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.     

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.     

A Stochastic Goal Program for Employee Scheduling*

Deterministic goal programs for employee scheduling decisions attempt to minimize expected operating costs by assigning the ideal number of employees to each feasible schedule. For each period in the planning horizon, managers must first determine the amount of labor that should be scheduled for duty. These requirements are often established with marginal analysis techniques, which use estimates for incremental labor costs and shortage expenses. Typically, each period in the planning horizon is evaluated as an independent epoch. An implicit assumption is that individual employees can be assigned to schedules with as little as a single period of work. If this assumption violates local work rules, the labor requirements parameters for the deterministic goal program may be suboptimal. As we show in this research, this well-known limitation can lead to costly staffing and scheduling errors. We propose an employee scheduling model that overcomes this limitation by integrating the labor requirements and scheduling decisions. Instead of a single, externally determined staffing goal for each period, the model uses a probability distribution for the quantity of labor required. The model is free to choose an appropriate staffing level for each period, eliminating the need for a separate goal-setting procedure. In most cases this results in better, less costly decisions. In addition, the proposed model easily accommodates both linear and nonlinear under- and overstaffing penalties. We use simple examples to demonstrate many of these advantages and to illustrate the key techniques necessary to implement our model. We also assess its performance in a study of more than 1,700 simulated stochastic employee scheduling problems.     

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.     

Scheduling with Sequencing Flexibility*

This study examines the effects of sequencing flexibility on the performance of rules used to schedule operations in manufacturing systems. The findings show that taking advantage of even low levels of sequencing flexibility in the set of operations required to do a job results in substantial improvement in the performance of scheduling rules with respect to mean flowtime. Differences in the mean flowtime measure for various rules also diminish significantly with increasing sequencing flexibility. Performance improvements additionally result for such due-date related performance measures as mean tardiness and the proportion of jobs tardy. At high levels of sequencing flexibility, some nonparametric scheduling rules outperform the shortest processing time rule in terms of the mean flowtime criterion. Rules based on job due dates also outperform rules based on operation milestones in terms of tardiness related criteria at high levels of sequencing flexibility. The implications of these findings for the design of manufacturing systems and product design are noted.     

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.     

Fundamental Insights into Part Family Scheduling: The Single Machine Case

A simulation study was conducted to investigate the behavior of family scheduling procedures in a dynamic dispatching environment. Two scheduling rules that incorporate setup avoidance mechanisms (FCFS-F and SPT-F) and two that do not (FCFS and SPT) were applied to a single machine. The scheduling environment was varied by controlling several important factors: the machine utilization, the number of setup configurations (families), the size of the family setup times relative to the job run times, the frequency by which members of the part families were released for processing, and the distribution of job interarrival and job run times. The major results from the study are the following: (1) The degree of stability in the system is the most influential factor with respect to mean flow time and flow time variance. Under low variance service and interarrival time distributions, the impact of scheduling rule selection is minor. (2) Conversely, under unstable scheduling situations, family scheduling procedures can have a substantial impact. (3) Clear interaction effects are noticed between all factors. The environment most conducive to family scheduling is characterized by high resource utilization, low setup-to-run time ratio, few part families, and erratic job arrivals. (4) Under conditions favorable to family scheduling, setup avoiding procedures can be used to increase output while at the same time reduce the mean and variance of flow time. (5) The shortest processing time rule (SPT) performs well with respect to mean flow time when relative setup times are small. Overall, however, SPT-F generates the lowest mean flow time while FCFS-F produces the lowest flow time variance. This study shows that scheduling procedures that consider setups in their structure can outperform rules that do not under many different operating conditions. However, the magnitude of this advantage very much depends on the scheduling environment. The results also highlight the fact that it may be better to try to reshape the manufacturing environment than worry about selecting the correct scheduling rule. If the environment cannot be stabilized, then the choice of a setup avoiding procedure, allocation of families to machines, and setup reduction become important issues.     

