Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs

Published Online:https://doi.org/10.1287/moor.2016.0833

References

  • Alp O, Huh WT, Tan T (2014) Inventory control with multiple setup costs. Manufacturing Service Oper. Management 16(1):89–103.LinkGoogle Scholar
  • Altintas N, Erhun F, Tayur S (2008) Quantity discounts under demand uncertainty. Management Sci. 54(4):777–792.LinkGoogle Scholar
  • Asmussen S (2003) Applied Probability and Queues, 2nd ed. (Springer, New York).Google Scholar
  • Asmussen S, Perry D (1998) An operational calculus for matrix-exponential distributions, with applications to a Brownian (q, Q) inventory model. Math. Oper. Res. 23(1):166–176.LinkGoogle Scholar
  • Ata B (2006) Dynamic control of a multiclass queue with thin arrival streams. Oper. Res. 54(5):876–892.LinkGoogle Scholar
  • Ata B, Harrison JM, Shepp LA (2005) Drift rate control of a Brownian processing system. Ann. Appl. Probab. 15(2):1145–1160.CrossrefGoogle Scholar
  • Bar-Ilan A, Sulem A (1995) Explicit solution of inventory problems with delivery lags. Math. Oper. Res. 20(3):709–720.LinkGoogle Scholar
  • Bather JA (1966) A continuous time inventory model. J. Appl. Probab. 3(2):538–549.CrossrefGoogle Scholar
  • Baurdoux EJ, Yamazaki K (2015) Optimality of doubly reflected Lévy processes in singular control. Stochastic Process. Appl. 125(7):2727–2751.CrossrefGoogle Scholar
  • Benkherouf L (2007) On a stochastic inventory model with a generalized holding costs. Eur. J. Oper. Res. 182(2):730–737.CrossrefGoogle Scholar
  • Benkherouf L, Bensoussan A (2009) Optimality of an (s, S) policy with compound Poisson and diffusion demands: A quasi-variational inequalities approach. SIAM J. Control Optim. 48(2):756–762.CrossrefGoogle Scholar
  • Bensoussan A, Liu RH, Sethi SP (2005) Optimality of an (s, S) policy with compound Poisson and diffusion demands: A quasi-variational inequalities approach. SIAM J. Control Optim. 44(5):1650–1676.CrossrefGoogle Scholar
  • Cadenillas A, Lakner P, Pinedo M (2010) Optimal control of a mean-reverting inventory. Oper. Res. 58(6):1697–1710.LinkGoogle Scholar
  • Caliskan-Demirag O, Chen Y, Yang Y (2012) Ordering policies for periodic-review inventory systems with quantity-dependent fixed costs. Oper. Res. 60(4):785–796.LinkGoogle Scholar
  • Chao X, Zipkin PH (2008) Optimal policy for a periodic-review inventory system under a supply capacity contract. Oper. Res. 56(1):59–68.LinkGoogle Scholar
  • Constantinides GM (1976) Stochastic cash management with fixed and proportional transaction costs. Management Sci. 22(12):1320–1331.LinkGoogle Scholar
  • Dai JG, Yao D (2013a) Brownian inventory models with convex holding cost, part 1: Average-optimal controls. Stochastic Systems 3(2):442–499.LinkGoogle Scholar
  • Dai JG, Yao D (2013b) Brownian inventory models with convex holding cost, part 2: Discount-optimal controls. Stochastic Systems 3(2):500–573.LinkGoogle Scholar
  • Dixit A (1993) The Art of Smooth Pasting (Harwood Academic Publishers, Chur, Switzerland).Google Scholar
  • Gallego G (1990) Scheduling the production of several items with random demands in a single facility. Management Sci. 36(12):1579–1592.LinkGoogle Scholar
  • Harrison JM (2013) Brownian Models of Performance and Control (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Harrison JM, Taksar MI (1983) Instantaneous control of Brownian motion. Math. Oper. Res. 8(3):439–453.LinkGoogle Scholar
  • Harrison JM, Sellke TM, Taylor AJ (1983) Impulse control of Brownian motion. Math. Oper. Res. 8(3):454–466.LinkGoogle Scholar
  • Hendrix EMT, G-Tóth B (2010) Introduction to Nonlinear and Global Optimization (Springer, New York).CrossrefGoogle Scholar
  • Iglehart DL (1963) Optimality of (s, S) policies in the infinite horizon dynamic inventory problem. Management Sci. 9(2):259–267.LinkGoogle Scholar
  • Iwaniec K (1979) An inventory model with full load ordering. Management Sci. 25(4):374–384.LinkGoogle Scholar
  • Karlin S, Taylor HM (1981) A Second Course in Stochastic Processes (Academic Press, New York).Google Scholar
