Purchasing, production, and sales strategies for a production system with limited capacity, fluctuating sales and purchasing prices

In many industries, the revenue and cost structures of manufacturers are directly affected by the volatility of purchasing and sales prices in the markets. We analyze the purchasing, production, and sales policies for a continuous-review discrete material flow production/inventory system with fluctuating and correlated purchasing and sales prices, exponentially distributed raw material and demand inter-arrival times, and processing time. The sales and purchasing prices are driven by the random environmental changes that evolve according to a discrete state space continuous-time Markov process. We model the system as an infinite-horizon Markov decision process under the average reward criterion and prove that the optimal purchasing, production, and sales strategies are state-dependent threshold policies. We propose a linear programming formulation to compute the optimal threshold levels. We examine the effects of the sales price variation, purchasing price variation, correlation between sales and purchasing prices, customer arrival rate and limited inventory capacities on the system performance measures, through a range of numerical experiments. We also examine under which circumstances the use of the optimal policy notably improves the system profit compared to the use of the buy low and sell high naive policy. We show that using the optimal purchasing, production, and sales policies allow manufacturers to improve their profits when the purchasing and sales prices fluctuate.