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Journal ArticleDOI

Dynamic pricing policies for an inventory model with random windows of opportunities

01 Dec 2018-Naval Research Logistics (University of Twente, Department of Applied Mathematics)-Vol. 65, Iss: 8, pp 660-675
TL;DR: In this article, the authors consider a single-product fluid-inventory model in which the procurement price of the product fluctuates according to a continuous time Markov chain and derive the associated steady-state distributions and cost functionals.
Abstract: We study a single-product fluid-inventory model in which the procurement price of the product fluctuates according to a continuous time Markov chain. We assume that a fixed order price, in addition to state-dependent holding costs are incurred, and that the depletion rate of inventory is determined by the sell price of the product. Hence, at any time the controller has to simultaneously decide on the selling price of the product and whether to order or not, taking into account the current procurement price and the inventory level. In particular, the controller is faced with the question of how to best exploit the random time windows in which the procurement price is low. We consider two policies, derive the associated steady-state distributions and cost functionals, and apply those cost functionals to study the two policies.© 2017 Wiley Periodicals, Inc. Naval Research Logistics, 2017

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Citations
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Journal ArticleDOI
12 May 2021
TL;DR: This paper looks at opportunistic-type inventory replenishment in which there is an independent point process that is used to model events that are called opportunistic for replenishing inventory.
Abstract: Combining the study of queuing with inventory is very common and such systems are referred to as queuing-inventory systems in the literature. These systems occur naturally in practice and have been studied extensively in the literature. The inventory systems considered in the literature generally include (s,S)-type. However, in this paper we look at opportunistic-type inventory replenishment in which there is an independent point process that is used to model events that are called opportunistic for replenishing inventory. When an opportunity (to replenish) occurs, a probabilistic rule that depends on the inventory level is used to determine whether to avail it or not. Assuming that the customers arrive according to a Markovian arrival process, the demands for inventory occur in batches of varying size, the demands require random service times that are modeled using a continuous-time phase-type distribution, and the point process for the opportunistic replenishment is a Poisson process, we apply matrix-analytic methods to study two of such models. In one of the models, the customers are lost when at arrivals there is no inventory and in the other model, the customers can enter into the system even if the inventory is zero but the server has to be busy at that moment. However, the customers are lost at arrivals when the server is idle with zero inventory or at service completion epochs that leave the inventory to be zero. Illustrative numerical examples are presented, and some possible future work is highlighted.

7 citations

Journal ArticleDOI
TL;DR: In this article , the authors proposed a new model for correlated customer arrivals in the NRM problem and derived a new linear programming (LP) approximation of the optimal policy for solving the problem under this model.
Abstract: The Network Revenue Management (NRM) problem is a well-known challenge in dynamic decision-making under uncertainty. In this problem, fixed resources must be allocated to serve customers over a finite horizon, while customers arrive according to a stochastic process. The typical NRM model assumes that customer arrivals are independent over time. However, in this paper, we explore a more general setting where customer arrivals over different periods can be correlated. We propose a new model that assumes the existence of a system state, which determines customer arrivals for the current period. This system state evolves over time according to a time-inhomogeneous Markov chain. Our model can be used to represent correlation in various settings and synthesizes previous literature on correlation models. To solve the NRM problem under our correlated model, we derive a new linear programming (LP) approximation of the optimal policy. Our approximation provides a tighter upper bound on the total expected value collected by the optimal policy than existing upper bounds. We use our LP to develop a new bid price policy, which computes bid prices for each system state and time period in a backward induction manner. The decision is then made by comparing the reward of the customer against the associated bid prices. Our policy guarantees to collect at least $1/(1+L)$ fraction of the total reward collected by the optimal policy, where $L$ denotes the maximum number of resources required by a customer. In summary, our work presents a new model for correlated customer arrivals in the NRM problem and provides an LP approximation for solving the problem under this model. We derive a new bid price policy and provides a theoretical guarantee on the performance of the policy.
Journal ArticleDOI
TL;DR: In this paper , the renewal reward theorem is used to derive the expected profit per unit of time for a retailer when the discount price arrives randomly and the time variable is discrete, and the optimal inventory policy can be obtained by considering the variations in the purchase price as a discrete-time Markov chain.
Abstract: Most of the time retailers are offered discount prices that are occurring at random points in time. One such scenario is the supplier offering discounts to the retailers to increase market share, cash flow, and to reduce the inventory of specific items. Surprisingly no models exist in the literature survey to model the randomly occurring discount price under discrete time. The primary objective of this article is to develop an optimal inventory policy for a retailer when the discount price arrives randomly and the time variable is discrete. Under such a scenario, the optimal inventory policy can be obtained by considering the variations in the purchase price as a discrete-time Markov chain. The renewal reward theorem is used to derive the expected profit per unit of time. To illustrate the application of the developed model a real case study is considered. The optimal solution of the developed model is compared with the EOQ policy and found that the developed model solution provides better profit. This justifies the significance of the developed model. The inventory manager can use the developed model as a tool to obtain the optimal solution for any two price problems that repeat randomly.
References
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Journal ArticleDOI
TL;DR: In this paper, the authors consider the replenishment and stocking decision for inventory systems in which price discounts, referred to as deals, are offered by the supplier or the market place at random points in time.
Abstract: This paper considers the replenishment and stocking decision for inventory systems in which price discounts, referred to as deals, are offered by the supplier or the market place at random points in time. Assuming that the demand is constant over time, the times between deal offerings are exponentially distributed and that the order leadtimes are negligible, we derive expressions for evaluating the operating characteristics of the model. Moreover, we derive expressions for determining the optimal policy parameters for such systems and present results on the behavior of the optimal policy parameters. Our results are easy to implement, intuitive and provide managerial insights and a better understanding on the effect of random deal offerings on replenishment and stocking decisions. In addition, we suggest a back of envelope heuristic solution for deriving the policy parameters.

