Lost-sales inventory theory: a review. (English) Zbl 1237.90007
Summary: In classic inventory models it is common to assume that excess demand is backordered. However, studies analyzing customer behavior in practice show that most unfulfilled demand is lost or an alternative item/location is looked for in many retail environments. Inventory systems that include this lost-sales characteristic appear to be more difficult to analyze and to solve. Furthermore, lost-sales inventory systems require different replenishment policies to minimize costs compared to backorder systems. In this paper, we classify the models in the literature based on the characteristics of the inventory system and review the proposed replenishment policies. For each classification and type of replenishment policy we discuss the available models and their performance. Furthermore, directions for future research are proposed.
MSC:
| 90B05 | Inventory, storage, reservoirs |
| 90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |
References:
| [1] | Aardal, K.; Jonsson, O.; Jonsson, H., Optimal inventory policies with service-level constraints, Journal of the Operational Research Society, 40, 65-73 (1989) · Zbl 0673.90028 |
| [2] | Abad, P. L., Optimal price and order size under partial backordering incorporating shortage, backorder and lost sale costs, International Journal of Production Economics, 114, 179-186 (2008) |
| [3] | Andersson, J.; Melchiors, P., A two-echelon inventory model with lost sales, International Journal of Production Economics, 69, 307-315 (2001) |
| [4] | Anupindi, R.; Bassok, Y., Centralization of stocks: Retailers vs. manufacturer, Management Science, 45, 178-191 (1999) · Zbl 1231.90007 |
| [5] | Archibald, B. C., Continuous review \((s, S)\) policies with lost sales, Management Science, 27, 1171-1177 (1981) · Zbl 0465.90021 |
| [6] | Bar-lev, S. K.; Parlar, M.; Perry, D., Impulse control of a Brownian inventory system with supplier uncertainty, Stochastic Analysis and Applications, 11, 11-27 (1993) · Zbl 0781.90028 |
| [7] | Beckmann, M. J.; Srinivasan, S. K., An \((s, S)\) inventory system with Poisson demands and exponential lead time, OR Spectrum, 9, 213-217 (1987) · Zbl 0637.90029 |
| [8] | Bellman, R.; Glicksberg, I.; Gross, O., On the optimal inventory equation, Management Science, 2, 83-104 (1955) · Zbl 0995.90501 |
| [9] | Bensoussan, A.; Crouhy, M.; Proth, J., Mathematical Theory of Production Planning (1983), North-Holland: North-Holland Amsterdam · Zbl 0564.90010 |
| [10] | Berk, E.; Arreola-Risa, A., Note on future uncertainty in EOQ models, Naval Research Logistics, 41, 129-132 (1994) · Zbl 0785.90041 |
| [11] | Berk, E.; Gürler, Ü., Analysis of the \((Q,r)\) inventory model for perishables with positive lead times and lost sales, Operations Research, 56, 1238-1246 (2008) · Zbl 1167.90311 |
| [12] | Bhargava, H. K.; Sun, D.; Xu, S. H., Stockout compensation: Joint inventory and price optimization in electronic retailing, INFORMS Journal on Computing, 18, 255-266 (2006) · Zbl 1241.90006 |
| [13] | Bhat, U. N., Elements of Applied Stochastic Processes (1984), Wiley: Wiley New York · Zbl 0646.60001 |
| [14] | Bijvank, M., Bhulai, S., Huh, W.T., 2010. Lost-sales Inventory Systems with Fixed Order Costs. Working Paper, Department of Computer Science and Operations Research, University of Montreal.; Bijvank, M., Bhulai, S., Huh, W.T., 2010. Lost-sales Inventory Systems with Fixed Order Costs. Working Paper, Department of Computer Science and Operations Research, University of Montreal. · Zbl 1339.90018 |
| [15] | Bijvank, M., Johansen, S.G., 2010. Periodic-review Lost-sales Inventory Models with Constant Lead Times of Any Length. Working Paper, Department of Computer Science and Operations Research, University of Montreal.; Bijvank, M., Johansen, S.G., 2010. Periodic-review Lost-sales Inventory Models with Constant Lead Times of Any Length. Working Paper, Department of Computer Science and Operations Research, University of Montreal. · Zbl 1253.90019 |