An Evaluation of Tour Scheduling Heuristics with Differences in Employee Productivity and Cost

This study focuses on the manpower tour scheduling problem using data from a lockbox system of a commercial bank. The lockbox system uses employees who differ in productivity, hourly cost, number of available working hours per week, and days-off constraints. These specific problem characteristics require a more general problem formulation and solution procedure for the manpower tour scheduling problem than addressed in previous research. Four heuristic methods for solving the problem (three developed here and a simple round-up procedure) are tested on a set of forty problems. The results of this study show the effort to develop sophisticated heuristic methods for this class of problems is well justified.     

A Study of Labor Allocation Strategies in Cellular Manufacturing

Current research studies in cellular manufacturing have considered environments constrained only by the machine resource, when in fact the flexibility of manufacturing cells is derived mainly from its allocation of the labor resource. This research specifically examines the labor resource in cellular manufacturing, also known as group technology (GT), through a series of simulation experiments on a hypothetical GT shop and recommends conditions under which different labor allocation strategies may be appropriate. The effects of various product routings and scheduling policies on labor allocation are also examined.     

An Investigation of Scheduling Policies in a Dual-Constrained Manufacturing Cell*

In previous group scheduling studies, labor has essentially been ignored by assuming that enough labor is assigned to each machine in the cell. In reality, however, management usually does not have the resources to employ a laborer at each machine in the cell (i.e., machines need to share labor). Both labor scheduling and group scheduling heuristics need to be administered to manage the cell effectively. This study develops and examines scheduling procedures for a dual-constrained (i.e., machine and labor) manufacturing cell. Eleven decision rules are developed and tested under 16 different experimental conditions. The experimental factors used are interarrival time distribution, cell load, setup-to-run-time ratio, and transfer-to-run-time ratio. Results show that interarrival time distribution and cell load have the greatest impact on the performance of the cell. This suggests that effective production planning aimed at reducing job arrival variation and leveling the cell load can substantially improve cell performance. Among the experimental factors, setup and transfer-to-run-time ratio factors had the strongest influence on the rankings of the decision rules. These rankings were fairly robust across all experimental conditions and performance measures. The results also indicated that the inclusion of labor as a contraint in the cell had a significant impact on the performance of several group scheduling heuristics. Finally, it was shown that the best performing decision rules consider both transfer time and subfamily setup times.     

Intelligent Procedures for Intra‐Day Updating of Call Center Agent Schedules

For nearly all call centers, agent schedules are typically created several days or weeks before the time that agents report to work. After schedules are created, call center resource managers receive additional information that can affect forecasted workload and resource availability. In particular, there is significant evidence, both among practitioners and in the research literature, suggesting that actual call arrival volumes early in a scheduling period (typically an individual day or week) can provide valuable information about the call arrival pattern later in the same scheduling period. In this paper, we develop a flexible and powerful heuristic framework for managers to make intra‐day resource adjustment decisions that take into account updated call forecasts, updated agent requirements, existing agent schedules, agents' schedule flexibility, and associated incremental labor costs. We demonstrate the value of this methodology in managing the trade‐off between labor costs and service levels to best meet variable rates of demand for service, using data from an actual call center.     

Reducing Surgical Ward Congestion Through Improved Surgical Scheduling and Uncapacitated Simulation

High surgical bed occupancy levels often result in heightened staff stress, frequent surgical cancellations, and long surgical wait times. This congestion is in part attributable to surgical scheduling practices, which often focus on the efficient use of operating rooms but ignore resulting downstream bed utilization. This paper describes a transparent and portable approach to improve scheduling practices, which combines a Monte Carlo simulation model and a mixed integer programming (MIP) model. For a specified surgical schedule, the simulation samples from historical case records and predicts bed requirements assuming no resource constraints. The MIP model complements the simulation model by scheduling both surgeon blocks and patient types to reduce peak bed occupancies. Scheduling guidelines were developed from the optimized schedules to provide surgical planners with a simple and implementable alternative to the MIP model. This approach has been tested and delivered to planners in a health authority in British Columbia, Canada. The models have been used to propose new surgical schedules and to evaluate the impact of proposed system changes on ward congestion.     

