Equivalent Alternate Solutions for the Tour Scheduling Problem*

Achieving minimum staffing costs, maximum employee satisfaction with their assigned schedules, and acceptable levels of service are important but potentially conflicting objectives when scheduling service employees. Existing employee scheduling models, such as tour scheduling or general employee scheduling, address at most two of these criteria. This paper describes a heuristic to improve tour scheduling solutions provided by other procedures, and generate a set of equivalent cost feasible alternatives. These alternatives allow managers to identify solutions with attractive secondary characteristics, such as overall employee satisfaction with their assigned tours or consistent employee workloads and customer response times. Tests with both full-time and mixed work force problems reveal the method improves most nonoptimal initial heuristic solutions. Many of the alternatives generated had more even distributions of surplus staff than the initial solutions, yielding more consistent customer response times and employee workloads. The likelihood of satisfying employee scheduling preferences may also be increased since each alternative provides a different deployment of employees among the available schedules.     

HEURISTIC LOT-SIZING PERFORMANCE IN A ROLLING-SCHEDULE ENVIRONMENT*

This paper examines the impact of a rolling-schedule implementation on the performance of three of the better known lot-sizing methods for single-level assembly systems——Part-Period-Cost-Balancing, Silver-Meal, and Wagner-Whitin algorithms—and a modified version of the Silver-Meal procedure. The main finding is that under certain conditions the computationally simpler Silver-Meal heuristic can provide cost performance superior to that of the Wagner-Whitin algorithm.     

Tour Scheduling and Task Assignment of a Heterogeneous Work Force: A Heuristic Approach

The dual problem of work tour scheduling and task assignment involving workers who differ in their times of availability and task qualifications is examined in this paper. The problem is presented in the context of a fast food restaurant, but applies equally well to a diverse set of service operations. Developing a week-long labor schedule is a nontrivial problem, in terms of complexity and importance, which a manager spends as much as a full workday solving. The primary scheduling objective (the manager's concern) is the minimization of overstaffing in the face of significant hourly and daily fluctuations in minimum staffing requirements. The secondary objective (the workers’ concern) is the minimization of the sum of the squared differences between the number of work hours scheduled and the number targeted for each employee. Contributing to scheduling complexity are constraints on the structure of work tours, including minimum and maximum shift lengths and a maximum number of workdays. A goal programming formulation of a representative problem is shown to be too large, for all practical purposes, to be solved optimally. Existing heuristic procedures related to this research possess inherent limitations which render them inadequate for our purposes. Subsequently, we propose and demonstrate a computerized heuristic procedure capable of producing a labor schedule requiring at most minor refinement by a manager.     

AN EVALUATION OF ORDER RELEASE MECHANISMS IN A JOB-SHOP ENVIRONMENT

Controlling the flow of material on the shop floor involves releasing and dispatching jobs to meet customer due-date requirements while attempting to keep operating costs low. This report presents an evaluation of five releasing mechanisms and four dispatching rules under various levels of aggregate due-date tightness, shop cost structure, and machine utilization using simulation. The performance criteria of total shop cost, jobs on shop floor, deviation from due dates, and job queue time are collected to demonstrate the interactive nature of releasing and dispatching on shop performance.     

DYNAMIC LOT SIZING FOR A SINGLE-FACILITY MULTIPRODUCT PROBLEM IN A ROLLING-HORIZON ENVIRONMENT

This paper considers a production planning model for a single-facility multiproduct problem where backlogging is not allowed. A planning-horizon theorem is derived. From that theorem, a forward algorithm for finding an optimal solution over a finite horizon and a procedure for selecting the first-period production in a rolling-horizon environment are developed. Computational results from a set of simulation experiments designed to investigate the cost effectiveness of the procedure demonstrate its effectiveness.     