| [16] | Bijvank, M., Vis, I.F.A., 2010. Lost-sales Inventory Systems with a Service Level Criterion. Working Paper, Department of Computer Science and Operations Research, University of Montreal.; Bijvank, M., Vis, I.F.A., 2010. Lost-sales Inventory Systems with a Service Level Criterion. Working Paper, Department of Computer Science and Operations Research, University of Montreal. · Zbl 1253.90020 |
| [17] | Broekmeulen, R. A.C. M.; van Donselaar, K. H., A heuristic to manage perishable inventory with batch ordering, positive lead-times, and time-varying demand, Computers & Operations Research, 36, 3013-3018 (2009) · Zbl 1162.90303 |
| [18] | Buchanan, D. J.; Love, R. F., A \((Q,R)\) inventory model with lost sales and Erlang-distributed lead times, Naval Research Logistics Quarterly, 32, 605-611 (1985) · Zbl 0595.90012 |
| [19] | Chang, C.-T.; Lo, T. Y., On the inventory model with continuous and discrete lead time, backorders and lost sales, Applied Mathematical Modelling, 33, 2196-2206 (2009) · Zbl 1185.90008 |
| [20] | Chen, J., Jackson, P.L., Muckstadt, J.A. 2011. Exact analysis of a lost sales model under stuttering Poisson demand. Operations Research doi:10.1287/opre.1100.0872.; Chen, J., Jackson, P.L., Muckstadt, J.A. 2011. Exact analysis of a lost sales model under stuttering Poisson demand. Operations Research doi:10.1287/opre.1100.0872. · Zbl 1217.90066 |
| [21] | Chen, Y. F.; Ray, S.; Song, Y., Optimal pricing an inventory control policy in periodic-review systems with fixed ordering cost and lost sales, Naval Research Logistics, 53, 117-136 (2006) · Zbl 1106.90008 |
| [22] | Cheng, F.; Sethi, S. P., Optimality of state-dependent \((s, S)\) policies in inventory models with Markov-modulated demand and lost sales, Production and Operations Management, 8, 183-192 (1999) |
| [23] | Chiang, C., Optimal ordering policies for periodic-review systems with replenishment cycles, European Journal of Operational Research, 170, 44-56 (2006) · Zbl 1079.90008 |
| [24] | Chiang, C., Optimal ordering policies for periodic-review systems with a refined intra-cycle time scale, European Journal of Operational Research, 177, 872-881 (2007) · Zbl 1110.90005 |
| [25] | Chu, C. W.; Patuwo, B. E.; Mehrez, A.; Rabinowitz, G., A dynamic two-segment partial backorder control of \((r,Q)\) inventory system, Computers & Operations Research, 28, 935-953 (2001) · Zbl 0985.90002 |
| [26] | Chu, P.; Yang, K.-L.; Liang, S.-K.; Niu, T., Note on inventory model with a mixture of back orders and lost sales, European Journal of Operational Research, 159, 470-475 (2004) · Zbl 1065.90002 |
| [27] | Chuang, B. R.; Lee, D.-W., A periodic review \((R,T)\) model with investment to reduce lost sales rate, Journal of Information & Optimization Sciences, 29, 241-252 (2008) · Zbl 1154.90303 |
| [28] | Cohen, M. A.; Kleindorfer, P. R.; Lee, H. L., Service constrained \((s, S)\) inventory system with priority demand classes and lost sales, Management Science, 34, 482-499 (1988) · Zbl 0644.90024 |
| [29] | Das, C., The \((S\)−1,S)\) inventory model under time limit on backorders, Operations Research, 25, 835-850 (1977) · Zbl 0383.90035 |
| [30] | de Kok, A. G., Approximations for a lost-sales production/inventory control model with service level constraints, Management Science, 31, 729-737 (1985) · Zbl 0609.90059 |
| [31] | Dekker, R.; Hill, R. M.; Kleijn, M. J.; Teunter, R. H., On the \((S\)−1,S) lost sales inventory model with priority demand classes, Naval Research Logistics, 49, 593-610 (2002) · Zbl 1007.90004 |
| [32] | Doshi, B. T.; van der Duyn Schouten, F. A.; Talman, A. J.J., A production-inventory control model with a mixture of back-orders and lost-sales, Management Science, 24, 1078-1086 (1978) · Zbl 0394.90034 |
| [33] | Downs, B.; Metters, R.; Semple, J., Managing inventory with multiple products, lags in delivery, resource constraints, and lost sales: A mathematical programming approach, Management Science, 47, 464-479 (2001) · Zbl 1232.90041 |
| [34] | Fadiloglu, M. M.; Bulut, Ö., A dynamic rationing policy for continuous-review inventory systems, European Journal of Operational Research, 202, 675-685 (2010) · Zbl 1176.90019 |
