An Integrated Inventory and Workforce Planning Markov Decision Process Model with a Variable Production Rate

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In the literature on inventory models, it is common to assume fixed production rates. However, in some cases, such as flexible production systems, this assumption is not realistic. In contrast, variable production rate models rarely define the mechanism through which the production rate is varied, and usually, a per-unit production cost function is assumed. In economics and econometrics, productivity is usually defined by means of the production function, a model that relates productivity to available resources, such as capital and labour. In this paper, we propose an integrated stochastic dynamic lot-sizing and workforce planning model. The novelty here is in modelling the variable production rates explicitly through workforce planning using the production function concept. The proposed model is demonstrated by an example, which shows that the integrated approach leads to an optimal production lot-sizing policy that is different from that obtained without considering workforce planning. This indicates the potential savings that can be obtained via the proposed integrated approach.