The impact of risk aversion and flexibility on stochastic and robust lot sizing decisions
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This paper presents a computational analysis of stochastic programming and robust optimization for solving the multi-item multi-echelon capacitated lot-sizing problem under uncertain demand. For decision makers facing an uncertain production environment the aspects of risk aversion and flexibility are highly relevant. Minimizing worst case overall costs usually comes at higher average case costs, but might be preferable to risk-averse decision makers. Being flexible in production by having a short response time to stochastic events might need additional planning effort, but can lead to significant cost savings during operation in many settings.
We compare two-stage stochastic programming models representing different capabilities of flexibly adjusting production quantities with budget-uncertainty robust optimization models representing different levels of risk aversion. A Benders decomposition approach is tailored to the problem, in order to solve large stochastic models. We investigate the tradeoff between computational time, average- and worst-case performance on a set of out-of-sample scenarios and provide managerial insights by analyzing the structure of the different obtained solutions, such as holding- and backlog costs, number of setups and average lot size.