Practical Implications of Preference‐Based Conference Scheduling

Conference scheduling involves organizing presentations into sessions which are assigned to time periods and rooms. This includes assuring a feasible utilization of time periods and rooms, and avoiding individual schedule conflicts. The problem increases in complexity by considering the preferences of presenters: for time periods, for rooms, etc. A greater level of complexity comes from considering the preferences of conference attendees, which we define as preference‐based conference scheduling (PBCS). This article provides a structure on which PBCS problems are founded, including empirical demonstration of solution techniques. In addition, real‐world strategic planning issues of flexibility and preference detail are explored.     

IMPLICIT OPTIMAL AND HEURISTIC LABOR STAFFING IN A MULTIOBJECTIVE,MULTILOCATION ENVIRONMENT*

This paper presents a tractable set of integer programming models for the days-off scheduling of a mix of full- and part-time employees working α to β days/week (cycle) in a multiple-objective, multiple-location environment. Previous models were formulated to specifically schedule part-time employees working either two or three days per week. These models were intractable because they required complete employee schedule information. The new models are deemed implicit optimal since they are required to supply only essential information. While the number of variables in previous models is an exponential increasing function of β-α, the size of three of the new models is independent of α and β. The first three models developed here (as in [18]) deal with the trade-offs between idle time, the number of employees required to work at multiple “locations,” and the size of the total labor pool. The inherent flexibility of the implicit modeling approach is illustrated by the presentation of various modifications of the basic models. These modifications permit the use of preference weights on the number of employee work days/week (cycle) or the minimization of payroll costs where differential pay rates exist. These latter models may also be formulated such that idle time is ignored, constrained or minimized. The execution time for the implicit models (on a CDC CYBER 730 computer with commercially available software) averaged well under five seconds on 1200 trial problems for the type of application considered in [18]. A solution was obtained in less than 46 seconds of CPU time for a trial problem which would have required over 1.4 million integer variables with previous models. The availability of optimal solutions was invaluable in the development of two heuristics designed to deal with the trade-offs of [16]. In an experimental analysis a previous heuristic produced results which averaged from 74 to 508 percent above optimum across six experimental conditions. The comparable new heuristic produced results which averaged from 3 to 8 percent above optimum for the same experimental conditions. The paper concludes by developing a framework to integrate the results of this research with the tour scheduling problem and by identifying several other areas for related research.     

Interactive Job Shop Scheduling: An Experiment

An experiment is discussed in which three computer-aided, interactive job shop scheduling approaches are compared using an interactive job shop scheduling simulator (JOB) developed for the project. All three approaches use a combination of computer and human capabilities to develop job shop schedules, but differ in terms of the timing and degree of human involvement required. The three scheduling approaches are (1) the successive approach, (2) the interactive approach, and (3) the semi-interactive approach. The successive approach is characterized by the computer scheduling all work orders without any human intervention. The interactive approach is distinguished by the human scheduling one work order at a time until all work orders are scheduled. The schedule is developed interactively by the person who must simultaneously consider work-order scheduling needs and machine group load capacities. The semi-interactive approach may be viewed as a combination of the successive and interactive approaches. Work orders are automatically scheduled one at a time using the successive approach criteria, but with prespecified machine-group load thresholds. As long as the load threshold is not exceeded, the successive approach is used to schedule work orders. When a threshold is exceeded, the algorithm (successive approach) pauses and human rescheduling (interactive approach) is required to rectify the overload situation. A second (reallocation) phase, identical for all three approaches, is used to overcome any scheduling problems generated in phase one. Experimental results based on nine different performance criteria (including scheduling time, makespan, machine group utilization, and work-in-process inventory) and 45 experimental runs indicate that there are differences between the results produced by the three scheduling approaches. The interactive approach yields the best overall scheduling results, but the other two approaches are clearly better than the interactive approach in some situations. The success of the interactive approach indicates that it is usually best for the human scheduler to become involved early in the computer-based job shop scheduling process.     

