Dynamic ordering decisions with approximate learning of supply yield uncertainty

Abstract

We consider the real-life problem of a coach bus manufacturer located in Turkey, facing the problem of setting ordering quantities for a part procured from an unreliable supplier, where the number of items delivered is binomially distributed with an unknown yield parameter, p. We use the well-defined finite-horizon planning context with deterministic demand per period, purchasing, holding, and shortage costs to investigate the effectiveness of a fill-rate based approximate learning scheme in comparison to an exact Bayesian learning scheme, where observations on the supplier's delivery performance are used to update the assumed distribution of p. We formulate the exact optimal learning problem as a Bayes-adaptive Markov decision process and solve the corresponding finite horizon stochastic dynamic program to provide insights on the value of online learning in comparison to the unrealistic perfect information (PI) and no information (NT) benchmarks. We contrast the performance of the so-called Bayesian Updating (BU) policy to other practical approaches such as using an assumed/guessed value of p and implementing a constant safety stock. Noting the significant value of learning, we finally study the effectiveness of an approximate learning formulation that does not enjoy the asymptotic consistency and convergence properties but involves much lower computational burden, and demonstrate its confounding performance, at times beating the BU policy with exact Bayesian updates.