  • Kuznetsov A, Kyprianou AE, Rivero V (2012) The theory of scale functions for spectrally negative Lévy processes. Lévy Matters II (Springer, Berlin), 97–186.CrossrefGoogle Scholar
  • Kyprianou AE (2006) Introductory Lectures on Fluctuations of Lévy Processes with Applications (Springer, Berlin).Google Scholar
  • Lewis M, Singh V, Fay S (2006) An empirical study of the impact of nonlinear shipping and handling fees on purchase incidence and expenditure decisions. Marketing Sci. 25(1):51–64.LinkGoogle Scholar
  • Lippman SA (1969) Optimal inventory policy with subadditive ordering costs and stochastic demands. SIAM J. Appl. Math. 17(3):543–559.CrossrefGoogle Scholar
  • Muthuraman K, Seshadri S, Wu Q (2015) Inventory management with stochastic lead times. Math. Oper. Res. 40(2):302–327.LinkGoogle Scholar
  • Øksendal B (2003) Stochastic Differential Equations: An Introduction with Applications, 6th ed. (Springer, Berlin).CrossrefGoogle Scholar
  • Ormeci M, Dai JG, Vande Vate J (2008) Impulse control of Brownian motion: The constrained average cost case. Oper. Res. 56(3):618–629.LinkGoogle Scholar
  • Paulsen J (2008) Optimal dividend payments and reinvestments of diffusion processes with both fixed and proportional costs. SIAM J. Control Optim. 47(5):2201–2226.CrossrefGoogle Scholar
  • Perera S, Janakiraman G, Niu S (2016) Optimality of (s, S) policies in EOQ models with general cost structures. Internat. J. Production Econom. Forthcoming. Google Scholar
  • Porteus EL (1971) On the optimality of generalized (s, S) policies. Management Sci. 17(7):411–426.LinkGoogle Scholar
  • Porteus EL (1972) The optimality of generalized (s, S) policies under uniform demand densities. Management Sci. 18(11):644–646.LinkGoogle Scholar
  • Porteus EL (2002) Foundations of Stochastic Inventory Theory (Stanford University Press, Stanford, CA).CrossrefGoogle Scholar
  • Protter MH (1998) Basic Elements of Real Analysis (Springer, New York).Google Scholar
  • Puterman ML (1994) Markov Decision Processes: Discrete Stochastic Dynamic Programming (John Wiley & Sons, New York).CrossrefGoogle Scholar
  • Rubino M, Ata B (2009) Dynamic control of a make-to-order, parallel-server system with cancellations. Oper. Res. 57(1):94–108.LinkGoogle Scholar
  • Scarf H (1960) The optimality of (S, s) policies in the dynamic inventory problem. Mathematical Methods in the Social Sciences, 1959 (Stanford University Press, Stanford, CA), 196–202.Google Scholar
  • Serfozo R (2009) Basics of Applied Stochastic Processes (Springer, Berlin).CrossrefGoogle Scholar
  • Sulem A (1986) A solvable one-dimensional model of a diffusion inventory system. Math. Oper. Res. 11(1):125–133.LinkGoogle Scholar
  • Taksar MI (1985) Average optimal singular control and a related stopping problem. Math. Oper. Res. 10(1):63–81.LinkGoogle Scholar
  • Veatch MH, Wein LM (1996) Scheduling a make-to-stock queue: Index policies and hedging points. Oper. Res. 44(4):634–647.LinkGoogle Scholar
  • Veinott AF Jr (1966) On the optimality of (s, S) inventory policies: New conditions and a new proof. SIAM J. Appl. Math. 14(5):1067–1083.CrossrefGoogle Scholar
  • Ward AR, Kumar S (2008) Asymptotically optimal admission control of a queue with impatient customers. Math. Oper. Res. 33(1):167–202.LinkGoogle Scholar
  • Wein LM (1992) Dynamic scheduling of a multiclass make-to-stock queue. Oper. Res. 40(4):724–735.LinkGoogle Scholar
  • Wu J, Chao X (2014) Optimal control of a Brownian production/inventory system with average cost criterion. Math. Oper. Res. 39(1):163–189.LinkGoogle Scholar
  • Yamazaki K (2017) Inventory control for spectrally positive Lévy demand processes. Math. Oper. Res. 42(1):212–237.LinkGoogle Scholar
  • Yao D, Chao X, Wu J (2015) Optimal control policy for a Brownian inventory system with concave ordering cost. J. Appl. Probab. 52(4):909–925.CrossrefGoogle Scholar
  • Zhou B, Katehakis MN, Zhao Y (2009) Managing stochastic inventory systems with free shipping option. Eur. J. Oper. Res. 196(1):186–197.CrossrefGoogle Scholar
  • Zipkin PH (2000) Foundations of Inventory Management (McGraw-Hill, New York).Google Scholar
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