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.     

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.     

USING SHORT-TERM DEDICATION FOR SCHEDULING MULTIPLE PRODUCTS ON PARALLEL MACHINES

In a multiproduct, parallel machine environment, it may be beneficial to dedicate one or more of the machines to a single product for consecutive time periods. However, previous lot-sizing and scheduling models usually do not allow for such short-term dedication. This paper presents a mixed-integer programming model that allows for short-term dedication in scheduling parallel machines serving multiple products with dynamic demands. It also describes a Lagrangian-based algorithm for solving such scheduling problems. An experiment verifies the effectiveness of the algorithm and demonstrates the importance of allowing for short-term dedication. Capacity utilization, one of six factors investigated, greatly affects the use of dedication. A strong interaction effect between the number of machines and the number of products is also seen with respect to the usefulness of short-term dedication. A measure of estimated production frequency incorporates these two factors along with magnitudes of periodic demands. This measure has a strong relationship with the amount of short-term dedication used in solutions. Operations managers employing parallel machines could use the experimental results in deciding whether to use short-term dedication to reduce costs.     

AN OPTIMIZATION-BASED METHODOLOGY FOR RELEASE SCHEDULING

Operational-level scheduling decisions on the factory floor include the release policy and the dispatching rule. Recent work by researchers suggests that factory performance depends heavily on the release policy. Several heuristic factory release rules have been developed that generate release decisions based on the status of the bottleneck machine. The heuristic rules perform very well in reducing the work-in-process inventory. However, factory output schedules generated by these rules generally fail to match the demand pattern, creating excessive finished goods inventory and/or excessive backorders. To overcome these difficulties, a computationally efficient integer programming model is proposed for release scheduling.     

DYNAMIC OPERATING RULES FOR MOTEL RESERVATIONS

When customers call a motel or a hotel to reserve a particular room (large, small, suites, single-bed, double-bed, etc.) decisions have to be made concerning the allocation of the available rooms. This paper presents a model for determining the maximum number of specific bookings that should be made for each type of room. The objective is to maximize the expected contribution to profit per rental day. The model considers the distribution of requests for reservations over time as well as cancellations. Also included are the effects of late (unbooked) arrivals and overbookings.     

A COMPARISON OF PRODUCTION SCHEDULING POLICIES ON COSTS,SERVICE LEVEL,AND SCHEDULE CHANGES

We consider a single product, single level, stochastic master production scheduling (Mps ) model where decisions are made under rolling planning horizons. Outcomes of interest are cost, service level, and schedule stability. The subject of this research is the Mps control system: the method used in determining the amount of stock planned for production in each time period. Typically, Mps control systems utilize a single buffer stock. Here, two Mps dual-buffer stock systems are developed and tested by simulation. We extend the data envelopment analysis (dea ) methodology to aid in the evaluation of the simulation results, where Dea serves to increase the scope of the experimental design. Results indicate that the dual-buffer control systems outperform existing policies.     

OPTIMAL SCHEDULING FOR INVESTMENT OF EXCESS CASH

A method is presented for the scheduling of a company's investments of its predictable, short-term, excess cash. The problem is structured in a way that leads to a fairly simple dynamic programming algorithm. The method is very flexible with regard to the type of investments considered; no structural properties of rates of return or availability are made except that they are predictable. The method allows the choice of holding to maturity or not and the choice can differ for different types of investments. A bank constraint, which fixes the average bank balance over the planning period, is added and the method of solution obtained.     

PRODUCTION SCHEDULING OF CONTINUOUS FLOW LINES: MULTIPLE PRODUCTS WITH SETUP TIMES AND COSTS

The problem of production planning and setup scheduling of multiple products on a single facility is studied in this paper. The facility can only produce one product at a time. A setup is required when the production switches from one type of product to another. Both setup times and setup costs are considered. The objective is to determine the setup schedule and production rate for each product that minimize the average total costs, which include the inventory, backlog, and setup costs. Under the assumption of a constant production rate, we obtain the optimal cyclic rotation schedule for the multiple products system. Besides the decision variables studied in the classical economic lot scheduling problem (ELSP), the production rate is also a decision variable in our model. We prove that our solutions improve the results of the classical ELSP.     

PRACTICE‐FOCUSED RESEARCH ISSUES FOR SCHEDULING SYSTEMS*

Scheduling research has had relatively little impact on manufacturing practice, yet within the last several years, there has been an explosive growth in the development and implementation of computer‐based scheduling systems in industry. Changes in the environment have increased the stakes and the opportunities for the results of scheduling research to influence manufacturing competitiveness. This paper draws on field‐related experiences with the development and implementation of scheduling systems to propose high‐impact research topics.     