A Mathematical Programming Approach to Production Decisions in the Emerging Aquaculture Industry

The creation of new food sources is an important advancement in the search for solutions to food shortages in both developing and underdeveloped countries. Aquaculture, the production of aquatic animals under controlled conditions, offers exciting new possibilities for alternative protein sources in a wide variety of locales. This paper presents a mathematical programming model designed to aid the manager of an aquaculture facility in production scheduling and the evaluation of new technologies in this rapidly changing environment.     

A PROCUREMENT STAFFING MODEL: ESTIMATING THE SERVICE AND COST IMPACTS OF ALTERING OPERATIONS*

Evaluating the service and cost impacts of altering procurement configurations is a common problem whenever an organization desires to be responsive to the changing needs of the populations being served. Changes relate to the volume of the work load, the degree of responsiveness required, or the technology and processes used. In real-world situations, personnel turnovers, uneven work loads, leaves, training requirements, and use of overtime all contribute to the complexity of the task. When a range of experience over different-sized operations is available, econometric approaches are applicable to estimate economies of scaie and technical substitution possibilities. Otherwise, queuing and job-shop modeling, combined with simulation approaches, can be helpful. This paper presents a case study of the analysis of a proposed reorganization for a large procurement activity in the U.S. Navy. The actual job-shop-scheduling and task-sequencing logic used in practice was modeled. Cost comparisons of four procurement configurations were generated under the constraints that prespecified levels of service be satisfied.     

A Comparative Evaluation of Labor Tour Scheduling Methods

This paper presents an initial study of relative performance for a number of the labor tour scheduling heuristic methods proposed in the literature. These heuristic methods were classified as either linear programming (LP) based or construction. Each of the methods was applied to a tour scheduling problem, subject to a variety of labor demand requirements distributions, with the singular objective being the minimization of total labor hours scheduled. Statistical analysis revealed that effective tour schedule solutions were generated by both LP-based and construction methods. Since the performances of the Keith [13], Morris and Showalter [18], and Bechtold and Showalter [5] methods were superior, their solutions were also compared across a number of secondary criteria. An overall analysis of the performances of these three methods resulted in the identification of a number of important managerial and decision-making issues. We conclude that service operations management should consider integrating these heuristic methods into a decision support system. Finally, suggestions for future research are provided.     

AN IMPLICIT/EXPLICIT APPROACH TO MULTIOBJECTIVE OPTIMIZATION WITH AN APPLICATION TO FOREST MANAGEMENT PLANNING*

Implicit utility/value maximization and explicit utility/value maximization are identified as two major classes of multiobjective optimization methods. Explicit methods have the advantage of being able to fully exploit the power of existing mathematical programming algorithms. A disadvantage is the high information burden they place on the decision maker. Implicit (i.e., interactive) methods have complementary strengths and weaknesses: they require less extensive information but do not lend themselves as easily to use with optimizing algorithms. We develop a hybrid implicit/explicit approach that attempts to combine the advantages of both by embedding within the implicit method a procedure that periodically formulates an approximate explicit representation of the multiobjective problem and then solves it optimally without user interaction. Operationally, this requires the frequent solution of two nonlinear programs. We also report on the implementation of this method in a forest management decision support system. This is a completely microcomputer-based implementation currently undergoing field testing for use in planning the timing and intensity of timber harvests on non-industrial forests in the southeastern United States. The system has been selected as a replacement for an earlier multiobjective program (Harrison and Rosenthal [28]) used by over 1,800 landowners.     

Determining Order Quantity and Selling Price by Geometric Programming: Optimal Solution,Bounds, and Sensitivity*

This paper presents a geometric programming (GP) approach to finding a profit-maximizing selling price and order quantity for a retailer. Demand is treated as a nonlinear function of price with a constant elasticity. The proposed GP approach finds optimal solutions for both no-quantity discounts and continuous quantity discounts cases. This approach is superior to the traditional approaches of solving a system of nonlinear equations. Since the profit function is not concave, the traditional approaches may require an exhaustive search, especially for the continuous discounts schedule case. By applying readily available theories in GP, we easily can find global optimal solutions for both cases. More importantly, the GP approach provides lower and upper bounds on the optimal profit level and sensitivity results which are unavailable from the traditional approaches. These bounding and sensitivity results are further utilized to provide additional important managerial implications on pricing and lot-sizing policies.     