一种基于带熵的遗传算法在车间调度中的应用

车间调度问题是现代制造业快速发展的瓶颈因素,因此提高车间调度的效率和有效性就成了生产制造领域大家普遍关注的问题。现行的车间调度问题遗传算法已经不能满足现代制造业快速发展的要求,多因为其静态性或效率差,表现为早熟或收敛停滞,究其根本原因还是GA的最优参数的选取问题,本文引入了信息熵的概念,以动态调整交叉概率和变异概率,从而给出了可以快速获得最优解的自适应遗传算法,并对此改进算法加以实例仿真验证其有效性。     

ANALYSIS OF ALTERNATIVE SCHEDULING POLICIES FOR HOSPITAL NURSES

The persistent shortage of nurses adversely affects the productivity, quality of care, and operating costs in most acute care hospitals. Aggravating the shortage are high nurse turnover rates, approaching 200% in some institutions. Policies to ensure adequate staffing levels and provide more attractive work schedules are alleged to improve nurse retention. However, their cost is seldom discussed. We compared expected nursing expense and workforce requirements to staff eight medical and surgical nursing units of a large hospital for 1 month, under 12 different scheduling policies alleged to improve turnover. Using simulation and an integrated staffing and scheduling methodology, we found that the expected nursing wages and workforce requirements for some policies differed by as much as 33%. In this hospital, the expected labor costs for certain policies could erode the benefits expected from improved retention. In contrast, other policies appear to allow high utilization of nursing resources, enhancing the expected benefits of reduced turnover with significant reductions in expenses for labor, recruiting, training, and fringe benefits.     

Scheduling with flexible process plans

When a process planning module is embedded into the scheduling paradigm, the solution space of the scheduling problem is expanded due to possible generation and use of alternative process plans, i.e. the combined system of process planning and scheduling is equivalent to scheduling with flexible process plans. This flexibility provides a potential for obtaining improved schedules, but it increases the complexity of the structure of the scheduling problem. This paper describes a solution approach for the integrated system and analyses the performance of a new algorithm under various simulated scenarios.     

The Value of Using Scheduling Information in Planning Material Requirements*

Current research and practice in the field of production and inventory planning is dominated by hierarchical, material requirements planning-based methods. The objective of this research is to determine the merits of a major redirection for the design of manufacturing planning systems—a direction that more directly exploits the capabilities of modern computer technology. We test the relative performance of two fundamentally different classes of manufacturing planning systems: (1) those that make no use of sequencing and scheduling information in the planning of material deliveries (for example, traditional MRP-based systems), and (2) those that use sequencing and scheduling information to plan delivery of materials. We first derive an analytical expression for the expected benefit (in terms of flow time reduction) of using scheduling information for a single machine system. We then describe and test a simple heuristic for predicting the improvement that could be realized in more complicated multimachine systems, under certain conditions. Results from controlled simulation experiments, over a wide range of operating environments, suggest that although the value of scheduling information is influenced by the operating environment, it could be substantial.     

Practical scheduling for call center operations

A practical spreadsheet-based scheduling method is developed to determine the optimal allocation of service agents to candidate tour types and start times in an inbound call center. A stationary Markovian queueing model with customer abandonment is employed to determine required staffing levels for a sequence of time intervals with varying call volumes, handling times, and relative agent availabilities. These staffing requirements populate a quadratic programming model for determining the distribution of agent tours that will maximize the fraction of offered calls beginning service within a target response time, subject to side constraints on tour type quantities. The optimal distribution is scaled to reflect the total number of scheduled agents, and a near-optimal integer solution is derived using rounding thresholds found by successive one-dimensional searches. This novel approach has been successfully implemented in large service centers at Qwest Communications and could easily be adapted to other operational environments.