Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs

He, Shuangchi; Yao, Dacheng; Zhang, Hanqin

doi:10.1287/moor.2016.0833

Cited by 30 publications

(44 citation statements)

References 53 publications

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“…Our results differ from those in [12,15,16,26,27]. These papers deal with the long-term average cost criterion for continuous-time models, and indicate that under the respective circumstances an (s, S) policy is optimal.…”

Section: Introductioncontrasting

confidence: 88%

Optimal policies for a deterministic continuous-time inventory model with several suppliers

Benkherouf

Gilding

2021

RAIRO-Oper. Res.

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This paper is concerned with determining the optimal inventory policy for an infinite-horizon deterministic continuous-time continuous-state inventory model, where, in the absence of intervention, changes in inventory level are governed by a differential evolution equation. The decision maker has the option of ordering from several suppliers, each of which entails differing ordering and purchasing costs. The objective is to select the supplier and the size of the order that minimizes the discounted cost over an infinite planning horizon. The optimal policy is formulated as the solution of a quasi-variational inequality. It is shown that there are three possibilities regarding its solvability: it has a unique solution that corresponds to an (s, S) policy; it does not admit a solution corresponding to an (s, S) policy but does have a unique solution that corresponds to a generalized (s, S) policy; or, it does not admit a solution corresponding to an (s, S) policy or a generalized (s, S) policy. A necessary and sufficient condition for each possibility is obtained. Examples illustrate their occurrence.

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Section: Introductioncontrasting

confidence: 88%

Optimal policies for a deterministic continuous-time inventory model with several suppliers

Benkherouf

Gilding

2021

RAIRO-Oper. Res.

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show abstract

“…We begin by examining the classical model that has been studied by Bather (1966), Sulem (1986), Dai and Yao (2013), and many others. In particular, we show that Theorem 5.1 extends the result in He et al (2017) and verifies optimality as a result of our analytical approach. We then examine a drifted Brownian motion process with reflection at {0} using a nontraditional cost structure.…”

Section: Drifted Brownian Motion Inventory Modelssupporting

confidence: 78%

“…In contrast, in Helmes et al (2017) we showed optimality in a smaller class of ordering policies for the general models under a more restrictive set of conditions. Optimality of (s, S) policies for the general class of admissible policies for two examples from He et al (2017) and Helmes et al (2017) was established using ad hoc methods specifically tuned to the examples.…”

Section: Introductionmentioning

confidence: 99%

A weak convergence approach to inventory control using a long-term average criterion

Helmes¹,

Stockbridge

Zhu

2018

Adv. Appl. Probab.

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This paper continues the examination of inventory control in which the inventory is modelled by a diffusion process and a long-term average cost criterion is used to make decisions. The class of such models under consideration have general drift and diffusion coefficients and boundary points that are consistent with the notion that demand should tend to reduce the inventory level. The conditions on the cost functions are greatly relaxed from those in Helmes et al. (2017). Characterization of the cost of a general (s, S) policy as a function of two variables naturally leads to a nonlinear optimization problem over the ordering levels s and S. Existence of an optimizing pair (s * , S * ) is established for these models under very weak conditions; non-existence of an optimizing pair is also discussed. Using average expected occupation and ordering measures and weak convergence arguments, weak conditions are given for the optimality of the (s * , S * ) ordering policy in the general class of admissible policies. The analysis involves an auxiliary function that is globally C 2 and which, together with the infimal cost, solves a particular system of linear equations and inequalities related to but different from the long-term average Hamilton-Jacobi-Bellman equation. This approach provides an analytical solution to the problem rather than a solution involving intricate analysis of the stochastic processes. The range of applicability of these results is illustrated on a drifted Brownian motion inventory model, both unconstrained and reflected, and on a geometric Brownian motion inventory model under two different cost structures.MSC Classifications. 93E20, 90B05, 60H30

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“…We do note however that in a recent study, He et al. () has shown that in a different stochastic setting where demand is governed by a Brownian motion, ( s , S )‐optimality holds when the fixed‐plus‐proportional ordering cost structure is relaxed to allow the setup cost to be a bounded and lower semicontinuous function of the order quantity.…”

Section: Introductionmentioning

confidence: 81%

Optimality of (s, S) Inventory Policies under Renewal Demand and General Cost Structures

Perera

Janakiraman

Niu

2018

Production and Operations Management

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W e study a single-stage, continuous-time inventory model where unit-sized demands arrive according to a renewal process and show that an (s, S) policy is optimal under minimal assumptions on the ordering/procurement and holding/backorder cost functions. To our knowledge, the derivation of almost all existing (s, S)-optimality results for stochastic inventory models assume that the ordering cost is composed of a fixed setup cost and a proportional variable cost; in contrast, our formulation allows virtually any reasonable ordering-cost structure. Thus, our paper demonstrates that (s, S)-optimality actually holds in an important, primitive stochastic setting for all other practically interesting ordering cost structures such as well-known quantity discount schemes (e.g., all-units, incremental and truckload), multiple setup costs, supplier-imposed size constraints (e.g., batch-ordering and minimum-order-quantity), arbitrary increasing and concave cost, as well as any variants of these. It is noteworthy that our proof only relies on elementary arguments.

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Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs

Cited by 30 publications

References 53 publications

Optimal policies for a deterministic continuous-time inventory model with several suppliers

Optimal policies for a deterministic continuous-time inventory model with several suppliers

A weak convergence approach to inventory control using a long-term average criterion

Optimality of (s, S) Inventory Policies under Renewal Demand and General Cost Structures

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