Decision Support for Bus Operations in a Mass Transit System*

A computerized system has been developed for assigning, parking, and dispatching buses so that each operator in the St. Louis metropolitan transit system generally drives the same bus each day. Combinations of optimizing routines, mathematical heuristics, decision rules from experienced personnel, and human intervention are used to manage the bus operations efficiently. This paper describes the tools created for this task and documents significant improvements in maintenance that occurred after the system became operational.     

RADIOISOTOPE PRODUCTION SCHEDULING IN A NUCLEAR REACTOR

A multiperiod mixed integer programming model has been developed for the production scheduling of several grades of a radioisotope in a nuclear reactor. Of special interest is the model's capability to evaluate possible future product “short falls” due to the acceptance of an unforecasted demand sales opportunity. The model is essential to decisions concerning reactor loading after an extended shutdown of several periods for modifications, maintenance, and upgrading.     

Optimal Delivery Time Quotation and Order Sequencing

This paper examines the problem of quoting a common delivery time for several orders. The decision maker responsible for the quote must trade off the cost associated with a long delivery time against the cost of tardy orders that might be induced by a short delivery time. First, an aggregate cost model is investigated where it is assumed that some cost is incurred if the quoted delivery time exceeds a given threshold and the cost of order tardiness is dependent on the order. Both exact and heuristic solution procedures are proposed for this model. Finally, for the situation where the costs cannot be quantified, a bicriteria formulation of the problem is pursued and the set of nondominated solutions is identified.     

Time‐Staged Overtime Staffing for Services with Updated Forecasts and Availabilities

This article develops a framework for staffing in a service environment when multiple opportunities exist for prescheduling overtime prior to the start of a shift. Demand forecasts improve as the shift approaches, while the availability of workers to be scheduled for overtime decreases. First, a single‐shift model is developed and used in computational studies to evaluate the benefits of time‐staged overtime staffing, which include slightly lower costs and significant reductions in unscheduled overtime and outside agents. A multishift model is then developed to consider constraints on consecutive hours worked and minimum rest intervals between shifts. A multishift computational study shows how the benefits of time‐staged overtime staffing depend on problem characteristics when interactions between shifts are considered. The article discusses how single‐shift and multishift models relate to each other and alternative ways the models may be used in practice, including decentralized open shift management and centralized overtime scheduling.     

A METHODOLOGY FOR LABOR SCHEDULING IN A SERVICE OPERATING SYSTEM

In the increasingly competitive services sector, utilization of the labor force can make the difference between profits or losses. Until recently, service operations managers had a limited set of tools, most of them computer-based, for scheduling labor. This paper offers a manual heuristic for labor scheduling that outperforms traditional algorithmic solution approaches. Specifically, this study examines the problem of scheduling employees in service delivery system subject to demand variability. The manual heuristic proposed asigns full-time empolyees to weekly work schedules with the objective of minimizing the total number of labor hours scheduled. The performance of the manual heuristic is compared to the classical algorithmic solution and to a lower bound for a variety of demand distributions and system operating conditions. The heuristic is shown to produce a smaller work force than the classical approach in 106 of the 108 demand-operating condition patterns examined.     

SCHEDULING PARALLEL PROCESSORS WITH SETUP COSTS AND RESOURCE LIMITATIONS

An integer linear programming model is presented for the scheduling of n products on m identical machines. The particular problem studied is one that occurs frequently in the fiberglass and textile industries. The model incorporates setup costs, lost production costs, and overtime costs. Due to the structure of the model, integer solutions can be obtained by explicitly restricting only a small number of the integer variables. This allows those responsible for scheduling to solve realistically sized problems in an efficient manner. Computational results are provided for a set of generated test problems.     

