A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case

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Fixed costs of ordering items or setting up a production process arise in many real-life scenarios. In their presence, the most widely used ordering policy in the stochastic inventory literature is the (s, S) policy. Optimality of (s, S) policies and (s, S)-type policies have been examined for various inventory models, including those with the inventory level being reviewed in every period or continuously, finite and infinite horizons, discounted-cost and average-cost criteria, backlogging and lost-sales practices, standard and generalized demands and/or costs, deterministic and stochastic lead times, single-product and multi-product settings, and coordinated pricing-inventory decisions. We comprehensively survey the vast literature accumulated over seven decades in two papers. This paper is devoted to discrete-time models, and the companion paper, also published in this journal issue, reviews continuous-time models. We go over model specifications, proof techniques, specific results, and limitations of the articles published in the literature. We conclude each paper by providing corresponding suggestions for extensions and directions for future research. K E Y W O R D Sdiscounted-and average-cost criteria, discrete-time inventory models, K-convexity, Markovian demand, optimality of (s, S)-type policies CONTENTS

“…With these relaxations, the

( {s, S} )

Section: Discounted Cost Criterionmentioning

confidence: 99%

Section: Concluding Remarks and Future Researchmentioning

confidence: 99%

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A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case

Perera

Sethi

2023

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“…(1951) and introducing K ‐convexity, and Veinott and Wagner (1965), Song and Zipkin (1993), or Sethi and Cheng (1997) generalize these findings (e.g., for Markovian demands, positive lead times). For a definition of K ‐convexity, see, for example, Porteus (2002), and for a survey of extensions of optimal

(s,S)

policies in the discrete‐time setting, see Perera and Sethi (2023b), and in the continuous‐time setting, Perera and Sethi (2023a). However, existing results require fixed costs to be either constant or at least nonincreasing in their values over time (or in their expected values of state‐dependent fixed order costs for the Markovian case).…”

Section: Literature Reviewmentioning

confidence: 99%

Optimal inventory control with cyclic fixed order costs

Taube

Minner

2023

We consider a periodic review single‐item inventory model under stochastic demand. Every m periods, in the regular order period, fixed order costs are K. In the periods in‐between, the intraperiods, higher fixed order costs of apply. The literature on optimal inventory policies under fixed order costs does not account for these time‐dependent fixed order costs. By generalizing existing proofs for optimal inventory policies, we close this gap in inventory theory. The optimal inventory policy is complex in the regular order period and in the intraperiods, a period‐dependent policy is optimal. We describe and prove this optimal policy based on the notion of K‐convexity and the optimal ordering behavior in the presence of non–K‐convex cost functions. In a numerical study, we find that a major driver of the optimal policy is a forward‐buying effect that shifts the probability of ordering from the intraperiods to the regular order period. The cost differences between the optimal and a pure period‐dependent policy are, however, small.

“…(1951) had formulated the lost sales case, Scarf treated the case of backlogging and Shreve (1976) extended Scarf's proof to the lost sales case. For a comprehensive survey of the literature on the ( s, S ) policy, see Perera and Sethi (2022).…”

Section: Direct Om Contributions Of Nobel Laureates Between 1972 and ...mentioning

confidence: 99%

Nobel laureates’ contributions to and impacts on operations management

Sethi

Gupta

Agrawal

et al. 2022

Operations management (OM) has evolved to its current status due to the contributions of researchers in many fields including economics, finance, behavioral sciences, operations research/management science, mathematics, statistics, and computer science. Many of these contributors are Nobel laureates—winners of the highest academic award. The Nobel Memorial Prize in Economic Sciences is awarded to those with monumental works in economics. Yet, some winners have also made contributions to operations management, the field of this journal. Others have developed important concepts and techniques that have made an enormous impact on OM research. Here, we describe the OM contributions as well as the impactful concepts of these Laureates.