A joint pricing and lot sizing models with discount: A geometric programming approach

Abstract

We propose a novel joint pricing and lot sizing model to enable manufacturers plan production and pricing. These types of models have proven to be very popular and are collectively known as the Joint Pricing and Lot sizing Models. We include a discount factor in our model to increase profit for the manufacturer. Our proposed model relies on the fact that demand influences production cost indirectly, while it is dependent on price and the discount offered. By considering the form of demand and production cost, it is apparent that the presented model is a Signomial Geometric Programming problem. We obtain optimal solutions for price, lot size and discount factor by applying the modified transformation method of geometric programming. Numerical examples, which include sensitivity analysis of the objective function and parameters, illustrate our model. References C. J. Corbett and X. de Groote. A supplier's optimal quantity discount policy under asymmetric information. Management Science, 46(3):444--450, 2000. R. J Duffin, E. L Peterson, and C. Zener. Geometric programming, Theory and Application. John Wiely and Sons, 1967. J. R. Freeland. Coordination strategies for production and marketing in a functionally decentralized firm. AIIE Transactions, 12:126--132, 1982. Woon J.Lee, Daesoo Kim, and A. Cabot. Optimal demand rate, lot sizing, and process reliability improvement decisions. IIE Transactions, 28:941--952, 1996. http://cat.inist.fr/?aModele=afficheN&cpsidt=2490704. Daesoo Kim and Woon J. Lee. Optimal joint pricing and lot sizing with fixed and variable capacity. European Journal of Operational Research, 109(1):212--227, 1998. http://www.sciencedirect.com/science/article/B6VCT-3TMR6M6-H/2/2d166a9b5fc0a9a27e923c495f256663. Woon J. Lee. Determining order quantity and selling price by geometric programming. Decision Sciences, 24:76--87, 1993. doi:10.1111/j.1540-5915.1993.tb00463.x. Woon J. Lee and Daesoo Kim. Optimal and heuristic decision strategies for integrated product and marketing planning. Decision Sciences, 24(6):1203--1213, 1993, doi:10.1111/j.1540-5915.1993.tb00511.x. Seyed J. Sajadi, Maryam Orouge, and M. B. Aryanezhad. Optimal production and marketing planning. Computational Optimization and Applications, 30(2):195--203, 2005. http://portal.acm.org/citation.cfm?id=1062644.1062668. Richard J. Tersine. Principles of Inventory And Materials Management. PTR Prentice Hall, Englewood Cliffs, New Jersey 07632, 1994. S. Viswanathan and Q.Wang. Discount pricing decisions in distribution channels with price sensitive demand. European Journal of Operational Research, 149(3):571--587, 2003. http://ideas.repec.org/a/eee/ejores/v149y2003i3p571-587.html. Prakash L. Abad. Determining optimal selling price and the lot size when the supplier offers all-unit quantity discounts. Decision Sciences, 3(19):622--634, 1988. Z. Kevin Weng. Channel coordination and quantity discounts. Management Sciences, 41(9):1509--1522, 1995. http://www.jstor.org/view/00251909/di012962/01p03025/0. Prakash L. Abad. Supplier pricing and lot sizing when demand is price sensitive. European Journal of Operational Research, (78):334--354, 1994. http://cat.inist.fr/?aModele=afficheN&cpsidt=3309143. Charles S. Beightler. Applied Geometric Programming. John Wiely and Sons, 1976. C. W. Chiang, J. Fitzsimmons, Z. Huang, and S. Li. A game theoretic approach to quantity discount problem. Decision Sciences, 25(1):153--168, 1994. doi:10.1111/j.1540-5915.1994.tb00521.x.