Abstract
In this paper, the economic production quantity problem for a single-product single-machine system is extended. It is assumed that annual demand of the product is a function of price set by manufacturer. This extension considers sales revenue, inventory and setup costs as well as a variable cost of production which is a function of the lot size. Several linear and non-linear functions of demand and variable cost are considered in this paper and a global solution methodology is presented for the models developed. Newton’s method is used to find local optima and asymptotic convergence of the solution algorithm to a global optimum is proved. Numerical studies followed by a discussion provide additional insights into the problem.
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References
Abad P.L.: Optimal price and order size for a reseller under partial backordering. Comput. Oper. Res. 28, 53–65 (2001)
Ardalan A.: A comparative analysis of approaches for determining optimal price and order quantity when a sale increases demand. Eur. J. Oper. Res. 84, 416–430 (1995)
Chao X., Chen H., Zheng S.: Joint replenishment and pricing decisions in inventory systems with stochastically dependent supply capacity. Eur. J. Oper. Res. 191, 142–155 (2008)
Chen X., Simchi-Levi D.: Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: the finite horizon case. Oper. Res. 52, 887–896 (2004)
Chen X., Simchi-Levi D: Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: the infinite horizon case. Math. Oper. Res. 29, 698–723 (2004)
Craven B.D.: Modeling inventories in a network. Optim. Lett. 1(4), 401–406 (2007)
Federgruen A., Heching A.: Combining pricing and inventory control under uncertainty. Oper. Res. 47, 454–475 (1999)
Federgruen A., Zipkin P.: An inventory model with limited production capacity and uncertain demands I. The average cost criterion. Math. Oper. Res. 11, 193–207 (1986)
Federgruen A., Zipkin P.: An inventory model with limited production capacity and uncertain demands II. The discounted cost criterion. Math. Oper. Res. 11, 208–215 (1986)
Gallego G., Moon I.: The effect of externalizing setups in the economic lot scheduling problem. Oper. Res. 40(3), 614–619 (1992)
Gallego G., Ozalp O.: Integrating replenishment decisions with advanced demand information. Manag. Sci. 47, 1344–1360 (2001)
Geunes, J., Pardalos, P., Romeijn, E. (eds): Supply Chain Optimization: Applications and Algorithms. Kluwer Academic Publishers, Dordrecht (2002)
Geunes, J., Pardalos, P. (eds): Supply Chain Optimization. Kluwer Academic Publishers, Dordrecht (2003)
Greene J.H.: Production and inventory control handbook. McGraw-Hill, New York (1997)
Harris F.W.: How many parts to make at once, factory. Mag. Manag. 10(2), 135–152 (1913)
Inderfurth K.: Optimal policies in hybrid manufacturing/remanufacturing systems with product substitution. Int. J. Prod. Econ. 90, 325–343 (2004)
Kabirian A.: Hybrid probabilistic search methods for simulation optimization. J. Ind. Syst. Eng., IIIE. 2(4), 259–270 (2009)
Kabirian A., Olafsson S.: Continuous optimization via simulation using golden region search. Eur. J. Oper. Res. 208(1), 19–27 (2011)
Kunreuther H.R., Francois J.: Optimal pricing and inventory decisions for non-seasonal items. Econometrica 39, 173–175 (1971)
Li Q., Zheng S.: Joint inventory replenishment and pricing control for systems with uncertain yield and demand. Oper. Res. 54, 696–705 (2006)
Luenberger D.G.: Linear and nonlinear programming. 2nd edn. Springer, Berlin (2003)
Ozalp O., Wei W.: Inventory control with limited capacity and advanced demand information. Oper. Res. 52, 998–1000 (2004)
Pap E.: Handbook of Measure Theory. Elsevier, North Holland (2002)
Parlar M., Weng Z.K.: Coordinating pricing and production decisions in the presence of price competition. Eur. J. Oper. Res. 170, 211–227 (2006)
Peterson R, Silver E.: Decision Systems for Inventory Management and Production Planning. Wiley, New York (1979)
Phelps R.I.: Optimal Inventory rule for a linear trend in demand with a constant replenishment period. J. Oper. Res. Soc. 31(5), 439–442 (1980)
Ritchie E.: The E.O.Q. for linear increasing demand: a simple optimal solution. J. Oper. Res. Soc. 35(10), 949–952 (1984)
Sharkey T.C.: Network flow problems with pricing decisions. Optim. Lett. 5(1), 71–83 (2011)
Tersine R.J.: Principles of Inventory and Materials Management. North Holland, New York (1982)
Wee H-M.: Joint pricing and replenishment policy for deteriorating inventory with declining market. Int. J. Prod. Econ. 40, 163–171 (1995)
Whitin T.T.: Inventory control and price theory. Manag. Sci. 2, 61–80 (1955)
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Kabirian, A. The economic production and pricing model with lot-size-dependent production cost. J Glob Optim 54, 1–15 (2012). https://doi.org/10.1007/s10898-011-9737-7
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DOI: https://doi.org/10.1007/s10898-011-9737-7