Abstract
We propose a continuously deterministic procurement-production-inventory model to optimize the raw material procurement and production problem with raw material inventory and finished products inventory when the raw material purchasing price, the production cost, the raw material inventory holding cost, the finished products holding cost, and the demand rate fluctuate over time. We use Hamilton-Lagrange function and Pontryagin’s maximum principle in optimal control theory to analyze the model, and we obtain the necessary and sufficiency conditions of the optimal solution to the model. We find some optimal policies regarding the procurement and production under some special circumstances.
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References
Khmelnitsky E, Tzur M. Parallelism of Continuous and Discrete-Time Production Planning Problem[J]. IIE Transactions, 2004, 36(7): 611–628.
Luhmer A. A Continuous Time, Deterministic, Nonstationary Model of Economic Ordering[J]. European Journal of Operational Research, 1986, 24(1): 123–135.
Silver E A, Robb D J, Rahnama M R. Random Opportunities for Reduced Cost Replenishments[J]. IIE Transactions, 1993, 25(2): 111–120.
Grubbstrom R, Kingsmanm B. Ordering and Inventory Policies for Step Change in the Unit Item Cost: A Discounted Cash Flow Approach[J]. Management Science, 2004, 50(2): 253–267.
Toktay L B, Wein L M. Analysis of a Forecasting-Production-Inventory System with Stationary Demand[J]. Management Science, 2001, 47(9): 1268–1281.
He Q M, Jewkes E M, Buzacott J. Optimal and Near-Optimal Inventory Control Policies for a Make-to-Order Inventory-Production System[J]. European Journal of Operational Research, 2002, 141(1): 113–132.
Golabi K. Optimal Inventory Policies When Ordering Prices are Random[J]. Operations Research, 1985, 33(3): 575–588.
Arnold J, Minner S, Eidam B. Raw Material Procurement with Fluctuating Prices[EB/OL]. [2007-02-08]. http://www.science direct.com/science .
Arslan H, Graves S C, Roemer T A. A Single-Product Inventory Model for Multiple Demand Classes[J]. Management Science, 2007, 53(9): 1486–1500.
Benjaafar S, EIHafsi M. Production and Inventory Control of a Single Product Assemble-to-Order System with Multiple Customer Classes[J]. Management Science, 2006, 52(12): 1896–1912.
Lin C, Lin Y. The Production Size and Inventory Policy for a Manufacturer in a Two-Echelon Inventory Model[J]. Computers and Operations Research, 2005, 32(5):1181–1196.
Rahman M A A, Sarker B R. Supply Chain Models for an Assembly System with Preprocessing of Raw Materials[J]. European Journal of Operational Research, 2007, 181(2): 733–752.
Sarker B R, Diponegoro A. Optimal Production Plans and Shipment Schedules in a Supply-Chain System with Multiple Suppliers and Multiple Buyers[J]. European Journal of Operational Research, 2009, 194(3): 753–773.
Sethi S L, Thompson G L. Optimal Control Theory: Applications to Management Science and Economics[M]. Dordrecht: Kluwer Academic Publishers, 2000.
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Foundation item: Supported by the National Natural Science Foundation of China (70771079) and the Foundation of China Scholarship Council (2007101668)
Biography: CAO Xiaogang(1982–), male, Ph. D. candidate, research direction: production and operations management.
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Cao, X., Huang, C. & Wen, H. Acquisition and production management with two inventories under fluctuating prices and demand. Wuhan Univ. J. Nat. Sci. 14, 293–298 (2009). https://doi.org/10.1007/s11859-009-0403-6
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DOI: https://doi.org/10.1007/s11859-009-0403-6