Abstract
A review is undertaken of lower bounding methodologies for lot-sizing production/inventory models. This is done for both dynamic discrete time demand and continuous review, constant demand situations. The view is taken that lower bounds are an essential ingredient in the evaluation of heuristics when optima are unknown or too computationally complex to comfortably evaluate. Several directions of future research are suggested.
Similar content being viewed by others
References
P. Afentakis and B. Gavish, Optimal lot-sizing algorithms for complex product structures, Oper. Res. 34(1986)237–249.
P. Afentakis, B. Gavish and U. Karmarkar, Computationally efficient optimal solutions to the lotsizing problem in multistage assembly systems, Manag. Sci. 30(1984)222–239.
E. Arkin, D. Joneja and R. Roundy, Computational complexity of uncapacitated multi-echelon production planning problems, Oper. Res. Lett. 8(1989)61–66.
D.R. Atkins, A lower bound to the dynamic assembly problem, Working Paper 1259, University of B.C., Vancouver, B.C., Canada (1988).
D.R. Atkins and P. Iyogun, A lower bound on a class of coordinated inventory/production problems, Oper. Res. Lett. 6(2)(1987)63–67.
D.R. Atkins and P. Iyogun, A lower bound and an efficient heuristic for multi-stage inventory distribution systems, Working Paper, University of B.C., Vancouver, B.C., Canada (1988).
D.R. Atkins and P. Iyogun, Periodic versus “can-order” policies for coordinated multi-item inventory systems, Manag. Sci. 34(1988)791–796.
D.R. Atkins and P. Iyogun, A heuristic with lower bound performance guarantee for the multiproduct dynamic lot-size problem, IIE Trans. 20(1988)369–373.
A.J. Clark and H. Scarf, Optimal policies for a multi-echelon inventory problem, Manag. Sci. 6(4)(1960)475–490.
A.J. Clark and H. Scarf, Approximate solutions to a simple multi-echelon inventory problem, in:Studies in Applied Probability and Management Science, ed. K.J. Arrow, S. Karlin and H. Scarf (Stanford University Press, Stanford, CA, 1962), pp. 88–110.
B. Deuermeyer and L.B. Schwarz, A model for the analysis of system service level in warehouse/retailer distribution systems, in:Multi-level Production/Inventory Control Systems (TIMS Studies in Management Science 16), ed. L. Schwarz (Elsevier, New York, 1981).
A. Federgruen and P. Zipkin, Approximations of dynamic multilocation production and inventory problems, Manag. Sci. 30(1984)69–84.
A. Federgruen, H. Gronevelt and H.C. Tijms, Coordinated replenishments in a multi-item inventory system with compound Poisson demands, Manag. Sci. 30(1984)344–357.
L. Gelders, J. Maes, J. McClain and L. Van Wassenhove, Mathematical programming approaches to solve lot-sizing problems, Working Paper, Katholieke Universiteit Leuven, Leuven, Belgium (1986).
P. Iyogun, Lower bounds for production/inventory problems by cost allocation, Ph.D. Dissertation, University of B.C., Vancouver, B.C., Canada (1987).
D. Joneja, Multi-echelon assembly systems with non-stationary demands: Heuristics and worst case performance bounds, Working Paper, Graduate School of Business, Columbia University, New York, NY (1988).
U. Karmarkar, The multi-location multi-period inventory problem: Bounds and approximations, Manag. Sci. 33(1987)86–93.
S. Love, A facilities in series inventory model with nested schedules, Manag. Sci. 18(1972)327–338.
M. Queyranne, A polynomial-time submodular extension to Roundy's 98% effective heuristic for production/inventory systems, Working Paper No. 1136, Commerce, University of B.C., Vancouver, B.C., Canada (1985).
S. Rajagopalan and G. Cornuejols, Dynamic lot-size models in multistage assemby systems, Working Paper 87-88-38, Graduate School of Industrial Administration, Carnegie-Mellon University (1988).
K. Rosling, Optimal inventory policies for assembly systems under random demands, Oper. Res. 37(1989)565–579.
R. Roundy, Efficient, effective lot-sizing for multi-product multi-stage production/distribution systems with correlated demands, Technical Report No. 671 School of Operations Research and Industrial Engineering, Cornell University (1985).
R. Roundy, A 98% effective lot-sizing rule for a multi-product multi-stage production/inventory system, Math. Oper. Res. 11(1986)699–727.
E.A. Silver, Establishing reorder points in the (S, c, s) coordinated control system under compound Poisson demand, Int. J. Prod. Res. 19(1981)743–750.
D. Sun, private communication (1988).
W.I. Zangwill, A backlogging model and a multi-echelon model of a dynamic economic lot size production system—a network approach, Manag. Sci. 19(1969)506–527.
W.I. Zangwill, Eliminating inventory in series facility production systems, Manag. Sci. 33(1987)1150–1164.
Y.S. Zheng, Replenishment strategies for production/distribution networks with general joint setup costs, Ph.D. Dissertation, Columbia University (1987).
A. Svoronos and P. Zipkin, Estimating the performance of multi-level inventory systems, Oper.-Res. 36(1988)57–72.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Atkins, D. A survey of lower bounding methodologies for production/inventory models. Ann Oper Res 26, 8–28 (1990). https://doi.org/10.1007/BF02248583
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02248583