An Operations Management Approach to Mitigating the Labor Shortage Problem

Project: Research

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In current operations management literature, the variable cost is usually assumed to be a linear function of the order/production quantity. A linear variable cost is applicable to the retail industry, where products are ordered from the manufacturer. However, in the manufacturing industry where products are made, the linear variable cost assumption can be troublesome because the labor cost is not necessary a linear function of production quantity. The labor standards acts of many countries, including China and the US, state that employees who work overtime must be paid much more than their standard salary. Hence, the variable cost is a piece-wise linear convex function of the production quantity.Given this cost structure, manufacturers need to make their production, pricing and capacity investment decisions carefully to minimize their total cost or maximize their total profit over a long term planning horizon. We will investigate two models in this project and assume in both that the manufacturer faces stochastic demand. In the first model, the manufacturer dynamically coordinates its production and pricing decisions to maximize its total expected profit over a finite/infinite horizon. Our aim is to characterize the structure of the optimal production and pricing strategy in this model. As overtime work can increase supply, and price can decrease (or increase) demand, we hope to determine when overtime work is necessary, when price should play a role in adjusting the demand, and the interplay between these two effects.In the second model, the manufacturer dynamically adjusts its capacity by determining the number of employees and makes production decisions in each period to maximize its total expected profit over a finite/infinite horizon. In many industries, employees receive a basic weekly ( or monthly) salary, which must be paid even if they work fewer than 40 hours in a workweek. To reduce this fixed cost, some employers ask employees to work overtime rather than risk employing too many workers. This strategy explains why many workers are laid off in times of economic recession while those who remain employed are required to work overtime. We will characterize the optimal capacity adjustment and production strategy of this model. More specifically, we will examine the tradeoff between capacity adjustment and overtime work and try to find the balance between these two. We will also explore how this balance depends on the various costs in this system.


Project number9041961
Grant typeGRF
Effective start/end date1/01/1422/12/16