A FRAMEWORK FOR MACHINE SCHEDULING PROBLEMS WITH CONTROLLABLE PROCESSING TIMES

This is a study of single and parallel machine scheduling problems with controllable processing time for each job. The processing time for job j depends on the position of the job in the schedule and is a function of the number of resource units allocated to its processing. Processing time functions and processing cost functions are allowed to be nonlinear. The scheduling problems considered here have important applications in industry and include many of the existing scheduling models as special cases. For the single machine problem, the objective is minimization of total compression costs plus a scheduling measure. The scheduling measures include makespan, total flow time, total differences in completion times, total differences in waiting times, and total earliness and tardiness with a common due date for all jobs. Except when the total earliness and tardiness measure is involved, each case the problem is solved efficiently. Under an assumption typically satisfied in just-in-time systems, the problem with total earliness and tardiness measure is also solved efficiently. Finally, for a large class of processing time functions; parallel machine problems with total flow time and total earliness and tardiness measures are solved efficiently. In each case we reduce the problem to a transportation problem.     

A MODEL-BASED DECISION SUPPORT SYSTEM FOR SCHEDULING LUMBER DRYING OPERATIONS

Raw lumber must be dried to a specified level of moisture content before it can be used to make furniture. This paper deals with a model-based decision support system (DSS) for a local furniture manufacturing company to assist its management in scheduling lumber drying operations. In addition to buying ready-to-use dried lumber from vendors at a premium, the company processes raw lumber in house using two production process that require various lengths of processing time in predryers and dry-kilns. Given the demand for various types of dried lumber over a specified planning horizon, the processing times and costs for each production process, technological restrictions, and management policies, the problem of interest is to satisfy the demand at a minimum cost. The DSS incorporates the mathematical formulation of this problem, is user friendly, maintains model and data independence, and generates the necessary reports, including loading and unloading schedules for the equipment.     

AN EVALUATION OF ORDER PICKING POLICIES FOR MAIL ORDER COMPANIES

This paper is concerned with the problem of order picking in mail order companies. Order picking is the retrieval of items from their warehouse storage locations to satisfy customer orders. Five order picking policies, strict order, batch, sequential zone, batch zone, and wave, are evaluated using labor requirements, processing time, and customer service as performance measures. A simulation model was developed to investigate these picking policies in a mail order environment. Prior research has focused on the study of individual picking policies. This study extends the prior research by evaluating multiple picking policies under varying operating conditions. The results of the study seem to indicate that (1) wave picking and batch picking perform well across the range of operating conditions considered in this study, and (2) sequential zone and batch zone picking do not perform well, especially as the order volume increases. However, the benefits and drawbacks to each picking policy must be taken into account. The key to effective implementation of an order picking system is to match the firm's business strategy, capabilities, technology, and space requirements with an order picking policy that maximizes the benefits of order picking to the firm and its customers.     

DYNAMIC COURSE SCHEDULING FOR COLLEGE FACULTY VIA ZERO-ONE PROGRAMMING*

This paper formulates a multi-period course scheduling problem as a zero-one programming model. Under various constraints, and for a planning horizon of several terms, the model seeks to maximize: (1) the faculty course preferences in assigning faculty members to courses, and (2) the faculty time preferences in allocating courses to time blocks, via a two-stage optimization procedure. The multi-period structure of the model, strengthened by the explicit inclusion of a wide-range of constraints designed to represent various special requirements has enabled the model to capture the many dynamic features of the course scheduling problem at the college level. As such, it can be used not only for long-range or short-range departmental planning, but also as a suitable framework toward the development of a larger, and all-inclusive course scheduling decision system. The paper begins with a brief review of several related studies and then presents a multi-period scheduling model and its extensions. Some numerical examples are used to test the model, and the authors' experience, resulting from such tests with several computer codes, is reported. The possible directions for future research are also suggested.     

A HEURISTIC ALGORITHM FOR RESOURCE LEVELING IN MULTI-PROJECT,MULTI-RESOURCE SCHEDULING

The utility of conventional project management techniques, such as PERT and CPM, is hampered by significant and realistic network attributes and managerial considerations. There are many situations which involve more than one project and numerous resources. Of major concern in such situations is the reduction of the maximum quantity of each required resource. The algorithm presented here is capable of scheduling the individual activities in multiple projects with multiple resources and leveling the overall quantity of each resource which is required. The basis of the algorithm is a sequencing procedure for examining various combinations of activity start times. The measure of effectiveness for each combination is the sum of the squares of the required quantity of each resource in each time period.     