| [35] | Federgruen, A.; Zheng, Y.-S., An efficient algorithm for computing an optimal \((r,Q)\) policy in continuous review stochastic inventory systems, Operations Research, 40, 808-813 (1992) · Zbl 0758.90021 |
| [36] | Federgruen, A.; Zipkin, P., An efficient algorithm for computing optimal \((s, S)\) policies, Operations Research, 32, 1268-1285 (1984) · Zbl 0553.90031 |
| [37] | Feeney, G. J.; Sherbrooke, C. C., The inventory policy under compound Poisson demand, Management Science, 12, 391-411 (1966) · Zbl 0131.18803 |
| [38] | Gaver, D. P., On base-stock level inventory control, Operations Research, 7, 689-703 (1959) · Zbl 1414.90040 |
| [39] | Goyal, S. K., Joint ordering of two products with lost sales permitted, Engineering Costs and Production Economics, 16, 209-212 (1989) |
| [40] | Grasman, S. E.; Olsen, T. L.; Birge, J. R., Setting basestock levels in multi-product systems with setups and random yield, IIE Transactions, 40, 1158-1170 (2008) |
| [41] | Gruen, T. W.; Corsten, D.; Bharadwaj, S., Retail out-of-stocks: A worldwide examination of extent causes and consumer responses, Grocery Manufacturers of America (2002) |
| [42] | Guide, V. D.R.; Srivastava, R., Repairable inventory theory: Models and applications, European Journal of Operational Research, 102, 1-20 (1997) · Zbl 0948.90037 |
| [43] | Gupta, D., The \((Q,r)\) inventory system with an unreliable supplier, INFOR, 34, 59-76 (1996) · Zbl 0868.90033 |
| [44] | Gurgur, C. Z.; Altiok, T., Analysis of decentralized multi-product pull systems with lost sales, Naval Research Logistics, 54, 357-370 (2007) · Zbl 1187.90026 |
| [45] | Ha, A. Y., Inventory rationing in a make-to-stock production system with several demand classes and lost sales, Management Science, 43, 1093-1103 (1997) · Zbl 0887.90053 |
| [46] | Ha, A. Y., Stock rationing in an \(M/E_k/1\) make-to-stock queue, Management Science, 46, 77-87 (2000) · Zbl 1231.90135 |
| [47] | Hadley, G.; Whitin, T. M., Analysis of Inventory Systems (1963), Prentice-Hall: Prentice-Hall Englewood Cliffs, New York · Zbl 0133.42901 |
| [48] | Harris, F. H., How many parts to make at once, Factory, The Magazine of Management, 10, 135-136 (1913) |
| [49] | Hill, R. M., Numerical analysis of a continuous-review lost-sales inventory model where two orders may be outstanding, European Journal of Operational Research, 62, 11-26 (1992) · Zbl 0764.90028 |
| [50] | Hill, R. M., Continuous review lost sales inventory models where two orders may be outstanding, International Journal of Production Economics, 35, 313-319 (1994) |
| [51] | Hill, R. M., Order splitting in continuous review \((Q,r)\) inventory models, European Journal of Operational Research, 95, 53-61 (1996) · Zbl 0955.90501 |
| [52] | Hill, R. M., On the suboptimality of \((S\)−1,S)\) lost sales inventory policies, International Journal of Production Economics, 59, 387-393 (1999) |
| [53] | Hill, R. M., Continuous-review, lost-sales inventory models with Poisson demand, a fixed lead time and no fixed order cost, European Journal of Operational Research, 176, 956-963 (2007) · Zbl 1103.90016 |
| [54] | Hill, R. M.; Johansen, S. G., Optimal and near-optimal policies for lost sales inventory models with at most one replenishment order outstanding, European Journal of Operational Research, 169, 111-132 (2006) · Zbl 1083.90002 |
| [55] | Hill, R. M.; Seifbarghy, M.; Smith, D. K., A two-echelon inventory model with lost sales, European Journal of Operational Research, 181, 753-766 (2007) · Zbl 1131.90004 |
| [56] | Hu, W.-T.; Kim, S.-L.; Banerjee, A., An inventory model with partial backordering and unit backorder cost linearly increasing with the waiting time, European Journal of Operational Research, 197, 581-587 (2009) · Zbl 1159.90370 |
| [57] | Huh, W. T.; Janakiraman, G., \((s, S)\) optimality in joint inventory-pricing control: An alternate approach, Operations Research, 56, 783-790 (2008) · Zbl 1167.90332 |
| [58] | Huh, W. T.; Janakiraman, G., Bases-tock policies in capacitated assembly systems: Convexity properties, Naval Research Logistics, 57, 109-118 (2010) · Zbl 1188.90011 |
