Original Article Computing nonstationary   s, S inventory policies via genetic algorithm Kannapha Amaruchkul* and Surapong Auwatanamongkol Graduate School of Applied Statistics, National Institute of Development Administration (NIDA), Bangkapi, Bangkok, 10240 Thailand. Received 14 February 2012; Accepted 29 October 2012 Abstract A periodic-review inventory model with nonstationary stochastic demand under an (s, S) policy is considered. We apply a genetic algorithm to solve for reorder points and order-up-to levels which minimize an expected total cost. A closed-form exact expression for the expected cost is obtained from a nonstationary discrete-time Markov chain. In our numerical experiments, our approach performs very well. Keywords: stochastic model applications; genetic algorithm; nonstationary inventory management Songklanakarin J. Sci. Technol. 35 (1), 115-121, Jan. - Feb. 2013 1. Introduction We consider a periodic-review single-item inventory problem. Demand process is nonstationary; specifically, demand in each time period is independent but not necessar- ily identically distributed. Demand distribution depends on the time period. Nonstationary demand process is commonly found in practice; e.g., repair parts of a machine in which the demand rate varies with time, parts for preventive mainte- nance where the maintenance schedule is pre-specified, and a seasonal retail product. In this article, we address an (s, S) inventory policy: if the inventory position is less than or equal to the reorder point, denoted by s, then an order is placed so that the inventory position is brought back to the order-up-to level, denoted by S. The policy is easy to implement in practice. The control parameters, s and S, are chosen such that an expected total inventory cost over a finite planning horizon is minimized. We investigate the use of a genetic algorithm (GA) to heuristically solve the optimization problem, in which the objective function is the expected cost and the decision variables are reorder points and order-up-to levels for all time periods. From numerical experiments, our method is very close to optimal for most problem instances. For a real-world problem instance in which the optimal policy could not be computed, our heuristic outperforms other heuristics of which variants may be found in practice. There are many papers concerning the (s, S) policy under the assumption of the stationary demand process. For instance, Sobel & Zhang (2001) show that the (s, S) policy is optimal. Zheng & Federgruen (1991) propose an algorithm to find the optimal s and S. Nevertheless, there are fewer papers on the (s, S) policy under the assumption of the non- stationary demand; e.g., Bollapragada & Morton (1999) propose a heuristic procedure to find the control parameters. They first transform the nonstationary problem into a sta- tionary problem, in which a demand distribution is identical throughout time period, and a parameter of the demand dis- tribution is averaged over a pre-specified length of time. Then, they apply the algorithm in Zheng & Federgruen (1991) to find the control parameters. Another related problem in which demand is non- stationary (time-varying) but deterministic, known as the dynamic lot sizing problem, has been solved by several solution procedures, including meta-heuristics such as tabu search, GA and simulated annealing; see Jans & Degraeve (2007) for a review. To the best of our knowledge, this article * Corresponding author. Email address: kamaruchkul@gmail.com http://www.sjst.psu.ac.th