Research On Production-Inventory Management Under Fluctuating Raw Material Prices

According to the observation and analysis of two steel manufacturers from the southeast of US we found that fluctuation is the common problem faced by many firms, especially those dealing with raw commodities. While the price factor is further influenced by inventory management, the task of managing raw material acquisition becomes more complex. That is because:if the raw material were pur-chased too early, the manufacturer may incur much unnecessary holding costs and miss the chance of purchasing at much cheaper price in the future; while if the raw material were purchased too late, the firm may incur costly backlogging cost and lose the opportunity of purchasing at much cheaper price at earlier time.Based on the above problem, this paper considers a procurement, production and inventory management problem faced by a make-to-order manufacturer. The main contribution of the article is as follows:1. Simultaneously considering raw material inventory and finished product inventory under fluctuating prices and demand, where, the raw material price, pro-duction cost, the inventory holding cost rate of raw material and finished products and the demand rate of finished products vary from the time. We assume that the finished products are not allowed to be backlogged, and both the ordering cost and the production lead time are zero. According to the Pontryagin maximum principle of the optimal control theory we derive the necessary and sufficient conditions of the optimal procurement and production policy. We find that when the raw material price and production cost increase slowly with the time, the manufacturer should execute the JIT procurement and production policy; while when the raw material and production cost increase fast with the time, the optimal policy is executing the procurement and production at the full speed in the very beginning of the planning horizon called bang-bang policy. Through the computation we expose some chang-ing trends of the average raw material and finished products inventory levels and the fluctuating rate of raw material and finished products when some parameters change, which can compensate the drawback of our theoretical results.2. We conduct the control problem of two echelons inventory including three inventories under dynamic prices and demand. Producing one unit of finished prod-uct needsα1 units of raw material RM1 andα2 units of raw material RM2. Two kinds of raw material price, production cost, all the inventory cost rate and demand rate all fluctuate over time. We analyze the necessary and sufficient conditions of the optimal procurement and production decision and obtain the optimal inven-tory policy under some special conditons, and we also extend the results to that of circumstance of two echelons including N inventories.3. We study the control problem of multi-echelons production-inventory system under dynamic prices and demand. Producing one unit of finished product needs a, units of semi-finished product SFPi (i=1,2,…, M). Producing one unit of semi-finished product SFPi needs bij units of raw material RMj (j=1,2,…, N). All the raw material price, processing cost of semi-finished product, production cost of finished product, inventory cost rate and finished product demand rate fluctuate over time. We analyze the necessary and sufficient conditions of the optimal procurement, processing and production decision and obtain the optimal inventory policy under some assumption conditons.4. We study the inventory problem including raw material inventory and prod-uct inventory, where raw material price obeys the continuous time, discrete state Markov processes, and the demand of products obey the compound Poisson distri-bution. We find that the optimal procurement and production policy are order-up-to policy and produce-up-to policy dependent on the current raw material price, re-spectively. We obtain two sufficient conditions for the Markov price process, and if the two conditions are satisfied the order-up-to level and produce-up-to level will be decreasing in the current raw material prices.