| [59] | Huh, W. T.; Janakiraman, G., On the optimal policy structure in serial inventory systems with lost sales, Operations Research, 58, 486-491 (2010) · Zbl 1226.90012 |
| [60] | Huh, W. T.; Janakiraman, G.; Muckstadt, J. A.; Rusmevichientong, P., Asymptotic optimality of order-up-to policies in lost sales inventory systems, Management Science, 55, 404-420 (2009) · Zbl 1232.90063 |
| [61] | Isotupa, K. P.S., An \((s,Q)\) Markovian inventory system with lost sales and two demand classes, Mathematical and Computer Modelling, 43, 687-694 (2006) · Zbl 1180.90015 |
| [62] | Jagers, A. A.; van Doorn, E. A., On the continued Erlang loss function, Operations Research Letters, 5, 43-46 (1986) · Zbl 0595.60089 |
| [63] | Janakiraman, G.; Roundy, R. O., Lost-sales problems with stochastic lead times: Convexity results for base-stock policies, Operations Research, 52, 795-803 (2004) · Zbl 1165.90322 |
| [64] | Janakiraman, G.; Seshadri, S.; Shanthikumar, J. G., A comparison of the optimal costs of two canonical inventory systems, Operations Research, 55, 866-875 (2007) · Zbl 1167.90335 |
| [65] | Johansen, S. G., Pure and modified base-stock policies for the lost sales inventory system with negligible set-up costs and constant lead times, International Journal of Production Economics, 71, 391-399 (2001) |
| [66] | Johansen, S. G., Base-stock policies for the lost sales inventory system with Poisson demand and Erlangian lead times, International Journal of Production Economics, 93-94, 429-437 (2005) |
| [67] | Johansen, S. G.; Hill, R. M., The \((r,Q)\) control of a periodic-review inventory system with continuous demand and lost sales, International Journal of Production Economics, 68, 279-286 (2000) |
| [68] | Johansen, S. G.; Thorstenson, A., Optimal and approximate \((Q,r)\) inventory policies with lost sales and gamma-distributed lead time, International Journal of Production Economics, 30-31, 179-194 (1993) |
| [69] | Johansen, S. G.; Thorstenson, A., Optimal \((r,Q)\) inventory policies with Poisson demands and lost sales: discounted and undiscounted cases, International Journal of Production Economics, 46-47, 359-371 (1996) |
| [70] | Johansen, S.G., Thorstenson, A., 2004. The \((rq\); Johansen, S.G., Thorstenson, A., 2004. The \((rq\) |
| [71] | Johansen, S.G., Thorstenson, A., 2008. Pure and Restricted Base-stock Policies for the Lost-sales Inventory System with Periodic Review and Constant Lead Times. Technical Report, Aarhus University.; Johansen, S.G., Thorstenson, A., 2008. Pure and Restricted Base-stock Policies for the Lost-sales Inventory System with Periodic Review and Constant Lead Times. Technical Report, Aarhus University. |
| [72] | Johnson, E. L., On \((s, S)\) policies, Management Science, 18, 80-101 (1968) · Zbl 0169.22501 |
| [73] | Jokar, M. R.A.; Seifbarghy, M., Cost evaluation of a two-echelon inventory system with lost sales and approximately normal demand, Scientia Iranica, 13, 105-112 (2006) · Zbl 1147.90305 |
| [74] | Kalpakam, S.; Arivarignan, G., A continuous review inventory system with semi-Markovian demands, Mathematical and Computer Modelling, 11, 1172-1177 (1988) · Zbl 0652.90030 |
| [75] | Kalpakam, S.; Arivarignan, G., A lost sales inventory system in a random environment, Stochastic Analysis and Applications, 7, 367-385 (1989) · Zbl 0684.90025 |
| [76] | Kalpakam, S.; Arivarignan, G., \((s, S)\) inventory systems with lost sales and Markov renewal demands, Mathematical and Computer Modeling, 12, 1511-1520 (1989) · Zbl 0704.90022 |
| [77] | Kalpakam, S.; Arivarignan, G., A lost sales inventory system with multiple reorder levels, (Subramanian, R.; Beckmann, M. J.; Gopalan, M. N., Stochastic Processes and Their Applications (1991), Springer: Springer Berlin) · Zbl 0755.90022 |
| [78] | Kalpakam, S.; Sapna, K. P., A control policy of an inventory system with compound Poisson demand, Stochastic Analysis and Applications, 11, 459-482 (1993) · Zbl 0798.90033 |
| [79] | Kalpakam, S.; Sapna, K. P., A modified \((s, S)\) inventory system with lost sales and emergency orders, Opsearch, 30, 321-335 (1993) · Zbl 0801.90035 |
