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Clearing Systems and ( s , S ) Inventory Systems with Nonlinear Costs and Positive Lead Times

Author

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  • Shaler Stidham

    (North Carolina State University, Raleigh, North Carolina)

Abstract

Stochastic clearing systems model many different applications, including certain bulk server queues, shuttle buses, and buffers in communication systems. We extend the characterization of the optimal parameters of a generalized stochastic clearing system (Stidham, S., Jr. 1977. Cost models for stochastic clearing systems. Opns. Res. 25 100–127.) from piece-wise linear to general convex cost-rate functions, and discuss applications to continuous-review and periodic-review ( s , S ) inventory models with nonlinear holding and storage costs and/or nonzero lead times. As in Stidham, we show that log-concavity of the sojourn function associated with the input process guarantees that the necessary conditions are also sufficient for optimality of the clearing parameters, which correspond to s and S in inventory examples. Our conditions are weaker and our model more general than those found in the previous literature on ( s , S ) inventory models.

Suggested Citation

  • Shaler Stidham, 1986. "Clearing Systems and ( s , S ) Inventory Systems with Nonlinear Costs and Positive Lead Times," Operations Research, INFORMS, vol. 34(2), pages 276-280, April.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:2:p:276-280
    DOI: 10.1287/opre.34.2.276
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    Citations

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    Cited by:

    1. Oded Berman & Mahmut Parlar & David Perry & M. J. M. Posner, 2005. "Production/Clearing Models Under Continuous and Sporadic Reviews," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 203-224, June.
    2. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    3. Qi‐Ming He & James H. Bookbinder & Qishu Cai, 2020. "Optimal policies for stochastic clearing systems with time‐dependent delay penalties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 487-502, October.
    4. David Perry & Wolfgang Stadje & Shelemyahu Zacks, 2005. "Sporadic and Continuous Clearing Policies for a Production/Inventory System Under an M / G Demand Process," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 354-368, May.
    5. Apurva Jain & Kamran Moinzadeh & Yong-Pin Zhou, 2012. "A Single-Supplier, Multiple-Retailer Model with Single-Season, Multiple-Ordering Opportunities, and Fixed Ordering Cost," Operations Research, INFORMS, vol. 60(5), pages 1098-1110, October.
    6. Perry, David & Stadje, Wolfgang, 2000. "Risk analysis for a stochastic cash management model with two types of customers," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 25-36, February.
    7. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.

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