A DECISION THEORY APPROACH TO PRIORITY DISPATCHING FOR JOB SHOP SCHEDULING

Recent developments in the design of job shop scheduling systems have inspired a new approach to priority dispatching. The basis for the approach is in elementary decision theory: at each decision juncture define the alternative courses of action, evaluate the consequences of each alternative according to a given criterion, and choose the best alternative. The experimental results of a simulated single machine queueing system reinforce earlier findings that a decision theory approach represents a significant advance over conventional priority dispatching.     

SIMULTANEOUS BATCHING AND SCHEDULING FOR CHEMICAL PROCESSING WITH EARLINESS AND TARDINESS PENALTIES

We consider the problem of determining the allocation of demand from different customer orders to production batches and the schedule of resulting batches to minimize the total weighted earliness and tardiness penalties in context of batch chemical processing. The problem is formulated as a mixed-integer nonlinear programming model. An iterative heuristic procedure that makes use of the network nature of the problem formulation is presented to approximate an optimal solution. An algorithm polynomial in the number of batches to produce is also presented that optimally solves the problem under special cost structures.     

AN IMPROVED HEURISTIC FOR STAFFING TELEPHONE CALL CENTERS WITH LIMITED OPERATING HOURS

Many telephone call centers that experience cyclic and random customer demand adjust their staffing over the day in an attempt to provide a consistent target level of customer service. The standard and widely used staffing method, which we call the stationary independent period by period (SIPP) approach, divides the workday into planning periods and uses a series of stationary independent Erlang‐c queuing models—one for each planning period—to estimate minimum staffing needs. Our research evaluates and improves upon this commonly used heuristic for those telephone call centers with limited hours of operation during the workday. We show that the SIPP approach often suggests staffing that is substantially too low to achieve the targeted customer service levels (probability of customer delay) during critical periods. The major reasons for SIPP‘ s shortfall are as follows: (1) SIPP's failure to account for the time lag between the peak in customer demand and when system congestion actually peaks; and (2) SIPP’ s use of the planning period average arrival rate, thereby assuming that the arrival rate is constant during the period. We identify specific domains for which SIPP tends to suggest inadequate staffing. Based on an analysis of the factors that influence the magnitude of the lag in infinite server systems that start empty and idle, we propose and test two simple “lagged” SIPP modifications that, in most situations, consistently achieve the service target with only modest increases in staffing.     

A MARKET UTILITY‐BASED MODEL FOR CAPACITY SCHEDULING IN MASS SERVICES

Only a small set of employee scheduling articles have considered an objective of profit or contribution maximization, as opposed to the traditional objective of cost (including opportunity costs) minimization. In this article, we present one such formulation that is a market utility‐based model for planning and scheduling in mass services (MUMS). MUMS is a holistic approach to market‐based service capacity scheduling. The MUMS framework provides the structure for modeling the consequences of aligning competitive priorities and service attributes with an element of the firm's service infrastructure. We developed a new linear programming formulation for the shift‐scheduling problem that uses market share information generated by customer preferences for service attributes. The shift‐scheduling formulation within the framework of MUMS provides a business‐level model that predicts the economic impact of the employee schedule. We illustrated the shift‐scheduling model with empirical data, and then compared its results with models using service standard and productivity standard approaches. The result of the empirical analysis provides further justification for the development of the market‐based approach. Last, we discuss implications of this methodology for future research.     

MODELING LEARNING CURVE AND LEARNING COMPLEMENTARITY FOR RESOURCE ALLOCATION AND PRODUCTION SCHEDULING*

Research on learning effects in mathematical programming models for optimum resource allocation has called attention to the difficulty in solving such models in their original nonlinear form. In this paper, systematically varying sizes of linear segments are designed to approximate productivity changes along the learning curve, and a single separable linear programming model is developed. With production complementarity and learning transmission between products, a more realistic resource allocation and production scheduling problem emerges. Two cases of learning transmissions are considered, and the model design process, which defines a decision problem that can be solved by a simplex algorithm, is demonstrated.     

COMMON DUE-WINDOW SCHEDULING

In this paper, we solve common due-window scheduling problems within the just-in-time window concept, i.e., scheduling problems including both earliness and tardiness penalties. We assume that jobs share the same due window and incur no penalty as long as they are completed within the due window. We further assume that the earliness and tardiness penalty factors are constant and that the size of the window is a given parameter. For cases where the location of the due window is a decision variable, we provide a polynomial algorithm with complexity O(n * log (n)) to solve the problem. For cases where the location of the due window is a given parameter, we use dynamic programming with pseudopolynomial complexity to solve the problem.