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Managing stochastic inventory systems with free shipping option. (English) Zbl 1159.90010
Summary: In many industries, customers are offered free shipping whenever an order placed exceeds a minimum quantity specified by suppliers. This allows the suppliers to achieve economies of scale in terms of production and distribution by encouraging customers to place large orders. In this paper, we consider the optimal policy of a retailer who operates a single-product inventory system under periodic review. The ordering cost of the retailer is a linear function of the ordering quantity, and the shipping cost is a fixed constant $K$ whenever the order size is less than a given quantity - the free shipping quantity (FSQ), and it is zero whenever the order size is at least as much as the FSQ. Demands in different time periods are i.i.d. random variables. We provide the optimal inventory control policy and characterize its structural properties for the single-period model. For multi-period inventory systems, we propose and analyze a heuristic policy that has a simple structure, the $(s, t, S)$ policy. Optimal parameters of the proposed heuristic policy are then computed. Through an extensive numerical study, we demonstrate that the heuristic policy is sufficiently accurate and close to optimal.

90B05Inventory, storage, reservoirs
90C59Approximation methods and heuristics
Full Text: DOI
[1] Aviv, Y.; Federgruen, A.: Capacitated multi-item inventory systems with random and seasonally fluctuating demands: implications for postponement strategies, Management science 47, 512-531 (2001) · Zbl 1232.90010 · doi:10.1287/mnsc.47.4.512.9829
[2] Bradley, J.; Robinson, L.: Improved base-stock approximations for independent stochastic lead times with order crossover, Manufacturing and service operations management 7, 319-329 (2005)
[3] Chen, F.; Zheng, Y.: Lower bounds for multi-echelon stochastic inventory problems, Management science 40, 1426-1443 (1994) · Zbl 0823.90034 · doi:10.1287/mnsc.40.11.1426
[4] Clark, A.; Scarf, S.: Optimal policies for a multi-echelon inventory problem, Management science 6, 475-490 (1960)
[5] Derman, C.: Finite state Markovian decision processes, (1970) · Zbl 0262.90001
[6] Federgruen, A.; Zipkin, P.: Computational issues in an infinite horizon, multi-echelon inventory model, Operations research 32, 818-836 (1984) · Zbl 0546.90026 · doi:10.1287/opre.32.4.818
[7] Fisher, M.; Raman, A.: Reducing the cost of demand uncertainty through accurate response to early sales, Operations research 44, 87-99 (1996) · Zbl 0847.90065 · doi:10.1287/opre.44.1.87
[8] Heyman, D.; Sobel, M.: Stochastic models in operations research, Stochastic models in operations research 2 (1984) · Zbl 0531.90062
[9] Kaplan, R.: A dynamic inventory model with stochastic lead times, Management science 17, 491-507 (1970) · Zbl 0193.19603 · doi:10.1287/mnsc.16.7.491
[10] Robb, D.; Silver, E.: Inventory management with periodic ordering and minimum order quantities, The journal of the operational research society 49, 1085-1094 (1998) · Zbl 1140.90321
[11] Ross, S.: Applied probability models with optimization applications, (1992) · Zbl 1191.60001
[12] Scarf, H.: The optimality of (s,S) policies in the dynamic inventory problem, Mathematical methods in the social sciences (1960) · Zbl 0203.22102
[13] Silver, E.; Pyke, D.; Peterson, R.: Inventory management and production planning and scheduling, (1998)
[14] Tijms, H. C.: Stochastic models: an algorithmic approach, (1994) · Zbl 0838.60075
[15] Veinott, A. F.: The status of mathematical inventory theory, Management science 12, 745-777 (1966) · Zbl 0143.21801
[16] Zalkind, D.: Order-level inventory systems with independent stochastic leadtimes, Management science 24, 1384-1392 (1978) · Zbl 0491.90032 · doi:10.1287/mnsc.24.13.1384
[17] Zhao, Y.; Katehakis, M. N.: On the structure of optimal ordering policy of stochastic inventory systems with minimum order quantity, Probability in the engineering and information sciences 20, 257-270 (2006) · Zbl 1141.90332 · doi:10.1017/S0269964806060165
[18] Zheng, Y.; Federgruen, A.: Finding the optimal (s, S) policies is about as simple as evaluating a single policy, Operations research 39, 654-665 (1991) · Zbl 0749.90024 · doi:10.1287/opre.39.4.654
[19] Zhou, B.; Zhao, Y.; Katehakis, M. N.: Effective control policies for stochastic inventory systems with a minimum order quantity and linear costs, International journal of production economics 106, 523-531 (2007)