Staffing a Multiskilled Workforce with Varying Levels of Productivity: An Analysis of Cross-training Policies*

Service operations that utilize cross-trained employees face complex workforce staffing decisions that have important implications for both cost and productivity. These decisions are further complicated when cross-trained employees have different productivity levels in multiple work activity categories. A method for policy analysis in such environments can be beneficial in determining low-cost staffing plans with appropriate cross-training configurations. In this paper, we present an integer linear programming model for evaluating cross-training configurations at the policy level. The objective of the model is to minimize workforce staffing costs subject to the satisfaction of minimum labor requirements across a planning horizon of a single work shift. The model was used to evaluate eight cross-training structures (consisting of 36 unique cross-training configurations) across 512 labor requirement patterns. These structures, as well as the labor requirement patterns, were established based on data collected from maintenance operations at a large paper mill in the United States. The results indicate that asymmetric cross-training structures that permit chaining of employee skill classes across work activity categories are particularly useful.     

Home healthcare integrated staffing and scheduling

Workforce planning for home healthcare represents an important and challenging task involving complex factors associated with labor regulations, caregivers’ preferences, and demand uncertainties. This task is done manually by most home care agencies, resulting in long planning times and suboptimal decisions that usually fail to meet the health needs of the population, to minimize operating costs, and to retain current caregivers. Motivated by these challenges, we present a two-stage stochastic programming model for employee staffing and scheduling in home healthcare. In this model, first-stage decisions correspond to the staffing and scheduling of caregivers in geographic districts. Second-stage decisions are related to the temporary reallocation of caregivers to neighboring districts, to contact caregivers to work on a day-off, and to allow under- and over-covering of demand. The proposed model is tested on real-world instances, where we evaluate the impact on costs, caregiver utilization, and service level by using different recourse actions. Results show that when compared with a deterministic model, the two-stage stochastic model leads to significant cost savings as staff dimensioning and scheduling decisions are more robust to accommodate changes in demand. Moreover, these results suggest that flexibility in terms of use of recourse actions is highly valuable as it helps to further improve costs, service level, and caregiver utilization.     

Schedule Recovery: Unplanned Absences in Service Operations*

The U.S. service sector loses 2.3% of all scheduled labor hours to unplanned absences, but in some industries, the total cost of unplanned absences approaches 20% of payroll expense. The principal reasons for unscheduled absences (personal illness and family issues) are unlikely to abate anytime soon. Despite this, most labor scheduling systems continue to assume perfect attendance. This oversight masks an important but rarely addressed issue in services management: how to recover from short‐notice, short‐term reductions in planned capacity. In this article, we model optimal responses to unplanned employee absences in multi‐server queueing systems that provide discrete, pay‐per‐use services for impatient customers. Our goal is to assess the performance of alternate absence recovery strategies under various staffing and scheduling regimes. We accomplish this by first developing optimal labor schedules for hypothetical service environments with unreliable workers. We then simulate unplanned employee absences, apply an absence recovery model, and compute system profits. Our absence recovery model utilizes recovery strategies such as holdover overtime, call‐ins, and temporary workers. We find that holdover overtime is an effective absence recovery strategy provided sufficient reserve capacity (maximum allowable work hours minus scheduled hours) exists. Otherwise, less precise and more costly absence recovery methods such as call‐ins and temporary help service workers may be needed. We also find that choices for initial staffing and scheduling policies, such as planned overtime and absence anticipation, significantly influence the likelihood of successful absence recovery. To predict the effectiveness of absence recovery policies under alternate staffing/scheduling strategies and operating environments, we propose an index based on initial capacity reserves.     

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.     

Representing employee requirements in labour tour scheduling

In this paper, we use the methodology of simulation to evaluate six approaches for handling employee requirements in an LP-based labour tour scheduling heuristic. We model employee requirements both as minimum acceptable staffing levels—where understaffing is unacceptable—and as target staffing levels—where both under- and overstaffing are acceptable. For each representation of employee requirements, we evaluate forms of the heuristic that use problem-specific and problem-independent information on the costs of employee surpluses and, if appropriate, employee shortages. Over an extensive test data set, the target-staffing approach using problem-specific cost information outperformed all other procedures. Specifically, it generated schedules costing less than 87% of those developed using the approach most commonly found in the literature. Its schedules were also almost 5% cheaper than those of its closest competitor. We discuss the managerial and research implications of the findings and provide suggestions for future research.     

