×

zbMATH — the first resource for mathematics

Inventory systems with stochastic demand and supply: properties and approximations. (English) Zbl 1188.90017
Summary: We model a retailer whose supplier is subject to complete supply disruptions. We combine discrete-event uncertainty (disruptions) and continuous sources of uncertainty (stochastic demand or supply yield), which have different impacts on optimal inventory settings. This prevents optimal solutions from being found in closed form. We develop a closed-form approximate solution by focusing on a single stochastic period of demand or yield. We show how the familiar newsboy fractile is a critical trade-off in these systems, since the optimal base-stock policies balance inventory holding costs with the risk of shortage costs generated by a disruption.

MSC:
90B05 Inventory, storage, reservoirs
90B06 Transportation, logistics and supply chain management
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Axsäter, S., Inventory control, (2000), Kluwer Academic Publishers Boston, MA
[2] Babich, V., 2008. Independence of capacity ordering and financial subsidies to risky suppliers. Working paper, Dept. of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI.
[3] Babich, V.; Burnetas, A.N.; Ritchken, P.H., Competition and diversification effects in supply chains with supplier default risk, Manufacturing and service operations management, 9, 2, 123-146, (2007)
[4] Berk, E.; Arreola-Risa, A., Note on “future supply uncertainty in EOQ models”, Naval research logistics, 41, 129-132, (1994) · Zbl 0785.90041
[5] Chopra, S.; Meindl, P., Supply chain management, (2004), Pearson Prentice Hall Upper Saddle River, NJ
[6] Chopra, S.; Reinhardt, G.; Mohan, U., The importance of decoupling recurrent and disruption risks in a supply chain, Naval research logistics, 54, 5, 544-555, (2007) · Zbl 1143.90302
[7] Dada, M.; Petruzzi, N.; Schwarz, L., A newsvendor’s procurement problem when suppliers are unreliable, Manufacturing and service operations management, 9, 1, 9-32, (2007)
[8] Golany, B.; Kaplan, E.H.; Marmur, A.; Rothblum, U.G., Nature plays with dice – terrorists do not: allocating resources to counter strategic versus probabilistic risks, European journal of operational research, 192, 198-208, (2009) · Zbl 1205.91096
[9] Güllü, R.; Önol, E.; Erki˙p, N., Analysis of a deterministic demand production/inventory system under nonstationary supply uncertainty, IIE transactions, 29, 703-709, (1997)
[10] Gupta, D., The \((Q, r)\) inventory system with an unreliable supplier, Infor, 34, 2, 59-76, (1996) · Zbl 0868.90033
[11] Parlar, M., Continuous-review inventory problem with random supply interruptions, European journal of operational research, 99, 366-385, (1997) · Zbl 0930.90006
[12] Parlar, M.; Berkin, D., Future supply uncertainty in EOQ models, Naval research logistics, 38, 107-121, (1991) · Zbl 0725.90025
[13] Parlar, M.; Perry, D., Analysis of a (\scq,r,\sct) inventory policy with deterministic and random yields when future supply is uncertain, European journal of operational research, 84, 431-443, (1995) · Zbl 0927.90006
[14] Parlar, M.; Perry, D., Inventory models of future supply uncertainty with single and multiple suppliers, Naval research logistics, 43, 191-210, (1996) · Zbl 0870.90054
[15] Qi, L.; Shen, Z.J.M.; Snyder, L.V., A continuous-review inventory model with disruptions at both supplier and retailer, Production and operations management, 18, 5, 516-532, (2009)
[16] Scherer, W.T.; Pomroy, T.A.; Fuller, D.N., The triangular density to approximate the normal density: decision rules-of-thumb, Reliability engineering and system safety, 82, 331-341, (2003)
[17] Schmitt, A.J., Singh, M., 2009. A quantitative analysis of disruption risk in a multi-echelon supply chain. Working paper, MIT Center for Transportation and Logistics, Cambridge, MA, 2009.
[18] Schmitt, A.J., Snyder. L.V., 2009. Infinite-horizon models for inventory control under yield uncertainty and disruptions. Working paper, P.C. Rossin College of Engineering and Applied Sciences, Lehigh University, Bethlehem, PA, 2009.
[19] Silver, E.A., Establishing the order quantity when the amount received is uncertain, Infor, 14, 1, 32-39, (1976)
[20] Snyder, L.V., 2008. A tight approximation for a continuous-review inventory model with supplier disruptions. Working paper, P.C. Rossin College of Engineering and Applied Sciences, Lehigh University, Bethlehem, PA.
[21] Snyder, L.V., Shen, Z.J.M., 2006. Supply and demand uncertainty in multi-echelon supply chains. Working paper, P.C. Rossin College of Engineering and Applied Sciences, Lehigh University, Bethlehem, PA.
[22] Snyder, L.V., Tomlin, B., 2008. Inventory management with advanced warning of disruptions. Working paper, P.C. Rossin College of Engineering and Applied Sciences, Lehigh University, Bethlehem, PA.
[23] Song, J.-S.; Zipkin, P.H., Inventory control with information about supply conditions, Management science, 42, 10, 1409-1419, (1996) · Zbl 0881.90044
[24] Tomlin, B., On the value of mitigation and contingency strategies for managing supply chain disruption risks, Management science, 52, 5, 639-657, (2006) · Zbl 1232.90200
[25] Wagner, S.M.; Bode, C.; Koziol, P., Supplier default dependencies: empirical evidence from the automotive industry, European journal of operational research, 199, 1, 150-161, (2009) · Zbl 1176.90326
[26] Yang, Z.; Aydin, G.; Babich, V.; Bell, D.R., Supply disruptions, asymmetric information and a backup production option, Management science, 55, 2, 192-209, (2009) · Zbl 1232.90203
[27] Yano, C.A.; Lee, H.L., Lot sizing with random yields: A review, Operations research, 43, 2, 311-334, (1995) · Zbl 0832.90031
[28] Zipkin, P.H., Foundations of inventory management, (2000), McGraw-Hill Higher Education Boston, MA · Zbl 1370.90005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.