56 citations

Book
16 Mar 2009
TL;DR: This research presents a novel approach to level crossing estimation called “Embedded Level Crossing Method”, which automates the very labor-intensive and therefore time-heavy and expensive process of manually crossing levels.
Abstract: Origin Of Level Crossing Method.- Sample Path And System Point.- M/G/1 Queues And Variants.- M/M/C Queues.- G/M/c Queues.- Dams and Inventories.- Multi-Dimensional Models.- Embedded Level Crossing Method.- Level Crossing Estimation.- Additional Applications.

52 citations

Journal ArticleDOI
TL;DR: A bijection is constructed from the PRR space to the space of positive roots of Lundberg's fundamental equation, to be referred to as the Lundberg positive rootLPR space, which allows for closed-form expressions for the aforementioned cost metrics with respect to the LPR variable, in lieu of thePRR variable.
Abstract: This paper considers a continuous-review, single-product, production-inventory system with a constant replenishment rate, compound Poisson demands, and lost sales. Two objective functions that represent metrics of operational costs are considered: 1 the sum of the expected discounted inventory holding costs and lost-sales penalties, both over an infinite time horizon, given an initial inventory level; and 2 the long-run time average of the same costs. The goal is to minimize these cost metrics with respect to the replenishment rate. It is, however, not possible to obtain closed-form expressions for the aforementioned cost functions directly in terms of positive replenishment rate PRR. To overcome this difficulty, we construct a bijection from the PRR space to the space of positive roots of Lundberg's fundamental equation, to be referred to as the Lundberg positive rootLPR space. This transformation allows us to derive closed-form expressions for the aforementioned cost metrics with respect to the LPR variable, in lieu of the PRR variable. We then proceed to solve the optimization problem in the LPR space and, finally, recover the optimal replenishment rate from the optimal LPR variable via the inverse bijection. For the special cases of constant or loss-proportional penalty and exponentially distributed demand sizes, we obtain simpler explicit formulas for the optimal replenishment rate.

49 citations

Journal ArticleDOI
TL;DR: This paper addresses the problem of inventory penalty pricing under the risk-neutral valuation principle by treating the penalties as a series of perpetual American options, and constructs auxiliary martingale processes in term of the inventory process.
Abstract: This paper addresses the problem of inventory penalty pricing under the risk-neutral valuation principle. The underlying production-inventory system has a constant replenishment rate and a compound renewal demand stream (i.e., iid demand interarrival times are independent of iid demand sizes), and is subject to underage and overage penalties. Our pricing approach treats the penalties as a series of perpetual American options, and constructs auxiliary martingale processes in term of the inventory process. We provide a necessary and sufficient martingale condition for general compound renewal demands. Explicit expressions of penalty functions for underage and overage are obtained for the case where demand arrivals follow a Poisson process.

44 citations


"Dynamic pricing policies for an inv..." refers background in this paper

  • ...) In [28], the authors consider an inventory model which replenishes at a constant deterministic rate, but decreases randomly (via jumps) when demand arrives (according to a compound renewal process); implying that the demand at each arrival epoch is relatively very large....

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Journal ArticleDOI
TL;DR: In this article, the authors present a model that incorporates variations in the demand rate at random time points into the inventory planning decision, which may occur due to economic recessions, labor strife starting or ending, or other events that result in a period of time during which the rate of demand is shifted up or down from its current level.
Abstract: This paper presents a model that incorporates variations in the demand rate at random time points into the inventory planning decision. These changes in demand may occur due to economic recessions, labor strife starting or ending, or other events that result in a period of time during which the rate of demand is shifted up or down from its current level. The paper uses system-point level-crossing theory to derive expressions for the distribution and expected value of on-hand inventory, ordering rate, and the expected total cost rate for a given ordering policy. A sensitivity analysis is conducted, and a number of qualitative properties are provided to illustrate the use of the results to obtain optimal order quantities.

38 citations


"Dynamic pricing policies for an inv..." refers background in this paper

  • ...The paper [6] considers a fluid-inventory model in which the demand rate changes according to a CTMC; whenever the inventory content hits 0 an order of size Qi is placed if the governing CTMC is at state i, i = 1, 2....

    [...]