A LOWER BOUND FOR THE SINGLE-LEVEL DYNAMIC HORIZON LOT-SIZING PROBLEM

Conventional production planning methods assume the existence of a medium- or longrange demand horizon. However, demand usually is known over a much shorter range; scheduling decisions must be made within this “decision window,” which rolls forward in time. This paper presents a new lower bound for lot-sizing heuristics in a rolling-horizon framework and compares it to the well-known Wagner-Whitin bound. The new bound indicates heuristic schedules that have costs close to the optimum. Rolling-horizon schedule costs are compared to corresponding static-horizon schedule costs (assuming the whole horizon is known in advance), using the ratio of decision-window size to the natural order cycle as a parameter. For values below unity, the rolling-horizon policy is significantly more costly. For values above one, the two policies have similar costs and actually converge as the parameter value increases.     

Traffic‐Based Labor Planning in Retail Stores

Staffing decisions are crucial for retailers since staffing levels affect store performance and labor‐related expenses constitute one of the largest components of retailers’ operating costs. With the goal of improving staffing decisions and store performance, we develop a labor‐planning framework using proprietary data from an apparel retail chain. First, we propose a sales response function based on labor adequacy (the labor to traffic ratio) that exhibits variable elasticity of substitution between traffic and labor. When compared to a frequently used function with constant elasticity of substitution, our proposed function exploits information content from data more effectively and better predicts sales under extreme labor/traffic conditions. We use the validated sales response function to develop a data‐driven staffing heuristic that incorporates the prediction loss function and uses past traffic to predict optimal labor. In counterfactual experimentation, we show that profits achieved by our heuristic are within 0.5% of the optimal (attainable if perfect traffic information was available) under stable traffic conditions, and within 2.5% of the optimal under extreme traffic variability. We conclude by discussing implications of our findings for researchers and practitioners.     

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.     

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.     

Strategies for Addressing the Nursing Shortage: Coordinated Decision Making and Workforce Flexibility

In this article, we present strategies to help combat the U.S. nursing shortage. Key considerations include providing an attractive work schedule and work environment—critical issues for retaining existing nurses and attracting new nurses to the profession—while at the same time using the set of available nurses as effectively as possible. Based on these ideas, we develop a model that takes advantage of coordinated decision making when managing a flexible workforce. The model coordinates scheduling, schedule adjustment, and agency nurse decisions across various nurse labor pools, each of differing flexibility levels, capabilities, and costs, allowing a much more desirable schedule to be constructed. Our primary findings regarding coordinated decision making and how it can be used to help address the nursing shortage include (i) labor costs can be reduced substantially because, without coordination, labor costs on average are 16.3% higher based on an actual hospital setting, leading to the availability of additional funds for retaining and attracting nurses, (ii) simultaneous to this reduction in costs, more attractive schedules can be provided to the nurses in terms of less overtime and fewer undesirable shifts, and (iii) the use of agency nurses can help avoid overtime for permanent staff with only a 0.7% increase in staffing costs. In addition, we estimate the cost of the shortage for a typical U.S. hospital from a labor cost perspective and show how that cost can be reduced when managers coordinate.     

Turning Over Turnover

Abstract

Human service programs often have major problems ensuring that all direct-care staff positions are filled and keeping staff members after they are hired. Work schedules may have an effect on maintaining the longevity of staff. The purpose of this study was to evaluate the effects of a revised direct-care staff-scheduling system in community homes serving adults with developmental disabilities. The revised direct-care staffing system, which used shift-style schedules, was compared on a variety of measures to existing staffing systems and to a staffing model using married couples and adaptations of the Teaching-Family Model (called Family-Teaching homes). The revised staff-scheduling system was evaluated before and after its implementation and then compared to the Family-Teaching homes using direct-care employee measures of: (1) turnover; (2) position vacancies; (3) number of different employees paid within a pay period; (4) average hourly wages; (5) number of hours worked; (6) average cost for employees per person served; and (7) employee satisfaction. The various staffing approaches were also compared on measures of parent/legal guardian satisfaction and overall program quality. The revised staff-scheduling system was superior when compared to the previous staff-scheduling system on measures of turnover (43% less), vacancies (57% fewer), number of direct-care employees involved in the care of the persons served (13% fewer), and hourly wages (8% more). All of this was achieved without affecting staff-to-client ratios. While these changes were positive, the Family-Teaching homes were associated with significantly better direct-care staff stability and lower costs.     

Reconstructing nurse schedules: Computational insights in the problem size parameters

Managing nursing personnel properly is of critical importance as these resources comprise a vast share of the hospital's operational costs. The organisational support and the managerial policy decisions on the scheduling level are important determinants for the nurses' working conditions and the related quality of care. In this paper, we gain insights and understanding in the consequences and outcomes of various personnel re-rostering characteristics and strategies. We explore the boundaries of the time horizon and the nurse staffing size to consider for the nurse re-rostering problem based on computational experiments in a real-life problem environment.     

