [11, 13]. We postulated that the absence of extraordinary overlap (EO) was a requirement for the equivalence of P1 and P2. We have defined EO as the condition in which the earliest and latest starts for a break in one shift are earlier and later than the earliest and latest starts for a break in any other shift(s). In this article, we prove that our earlier postulate was accurate. Additionally, we discuss research extensions and note other scheduling problems for which implicit modeling may be appropriate.

Starting-time decisions in labor tour scheduling: An experimental analysis and case study

Abstract Many service organizations limit the number of daily planning periods in which employees may begin their shifts to a fixed number, S . Even for relatively small values of S , which are quite common in practice, there may be hundreds, thousands or millions of possible subsets of starting times. This paper presents the results of a large experimental study that revealed that, in many instances, only a very small portion of starting-time subsets was capable of providing the minimum workforce size. The importance of effective starting-time selection is further supported by a case study that describes a spreadsheet-based program designed for scheduling customer service representatives in the System Support Center, United States and Canada Group, Radio Network Solutions Group, Land Mobile Products Sector, Motorola.

An interactive, optimization-based decision support system for scheduling part-time, computer lab attendants

The labor tour scheduling problem has attracted much recent research, focusing on the development and evaluation of optimal and heuristic methods to minimize labor costs while satisfying demand for labor. Researchers typically assume that a sufficient labor pool is available. However, service organizations such as fast-food restaurants, grocery stores, and video rental stores, as well as not-for-profit organizations using volunteer workers, typically use a large number of part-time employees with limited availabilities for work. This study presents an interactive decision support system that addresses the conflicting objectives of efficient labor scheduling and accommodating employee needs. The system uses a linear programming model to provide sets of optimal shifts from which employees can construct acceptable weekly schedules; the manager may override the schedule if necessary. The decision support system is used to schedule student computer lab attendants at a major university in an efficient and equitable manner.

Scheduling collection of recyclable material at Northern Illinois University campus using a two-phase algorithm

This paper considers the problem of collecting recyclable materials in a large university campus with many buildings. It models the problem as a vehicle routing problem with additional constraints and applies a two-phase algorithm in order to provide a heuristic solution.

Eliminating redundant columns in continuous tour scheduling problems

This paper presents a procedure for eliminating redundant columns in generalized set-covering formulations (GSCFs) of continuous tour scheduling problems that are characterized by labor requirements of zero in some planning periods. We describe the procedure and discuss properties of certain scheduling environments that may affect the appropriateness of its use. The procedure was applied to actual labor requirements and problem characteristics associated with 27 United Airlines Airport Stations and reduced the number of columns (tours) by an average of 56%.