| [80] | Kalpakam, S.; Sapna, K. P., A two reorder level inventory system with renewal demands, European Journal of Operational Research, 84, 402-415 (1995) · Zbl 0909.90133 |
| [81] | Kalpakam, S.; Sapna, K. P., A lost sales \((S\)−1,S)\) perishable inventory system with renewal demand, Naval Research Logistics, 43, 129-142 (1996) · Zbl 0870.90053 |
| [82] | Kalpakam, S.; Sapna, K. P., A lost sales inventory system with supply uncertainty, Computers and Mathematics with Applications, 33, 81-93 (1997) · Zbl 0872.90032 |
| [83] | Kalpakam, S.; Shanthi, S., A perishable inventory system with modified (S-1,S) policy and arbitrary processing times, Computers & Operations Research, 28, 453-471 (2001) · Zbl 1080.90503 |
| [84] | Kapalka, B. A.; Katircioglu, K.; Puterman, M. L., Retail inventory control with lost sales service constraints, and fractional lead times, Production and Operations Management, 8, 393-408 (1999) |
| [85] | Karlin, S.; Scarf, H., Inventory models of the Arrow-Harris-Marschak type with time lag, (Arrow, K.; Karlin, S.; Scarf, H., Studies in the Mathematical Theory of Inventory and Production (1958), Stanford University: Stanford University Stanford, Ca), (Chapter 10) · Zbl 0079.36003 |
| [86] | Karush, W., A queueing model for an inventory problem, Operations Research, 5, 693-703 (1957) · Zbl 1414.90107 |
| [87] | Kenné, J.-P.; Gharbi, A.; Beit, M., Age-dependent production planning and maintenance strategies in unreliable manufacturing systems with lost sale, European Journal of Operational Research, 278, 408-420 (2007) · Zbl 1107.90012 |
| [88] | Kennedy, W. J.; Patterson, J. W.; Fredendall, L. D., An overview of recent literature on spare-parts inventories, International Journal of Production Economics, 76, 201-215 (2002) |
| [89] | Kim, E.; van Oyen, M. P., Dynamic scheduling to minimize lost sales subject to set-up costs, Queueing Systems, 29, 193-229 (1998) · Zbl 0916.90107 |
| [90] | Kranenburg, A. A.; van Houtum, G. J., Cost optimization in the \((S\)−1,S)\) lost sales inventory model with multiple demand classes, Operations Research Letters, 35, 493-502 (2007) · Zbl 1145.90005 |
| [91] | Krieg, G. N.; Kuhn, H., A decomposition method for multi-product Kanban systems with setup times and lost sales, IIE Transactions, 34, 613-625 (2002) |
| [92] | Krieg, G. N.; Kuhn, H., Analysis of multi-product Kanban systems with state-dependent setups and lost sales, Annals of Operations Research, 125, 141-166 (2004) · Zbl 1048.90098 |
| [93] | Krishnamoorthy, A.; Islam, M. E., \((s, S)\) inventory system with postponed demands, Stochastic Analysis and Applications, 22, 827-842 (2005) · Zbl 1151.90314 |
| [94] | Lee, J. E.; Hong, Y., A stock rationing policy in a \((s, S)\)-controlled stochastic production system with 2-phase Coxian processing times and lost sales, International Journal of Production Economics, 83, 299-307 (2003) |
| [95] | Lee, W.-C.; Wu, J.-W.; Hsu, J.-W., Computational algorithm for inventory model with a service level constraint, lead time demand with the mixture of distributions and controllable negative exponential backorder rate, Applied Mathematics and Computation, 175, 1125-1138 (2006) · Zbl 1131.60307 |
| [96] | Leung, K.-N. F., Technical note: A use of the complete squares method to solve and analyze a quadratic objective function with two decision variables exemplified via a deterministic inventory model with a mixture of backorders and lost sales, International Journal of Production Economics, 113, 275-281 (2008) |
| [97] | Leung, K.-N. F., A generalization of Chu and Chungs (2004) sensitivity of the inventory model with partial backorders, European Journal of Operational Research, 196, 554-562 (2009) · Zbl 1163.90335 |
| [98] | Levi, R.; Janakiraman, G.; Nagarajan, M., A 2-approximation algorithm for stochastic inventory control models with lost sales, Mathematics of Operations Research, 33, 351-374 (2008) · Zbl 1231.90045 |
| [99] | Liang, S.-K.; Chu, P.; Yang, K.-L., Improved periodic review inventory model involving leadtime with crashing components and service level, International Journal of Systems Science, 39, 421-426 (2008) · Zbl 1167.90343 |