THE TIMING OF LABOR TRANSFERS IN DUAL RESOURCE-CONSTRAINED SYSTEMS: “PUSH” VS. “PULL” RULES*

Altough the dual resource-constrained (DRC) system has been studied, the decision rule used to determine when workers are eligible for transfer largely has been ignored. Some earlier studies examined the impact of this rule [5] [12] [15] but did not include labor-transfer times in their models. Gunther [6] incorporated labour-transfer times into his model, but the model involved only one worker and two machines. No previous study has examined decision rules that initiate labor transfers based on labor needs (“pull” rules). Labor transfers always have been initiated based on lack of need (“push” rules). This study examines three “pull” variations of the “When” labor-assignment decision rule. It compares their performances to the performances of two “push” rules and a comparable machine-limited system. A nonparametric statistical test, Jonckheere's S statistic, is used to test for significance of the rankings of the rules: a robust parametric multiple-comparison statistical test, Tukey's B statistic, is used to test the differences. One “pull” and one “push” decision rule provide similar performances and top the rankings consistently. Decision rules for determining when labor should be transferred from one work area to another are valuable aids for managers. This especially is true for the ever-increasing number of managers operating in organizations that recognize the benefits of a cross-trained work force. Recently there has been much interest in cross-training workers, perhaps because one of the mechanisms used in just-in-time systems to handle unbalanced work loads is to have cross-trained workers who can be shifted as demand dictates [8]. If management is to take full advantage of a cross-trained work force, it need to know when to transfer workers.     

A Game-Theoretic Approach to Quantity Discount Problems*

The traditional quantity discount problem is analyzed from the perspective of game theory, including both noncooperative and cooperative models. For the noncooperative case, the Stackelberg equilibrium is derived. For the cooperative case, the Pareto Optimality criteria are used to find a group of optimal strategies. Both scenarios are illustrated through an example which quantifies the benefits resulting from cooperation between the buyer and the seller for game-theoretic solutions using geometric programming.     

Concepts,Theory, and Techniques PRINCIPLES OF MULTIOBJECTIVE OPTIMIZATION*

This paper attempts to isolate and analyze the principal ideas of multiobjective optimization. We do this without casting aspersions on single-objective optimization or championing any one multiobjective technique. We examine each fundamental idea for strengths and weaknesses and subject two—efficiency and utility—to extended consideration. Some general recommendations are made in light of this analysis. Besides the simple advice to retain single-objective optimization as a possible approach, we suggest that three broad classes of multiobjective techniques are very promising in terms of reliably, and believably, achieving a most preferred solution. These are: (1) partial generation of the efficient set, a rubric we use to unify a wide spectrum of both interactive and analytic methods; (2) explicit utility maximization, a much-overlooked approach combining multiattribute decision theory and mathematical programming; and (3) interactive implicit utility maximization, the popular class of methods introduced by Geoffrion, Dyer, and Feinberg [24] and extended significantly by others.     

Inventory Positioning/Partitioning for Backorders Optimization for a Class of Multi-Echelon Inventory Problems*

Inventory management has undergone significant philosophical changes in recent decades such as the advent of the zero inventory concept. However, as attractive as the concept of minimal inventories may be, it is often unrealistic in application. Attention to basic features of inventory control systems such as order quantities, base stock levels, and reorder points remain crucial to ensure customer service at minimal cost. A nonlinear optimization model for determining base stock levels in a multi-echelon inventory network is presented. Lagrangian relaxation results in (1) newsboy-style relations that provide the optimal solutions, and (2) instantaneous shadow prices for the budget constraint. Sensitivity analysis of this model will facilitate making decisions concerning the desired investment in inventory for the entire system. This model may be solved on standard nonlinear programming software and is generalizable to problems in both production and distribution settings.