Testing the robustness of deterministic models of optimal dynamic pricing and lot-sizing for deteriorating items under stochastic conditions

Many models within the field of optimal dynamic pricing and lot-sizing models for deteriorating items assume everything is deterministic and develop a differential equation as the core of analysis. Two prominent examples are the papers by Rajan et al. (Manag Sci 38:240-262, 1992) and Abad (Manag Sci 42:1093-1104, 1996). To our knowledge, nobody has ever tested whether the optimal solutions obtained in those papers are valid if the real system is exposed to randomness: with regard to demand process as well as with regard to the deterioration process. The motivation is that although the real world is indeed stochastic, it is often more convenient to work with a deterministic decision model providing a nice closed form solution. The crucial thing is of course whether the results derived in the deterministic setting are robust when tested in a stochastic environment. Therefore, in this paper, we will try to expose the model by Abad (1996) and Rajan et al. (1992) to stochastic inputs; however, designing these stochastic inputs such that they as closely as possible are aligned with the assumptions of those papers. We do our investigation through a numerical test where we test the robustness of the numerical results reported in Rajan et al. (1992) and Abad (1996) in a simulation model. Our numerical results seem to confirm that the results stated in these papers are indeed robust when being imposed to stochastic inputs.