Abstract
We present here some recent results in single-product, capacitated production-inventory systems in discrete time. The key results are: (1) structure of optimal policy for single stage systems; (2) analysing via a shortfall process; (3) using simulation to optimize; (4) an approximation using tail probabilities. We consider periodic demand, and multiple stages — serial, distribution and assembly. Related topics of re-entrant flow shops, lead time quotation and value of information are also discussed briefly.
Similar content being viewed by others
References
Asmussen S 1987Applied probability and queues (New York: Wiley)
Bertsekas D P 1987Dynamic programming: Deterministic and stochastic models (Englewood Cliffs, NJ: Prentice-Hall)
Bispo C, Tayur S 1996 Re-entrant flow lines. GSIA Working Paper
Buzacott J, Shanthikumar J G 1993Stochastic models of manufacturing systems (New York: Prentice-Hall)
Clark A, Scarf H 1960 Optimal policies for a multi-echelon inventory problem.Manage. Sci. 6: 474–490
Ciarallo F, Akella R, Morton T E 1994 A periodic review, production-planning model with uncertain capacity.Manage. Sci. 40: 320–332
Cohen M A, Lee H L 1990 Scale economics, manufacturing complexity, and transportation costs on supply chain facility networks.J. Manuf. Oper. Manage. 3: 269–292
Cohen M A, Moon S 1990 Impact of production: Scale economics, manufacturing complexity, and transportation costs on supply chain facility networks.J. Manuf. Oper. Manage. 3: 269–292
Debodt M, Graves S C 1985 Continuous review policies for a multi-echelon inventory problem with stochastic demand.Manage. Sci. 31: 1286–1299
Federgruen A, Zipkin P 1984a Approximations of dynamic multilocation production and inventory problems.Manage. Sci. 30: 69–84
Federgruen A, Zipkin P 1984b Computational issues in an infinite horizon multi-echelon inventory model.Oper. Res. 32: 218–236
Federgruen A, Zipkin P 1986a An inventory model with limited production capacity and uncertain demands I: The average-cost criterion.Math. Oper. Res. 11: 193–207
Federgruen A, Zipkin P 1986b An inventory model with limited production capacity and uncertain demands II: The discounted-cost criterion.Math. Oper. Res. 11: 208–215
Federgruen A, Schweitzer P, Tijms H 1983 Denumerable undiscounted decision processes with unbounded rewards.Math. Oper. Res. 8: 298–314
Gavirneni S, Kapuscinski R, Tayur S 1996 Value of information in capacitated supply chains. GSIA Working Paper, CMU, Pittsburgh, PA 15213
Glasserman P 1991Gradient estimation via perturbation analysis (Norwell, MA: Kluwer)
Glasserman P 1994 Bounds and asymptotics for planning critical safety stocks. Columbia University Working Paper (to appear inOper. Res.)
Glasserman P, Tayur S 1994 The stability of a capacitated, multi-echelon production-inventory system under a base-stock policy.Oper. Res. 42: 913–925
Glasserman P, Tayur S 1995 Sensitivity analysis for base stock levels in multi-echelon production-inventory system.Manage. Sci. 41: 263–281
Glasserman P, Tayur S 1996 A simple approximation for a multistage capacitated production-inventory system.Naval Res. Log. 43: 41–58
Graves S C, Rinnooy Kan A, Zipkin P (eds) 1992Logistics of production and inventory: Handbooks in operations research and management science (Amsterdam: North Holland, Elsevier) vol. 4
Kamesam P V, Tayur S 1993 Algorithms for multistage, capacitated assembly systems with stochastic demand. IBM Report
Karlin S 1960a Dynamic inventory policy with varying stochastic demands.Manage. Sci. 6: 231–258
Karlin S 1960b Optimal policy for dynamic inventory process with stochastic demands subject to seasonal variations.J. Soc. Indust. Appl. Math. 8: 611–629
Kapuscinski R, Tayur S 1996a A capacitated production-inventory model with periodic demand. GSIA Working Paper (to appear inOper. Res.)
Kapuscinski R, Tayur S 1996b 100% Reliable quoted lead times. GSIA Working Paper
Karmarkar U 1987 Lot sizes, lead times and in-process inventories,Manage. Sci. 33: 409–418
Langenhoff L J G, Zijm W H M 1989 An analytical theory of multi-echelon production/distribution systems. Working Paper, Eindhoven University of Technology, Department of Mathematics and Computer Sciences (to appear inStat. Neerlandica)
Lee H L, Billington C, Carter B 1991 Gaining control of inventory and service through design for localization. Working Paper
Morton T 1978 The non-stationary infinite horizon inventory problem.Manage. Sci. 24: 1474–1482
Morton T, Pentico D 1995 The finite horizon non-stationary stochastic inventory problem.Manage. Sci. 41: 334–343
Muckstadt J, Lambrecht M, Luyten R 1984 Protective stocks in multistage production systems.Int. J. Prod. Res. 6: 1001–1025
Prabhu U 1965Queues and inventories (New York: Wiley)
Prabhu U 1980Stochastic storage processes (New York: Springer-Verlag)
Rosling K 1989 Optimal inventory policies for assembly systems under random demands.Oper. Res. 37: 565–579
Scheller-Wolf A, Tayur S 1997 Reducing international risk through quantity contracts. GSIA Working Paper, CMU, Pittsburgh
Schmidt C, Nahmias S 1985 Optimal policy for a two-stage assembly system under random demand.Oper. Res. 33: 1130–1145
Speck C J, Van der Waal J 1991 The capacitated multi-echelon inventory system with serial structure: The average cost criterion. COSOR 91-39, Dept. of Math. and Comp. Sci., Eindhoven Institute of Technology, Eindhoven, The Netherlands
Tayur S 1993 Computing the optimal policy in capacitated inventory models.Stochast. Models 9:
Van Houtum G J, Zijm W H M 1990 Computational procedures for stochastic multi-echelon production systems, Centre for Quantitative Methods, Nederlandse Philips Bedrijven, B.V.
Van Houtum G J, Zijm W H M 1994 On multi-stage production/inventory systems under stochastic demand.Int. J. Prod. Econ. 35: 391–400
Van Houtum G J, Inderfuth K, Zijm W H M 1995 Materials co-ordination in stochastic multiechelon systems, University of Twente, Enschede
Zipkin P 1989 Critical number policies for inventory models with periodic data.Manage. Sci. 35: 71–80
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tayur, S. Recent developments in single product, discrete-time, capacitated production-inventory systems. Sadhana 22, 45–67 (1997). https://doi.org/10.1007/BF02744126
Issue Date:
DOI: https://doi.org/10.1007/BF02744126