| [100] | Lodree, E. J., Advanced supply chain planning with mixtures of backorders, lost sales, and lost contract, European Journal of Operational Research, 181, 168-183 (2007) · Zbl 1121.90013 |
| [101] | Melchiors, P., Restricted time-remembering policies for the inventory rationing problem, International Journal of Production Economics, 81-82, 461-468 (2003) |
| [102] | Melchiors, P.; Dekker, R.; Kleijn, M. J., Inventory rationing in an \((s,Q)\) inventory model with lost sales and two demand classes, Journal of the Operational Research Society, 51, 111-122 (2000) · Zbl 1107.90311 |
| [103] | Minner, S.; Transchel, S., Periodic review inventory-control for perishable products under service-level constraints, OR Spectrum, 32, 979-996 (2010) · Zbl 1230.90020 |
| [104] | Mohebbi, E., Supply interruptions in a lost-sales inventory system with random lead time, Computers & Operations Research, 30, 411-426 (2003) · Zbl 1029.90007 |
| [105] | Mohebbi, E., A replenishment model for the supply-uncertainty problem, Internationa Journal of Production Economics, 87, 25-37 (2004) |
| [106] | Mohebbi, E.; Posner, M. J.M., A continuous-review inventory system with lost sales and variable lead time, Naval Research Logistics, 45, 259-278 (1998) · Zbl 0941.90001 |
| [107] | Mohebbi, E.; Posner, M. J.M., Sole versus dual sourcing in a continuous-review inventory system with lost sales, Computers & Industrial Engineering, 34, 321-336 (1998) |
| [108] | Mohebbi, E.; Posner, M. J.M., A lost-sales continuous-review inventory system with emergency ordering, International Journal of Production Economics, 58, 93-112 (1999) |
| [109] | Mohebbi, E.; Posner, M. J.M., Multiple replenishment orders in a continuous-review inventory system with lost sales, Operations Research Letters, 30, 117-129 (2002) · Zbl 1030.90006 |
| [110] | Moinzadeh, K.; Schmidt, C. P., An \((S\)−1,S)\) inventory system with emergency orders, Operations Research, 39, 308-321 (1991) · Zbl 0738.90023 |
| [111] | Montgomery, D. C.; Bazaraa, M. S.; Keswani, A. K., Inventory models with a mixture of backorders and lost sales, Naval Research Logistics Quarterly, 20, 255-264 (1973) · Zbl 0262.90020 |
| [112] | Morse, P. M., Queues, Inventories and Maintenance (1958), Wiley: Wiley New York |
| [113] | Morse, P. M., Solutions of a class of discrete-time inventory problems, Operations Research, 7, 67-78 (1959) · Zbl 1414.90044 |
| [114] | Morton, T. E., Bounds on the solution of the lagged optimal inventory equation with no demand backlogging and proportional costs, SIAM Review, 11, 572-596 (1969) · Zbl 0193.19702 |
| [115] | Morton, T. E., The near myopic nature of the lagged proportional cost inventory problem with lost sales, Operations Research, 19, 1708-1716 (1971) · Zbl 0225.90011 |
| [116] | Nahmias, S., Simple approximations for a variety of dynamic leadtime lost-sales inventory models, Operations Research, 27, 904-924 (1979) · Zbl 0426.90027 |
| [117] | Nahmias, S., Perishable inventory theory: A review, Operations Research, 30, 680-708 (1982) · Zbl 0486.90033 |
| [118] | Nahmias, S.; Smith, S. A., Optimizing inventory levels in a two-echelon retailer system with partial lost sales, Management Science, 40, 582-596 (1994) · Zbl 0807.90047 |
| [119] | Netessine, S.; Rudi, N.; Wang, Y., Inventory competition and incentives to back-order, IIE Transactions, 38, 883-902 (2006) |
| [120] | Nobel, R. D.; van der Heeden, M., A lost-sales production/inventory model with two discrete production modes, Stochastic Models, 16, 453-478 (2000) · Zbl 0983.91031 |
| [121] | Ouyang, L.-Y.; Chuang, B.-R.; Lin, Y.-J., Periodic review inventory models with controllable lead time and lost sales rate reduction, Journal of the Chinese Institute of Industrial Engineers, 22, 355-368 (2005) |
| [122] | Ouyang, L.-Y.; Chuang, B.-R.; Lin, Y.-J., Effective investment to reduce lost-sales rate in a periodic review inventory model, OR Spectrum, 29, 681-697 (2007) · Zbl 1168.90335 |
