Exploiting structure in adaptive dynamic programming algorithms for a stochastic batch service problem

The purpose of this paper is to illustrate the importance of using structural results in dynamic programming algorithms. We consider the problem of approximating optimal strategies for the batch service of customers at a service station. Customers stochastically arrive at the station and wait to be served, incurring a waiting cost and a service cost. Service of customers is performed in groups of a fixed service capacity. We investigate the structure of cost functions and establish some theoretical results including monotonicity of the value functions. Then, we use our adaptive dynamic programming monotone algorithm that uses structure to preserve monotonicity of the estimates at each iterations to approximate the value functions. Since the problem with homogeneous customers can be solved optimally, we have a means of comparison to evaluate our heuristic. Finally, we compare our algorithm to classical forward dynamic programming methods.