Scheduling professionals in the retail pharmacy chain

To control operating costs, a zero-one integer programming model is developed to assist pharmacy staff scheduling decisions. Variable scheduling needs are met by the assignment of relief (mobile) pharmacists to help or temporarily replace full-time pharmacists. Assignments of relief pharmacists over a two-week planning horizon are determined with consideration given to variations in wage rates and travel costs together with the underlying corporate, contractual and operating constraints. The developed model has been applied with considerable success using data collected from a business district in the US located in northern Louisiana related to a national retail chain pharmacy. Forecasting the number of chain retail outlets in the near future has been also performed and the results obtained argue in favor of adopting the model by the entire chain.     

Reexamining the Nurse Scheduling Problem: Staffing Ratios and Nursing Shortages*

Legislators at the state and national levels are addressing renewed concerns over the adequacy of hospital nurse staffing to provide quality care and ensure patient safety. At the same time, the well‐known nursing shortage remains an ongoing problem. To address these issues, we reexamine the nurse scheduling problem and consider how recent health care legislation impacts nursing workforce management decisions. Specifically, we develop a scheduling model and perform computational experiments to evaluate how mandatory nurse‐to‐patient ratios and other policies impact schedule cost and schedule desirability (from the nurses' perspective). Our primary findings include the following: (i) nurse wage costs can be highly nonlinear with respect to changes in mandatory nurse‐to‐patient ratios of the type being considered by legislators; (ii) the number of undesirable shifts can be substantially reduced without incurring additional wage cost; (iii) more desirable scheduling policies, such as assigning fewer weekends to each nurse, have only a small impact on wage cost; and (iv) complex policy statements involving both single‐period and multiperiod service levels can sometimes be relaxed while still obtaining good schedules that satisfy the nurse‐to‐patient ratio requirements. The findings in this article suggest that new directions for future nurse scheduling models, as it is likely that nurse‐to‐patient ratios and nursing shortages will remain a challenge for health care organizations for some time.     

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.     

Interfacing aggregate plans and master production schedules via a rolling horizon feedback procedure

Aggregate planning and master scheduling are two important levels of a hierarchical production planning process. They serve as the front end of production and operations planning and control systems. It is imperative to have the front end well planned and coordinated. In this study, we demonstrate that a rolling horizon feedback procedure can be an effective coordination mechanism for interfacing aggregate planning and master scheduling. Each time the schedule is rolled ahead, the feedback of performance results from master scheduling provides the aggregate planning subsystem useful information for improving its planning activities. Our experiments show that there are at least three factors that make a rolling horizon procedure attractive: (i) the use of a horizon with a fractional portion of a seasonal cycle, (ii) high smoothing costs, and (iii) high setup costs. Using rolling horizons reduces the total aggregate costs in these situations relative to not using rolling horizons. The potential impacts of the rolling-horizon strategy are greater under some circumstances than others.     

An integrated nurse staffing and scheduling analysis for longer-term nursing staff allocation problems

The efficient and effective management of nursing personnel is of critical importance in a hospital's environment comprising a vast share of the operational costs. The adopted nurse workforce practices and policies highly affect the nurses' working conditions and the provided quality of care. Policy decisions on the staffing level have an impact on the outcome of the scheduling level and vice versa. Isolated reasoning typically leads to suboptimal decisions often resulting in ineffective outcomes of care. In order to overcome these inefficiencies, we propose in this paper a new integrative nurse staffing and shift scheduling approach. We test and assess the benefits of our approach in a reallife environment. Moreover, we examine the impact of several personnel policies on the staffing decision.     

Modeling Take-or-Pay Contract Decisions

Long-term purchase contracts for natural resources, such as natural gas, often contain take-or-pay provisions that penalize the buyer for not purchasing (taking) a minimum quantity of output over some period of time. In some contracts for a limited time interval, known as the make-up period, the penalty payments can be credited against future “takes” in excess of the take-or-pay level. Additionally, options to “buy down” or “buy out” existing contracts, or to initiate new contracts, may exist. The purchaser, faced with projected requirements over some planning horizon, must determine purchase levels from a selected set of take-or-pay contracts so as to minimize purchase, inventory holding, penalty costs, contract initiation, and buy-out or buy-down costs. This paper presents a mixed-integer programming model of take-or-pay decisions with and without make-up provisions.     

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.     

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.