| [123] | Parlar, M.; Berkin, D., Future supply uncertainty in EOQ models, Naval Research Logistics, 38, 107-121 (1991) · Zbl 0725.90025 |
| [124] | Paul, B.; Rajendran, C., Rationing mechanisms and inventory control-policy parameters for a divergent supply chain operating with lost sales and costs of review, Computers & Operations Research, 38, 1117-1130 (2011) · Zbl 1208.90010 |
| [125] | Pentico, D. W.; Drake, M. J., The deterministic EPQ with partial backordering: A new approach, European Journal of Operational Research, 194, 102-113 (2009) · Zbl 1179.90016 |
| [126] | Pentico, D. W.; Drake, M. J.; Toews, C., The deterministic EPQ with partial backordering: A new approach, Omega, 37, 624-636 (2009) |
| [127] | Porteus, E. L., Numerical comparisons of inventory policies for periodic review systems, Operations Research, 33, 134-152 (1985) · Zbl 0571.90016 |
| [128] | Posner, M. J.M., Class of inventory models with customer impatience, Naval Research Logistics Quarterly, 19, 483-492 (1981) · Zbl 0252.90016 |
| [129] | Pressman, I., An order-level-scheduling-period system with lost sales, Management Science, 17, 1328-1335 (1977) · Zbl 0366.90070 |
| [130] | Ravichandran, N., Note on \((s, S)\) inventory policy, IIE Transactions, 16, 387-390 (1984) |
| [131] | Reiman, M., 2004. A New and Simple Policy for the Continuous Review Lost Sales Inventory Model. Technical Report. Working Paper, Bell Labs, Murray Hill, NJ.; Reiman, M., 2004. A New and Simple Policy for the Continuous Review Lost Sales Inventory Model. Technical Report. Working Paper, Bell Labs, Murray Hill, NJ. |
| [132] | Rosenberg, D., A new analysis of a lot-size model with partial back-logging, Naval Research Logistics Quarterly, 26, 349-353 (1979) · Zbl 0401.90038 |
| [133] | Rosling, K., 1998. The \((rQ\); Rosling, K., 1998. The \((rQ\) |
| [134] | San José, L. A.; Sicilia, J.; García-Laguna, J., The lot size-reorder level inventory system with customers impatience functions, Computers & Industrial Engineering, 49, 349-362 (2005) |
| [135] | San José, L. A.; Sicilia, J.; García-Laguna, J., Analysis of an inventory system with exponential partial backordering, International Journal of Production Economics, 100, 76-86 (2006) |
| [136] | San-José, L. A.; Sicilia, J.; García-Laguna, J., A general model for EOQ inventory systems with partial backlogging and linear shortage costs, International Journal of Systems Science, 40, 59-71 (2009) · Zbl 1155.90316 |
| [137] | Scarf, H., The optimality of \((s, S)\) policies in the dynamic inventory problem, (Arrow, K. J.; Karlin, S.; Suppes, P., Mathematical Methods in the Social Sciences (1960), Stanford University: Stanford University Stanford, CA), (Chapter 13) · Zbl 0203.22102 |
| [138] | Schmidt, C. P.; Nahmias, S., \((S\)−1,S)\) policies for perishable inventory, Management Science, 31, 719-728 (1985) · Zbl 0615.90035 |
| [139] | Seifbarghy, M.; Jokar, M. R.A., Cost evaluation of a two-echelon inventory system with lost sales and approximately Poisson demand, International Journal of Production Economics, 102, 244-254 (2006) · Zbl 1147.90305 |
| [140] | Sezen, B., Changes in performance under various lengths of review periods in a periodic review inventory control system with lost sales, International Journal of Physical Distribution & Logistics Management, 36, 360-373 (2006) |
| [141] | Sheopuri, A.; Janakiraman, G.; Seshadri, S., New policies for the stochastic inventory control problem with two supply sources, Operations Research, 58, 734-745 (2010) · Zbl 1231.90061 |
| [142] | Shreve, S. E., Abbreviated proof [in the lost sales case], (Bertsekas, D. P., Dynamic Programming and Stochastic Control (1976), Academic Press: Academic Press New York), 105-106 |
| [143] | Silver, E. A., Inventory management: A tutorial, Canadian publications, practical applications, and suggestions for future research, Information Systems and Operational Research, 46, 15-28 (2008) · Zbl 07683679 |
| [144] | Silver, E. A.; Pyke, D. F.; Peterson, R., Inventory Management and Production Planning and Scheduling (1998), John Wiley & Sons: John Wiley & Sons New York |
