Budget allocation for permanent and contingent capacity under stochastic demand

We develop a model of budget allocation for permanent and contingent workforce under stochastic demand. The level of permanent capacity is determined at the beginning of the horizon and is kept constant throughout whereas the number of temporary workers to be hired must be decided in each period. Compared to existing budgeting models, this paper explicitly considers a budget constraint. Under the assumption of a restricted budget, the objective is to minimize capacity shortages. When over-expenditures are allowed, both budget deviations and shortage costs are to be minimized. The capacity shortage cost function is assumed to be either linear or quadratic with the amount of shortage, which corresponds to different market structures or different types of services. We thus examine four variants of the problem that we model and solve either approximately or to optimality when possible. A comprehensive simulation study is designed to analyze the behavior of our models when several levels of demand variability and parameter values are considered. The parameters consist of the initial budget level, the unit cost of temporary workers and the budget deviation penalty/reward rates. Varying these parameters produce several trade-off between permanent and temporary workforce levels, and between capacity shortages and budget deviations. Simulation results also show that the quadratic cost function leads to smooth and moderate capacity shortages over the time periods, whereas all shortages are either avoided or accepted when the cost function is linear

A staffing decision support methodology using a quality loss function : a cross-disciplinary quantitative study

Background Understanding the quality loss implications of short staffing is essential in maintaining service quality on a limited budget. Objectives For elaborate financial control on staffing decisions, it is necessary to quantify the cost of the incidental quality loss that a given workload and staffing level entail. Design We develop a quantitative methodology that uses a quality loss function to support staffing decisions. Loss function candidates are compared based on their mean squared error of retest. Data source Our methodology is presented on previously collected data on the nursing service of an adolescent mental health unit. This data was used to test commonly used hypotheses on the quality loss function. Results A quality-centred methodology was developed to support daily staffing decisions, creating a synthesis of the literature on quality and workload measurement based on operations research techniques. For quality loss function development, the quadratic form hypothesis resulted in a mean squared error of 10.93, the patient-to-nurse ratio hypothesis was 8.27, and the ridge estimator was 7.04. Conclusions Using proper data collection, quality data can help in making rational staffing decisions via the development of a quality loss function. Our tests indicate that the quadratic form hypothesis on the quality loss function is weak, whereas the patient-to-nurse hypothesis has potential for practical use

Workload-dependent capacity control in production-to-order systems

The development of job intermediation and the increasing use of the Internet allow companies to carry out ever quicker capacity changes. In many cases, capacity can be adapted rapidly to the actual workload, which is especially important in production-to-order systems, where inventory cannot be used as a buffer for demand variation. We introduce a set of Markov chain models to represent workload-dependent capacity control policies. We present two analytical approaches to evaluate the policies’ due-date performance based on stationary analysis. One provides an explicit expression of throughput time distribution, the other is a fixed-point iteration method that calculates the moments of the throughput time. We compare due-date performance, capacity, capacity switching, and lost sales costs to select optimal policies. We also give insight into which situations a workload-dependent policy is beneficial to introduce. Our results can be used by manufacturing and service industries when establishing a static policy for dynamic capacity planning

Workload-dependent capacity control in production-to-order systems

The development of job intermediation and the increasing use of the Internet allow companies to carry out ever quicker capacity changes. In many cases, capacity can be adapted rapidly to the actual workload, which is especially important in production-to-order systems, where inventory cannot be used as a buffer for demand variation. We introduce a set of Markov chain models to represent workload-dependent capacity control policies. We present two analytical approaches to evaluate the policies’ due-date performance based on stationary analysis. One provides an explicit expression of throughput time distribution, the other is a fixed-point iteration method that calculates the moments of the throughput time. We compare due-date performance, capacity, capacity switching, and lost sales costs to select optimal policies. We also give insight into which situations a workload-dependent policy is beneficial to introduce. Our results can be used by manufacturing and service industries when establishing a static policy for dynamic capacity planning

Workload-dependent capacity control in production-to-order systems

The development of job intermediation and the increasing use of the Internet allow companies to carry out ever quicker capacity changes. In many cases, capacity can be adapted rapidly to the actual workload, which is especially important in production-to-order systems, where inventory cannot be used as a buffer for demand variation. A set of Markov chain models is introduced that are able to represent workload-dependent capacity control policies. Two analytical approaches to evaluate the policies' due date performance based on a stationary analysis are presented. One provides an explicit expression of throughput time distribution, the other is a fixed-point iteration method that calculates the moments of the throughput time. The due date performance, capacity, capacity switching and lost sales costs are compared to select optimal policies. Insights into situations in which a workload-dependent policy can be beneficial are presented. The results can be used by manufacturing and service industries when establishing a static policy for dynamic capacity planning

Stochastic dynamic nursing service budgeting

We address the nursing service budgeting problem from the department manager’s point of view. The model allocates the budget dynamically to three types of nursing care capacities: 1) permanent nurses, 2) temporary nurses, and 3) overtime. The quarterly tactical decisions are the aggregate weekly shift pattern of permanent nurses and the policy for hiring temporary nurses and using overtime. The decisions are optimized with respect to nursing care shortage and a soft-constraint on the annual budget. For the aggregate weekly shift pattern, permanent nurses require a notification lead-time of one quarter to prepare the personal rosters. Our model offers a solution to the nursing service budgeting problem that extends the existing literature by using a Markovian demand model, resolving the anticipation of the operational decisions, and applying general budget as well as shortage penalty functions