The optimization of worker's quantity based on cross-utilization in two departments

Abstract

Cross-utilization of workers has been used in manufacturing and service settings to produce higher throughput, lower inventory, shorter cycle times, and/or improved service without significant additional investment in equipment and labor. However, cross-trained workers may not be as productive as home workers in carrying out their tasks because of a new work environment and unfamiliar protocols in the new department. This leads to the research question: What is the impact of cross-utilization on optimal workers staffing decision. In the paper, we investigate the effect of the worker cost, the penalty factor and the worker efficiency, on a two-department, full-flexibility configuration, and develop a general framework which consists of a two-stage stochastic programming model. The framework may help in trade-offs between worker costs and met demands in both manufacturing and service settings. The Stage 1 optimization model is to minimize the total cost, and the Stage 2 model seeks to minimize the penalty, which is quantified by the unmet demands mathematical expectation during assigning two-skill workers across departments. We derive a general expression for the optimal quantity of workers staffed in two departments when their demands follow corresponding uniform distributions. From the numerical simulations, in the two perfectly symmetrical departments with increasing demand in one department the quantity of workers optimized in the department increases and the total cost increases, while the worker's quantity optimized in the other remains the same. In addition, studies also show that the total cost is more affected by the upper limit of the demand distribution than the lower limit of that.