| [145] | Silver, E. A.; Smith, S. A., A graphical aid for determining optimal inventories in a unit replenishment inventory system, Management Science, 24, 358-359 (1977) · Zbl 0372.90047 |
| [146] | Sivakumar, B.; Arivarignan, G., A modified lost sales inventory system with two types of customers, Quality Technology & Quantitative Management, 5, 339-349 (2008) |
| [147] | Smith, S. A., Optimal inventories for an \((S\)−1,S)\) system with no backorders, Management Science, 23, 522-528 (1977) · Zbl 0338.90028 |
| [148] | Song, Y.; Ray, S.; Boyaci, T., Optimal dynamic joint inventory-pricing control for multiplicative demand with fixed order costs and lost sales, Operations Research, 57, 245-250 (2009) · Zbl 1181.90024 |
| [149] | Tijms, H. C.; Groenevelt, H., Simple approximations for the reorder point in periodic and continuous review \((s, S)\) inventory systems with service level constraints, European Journal of Operational Research, 17, 175-190 (1984) · Zbl 0547.90025 |
| [150] | van Donselaar, K.; de Kok, T.; Rutten, W., Two replenishment strategies for the lost sales inventory model: A comparison, International Journal of Production Economics, 46-47, 285-295 (1996) |
| [151] | Veinott, A. F., Optimal policy in a dynamic, single product, nonstationary inventory model with several demand classes, Operations Research, 13, 761-778 (1965) · Zbl 0143.21704 |
| [152] | Veinott, A. F., On the optimality of \((s, S)\) inventory policies: New conditions and a new proof, SIAM Journal of Applied Mathematics, 14, 1067-1083 (1966) · Zbl 0173.47603 |
| [153] | Veinott, A. F.; Wagner, H. M., Computing optimal \((s, S)\) inventory policies, Management Science, 11, 525-552 (1965) · Zbl 0137.14102 |
| [154] | Verhoef, P. C.; Sloot, L. M., Out-of-stock: Reactions, antecedents, management solutions, and a future perspective, (Krafft, M.; Mantrala, M. K., Retailing in the 21st Century: Current and Future Trends (2006), Springer Publishers: Springer Publishers Philadelphia, Pennsylvania, USA), 239-253 |
| [155] | Weinstock, J.; Young, D., The influence of correlation of replenishment times on inventory control systems, Operations Research, 5, 145-146 (1957) |
| [156] | Williams, B. D.; Tokar, T., A review of inventory management research in major logistics journals - Themes and future directions, The International Journal of Logistics Management, 19, 212-232 (2008) |
| [157] | Xu, Y.; Bisi, A.; Dada, M., New structural properties of \((s, S)\) policies for inventory models with lost sales, Operations Research Letters, 38, 441-449 (2010) · Zbl 1217.90027 |
| [158] | Yadavalli, V. S.S.; Anbazhagan, N.; Arivarignan, G., A two-commodity stochastic inventory system with lost sales, Stochastic Analysis and Applications, 22, 479-497 (2004) · Zbl 1151.90321 |
| [159] | Yang, G. K.; Chou, S.-Y.; Hung, C.-Y.; Lin, J. S.-J.; Chu, P., Research note on the criteria for the optimal solution of the inventory model with a mixture of partial backordering and lost sales, Applied Mathematical Modelling, 32, 1758-1768 (2008) · Zbl 1145.90318 |
| [160] | Yaspan, A., An inclusive solution to the inventory problem, Operations Research, 9, 371-382 (1961) · Zbl 0096.14107 |
| [161] | Yaspan, A., Fixed-stockout-probability order quantities with lost sales and time lag, Operations Research, 20, 903-904 (1972) |
| [162] | Zabel, E., A note on the optimality of \((s, S)\) policies in inventory theory, Management Science, 9, 123-125 (1962) |
| [163] | Zabel, E., Equilibrium and adjustments in noncompetitive markets: Lost sales versus backlogging processes, Engineering Cost and Product Economics, 19, 91-99 (1990) |
| [164] | Zheng, Y. S.; Federgruen, A., Finding optimal \((s, S)\) policies is about as simple as evaluating a single policy, Operations Research, 39, 654-665 (1991) · Zbl 0749.90024 |
| [165] | Zipkin, P. H., Old and new methods for lost-sales inventory systems, Operations Research, 56, 1256-1263 (2008) · Zbl 1167.90370 |
| [166] | Zipkin, P. H., On the structure of lost-sales inventory models, Operations Research, 56, 937-944 (2008) · Zbl 1167.90369 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
