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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

AbstractWe 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

Topics: Limit price (65%), Procurement (56%), Dynamic pricing (55%), Holding cost (54%), Order (exchange) (52%)

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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.

1 citations


References
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Book
10 Feb 1989
TL;DR: An integrated treatment of applied stochastic processes and queueing theory, with an emphasis on time-averages and long-run behavior.
Abstract: An integrated treatment of applied stochastic processes and queueing theory, with an emphasis on time-averages and long-run behavior. Theory demonstrates practical effects, such as priorities, pooling of queues, and bottlenecks. Appropriate for Sr/Grad courses in queueing theory in Operations Research, Computer Science, Statistics, or IE departments.

1,673 citations


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

  • ...Since the expensive period is exponentially distributed with rate λ, it follows by the well-known PASTA (Poisson Arrivals See Time Average [33]) property that if C1(τ−) > 0, then C1(τ−) and C1 are equal in distribution, and the rate at which level x is upcrossed is λ....

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Journal ArticleDOI
Abstract: In many industries, managers face the problem of selling a given stock of items by a deadline We investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm's objective is to maximize expected revenues Examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry, which markets space such as seats on airline flights, cabins on vacation cruises, and rooms in hotels that become worthless if not sold by a specific time We formulate this problem using intensity control and obtain structural monotonicity results for the optimal intensity resp, price as a function of the stock level and the length of the horizon For a particular exponential family of demand functions, we find the optimal pricing policy in closed form For general demand functions, we find an upper bound on the expected revenue based on analyzing the deterministic version of the problem and use this bound to prove that simple, fixed price policies are asymptotically optimal as the volume of expected sales tends to infinity Finally, we extend our results to the case where demand is compound Poisson; only a finite number of prices is allowed; the demand rate is time varying; holding costs are incurred and cash flows are discounted; the initial stock is a decision variable; and reordering, overbooking, and random cancellations are allowed

1,427 citations


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

  • ...In practice, that probability, and thus the response function, are not known in complete certainty, although they can typically be evaluated via past demand data; see [17] and the reference therein....

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Book
01 Dec 1992
TL;DR: Chapter 1 Strategy and Competition Chapter 2 Forecasting Chapter 3 Aggregate Planning Supplement 1 Linear Programming Chapter 4 Inventory Control Subject to Known Demand Chapter 5 Inventory Control subject to Uncertain Demand Chapter 6 Supply Chain Management Chapter 7 Push and Pull Production Control Systems: MRP and JIT.
Abstract: Chapter 1 Strategy and Competition Chapter 2 Forecasting Chapter 3 Aggregate Planning Supplement 1 Linear Programming Chapter 4 Inventory Control Subject to Known Demand Chapter 5 Inventory Control Subject to Uncertain Demand Chapter 6 Supply Chain Management Chapter 7 Push and Pull Production Control Systems: MRP and JIT Chapter 8 Operations Scheduling Supplement 2 Queuing Theory Chapter 9 Project Scheduling Chapter 10 Facilities Layout and Location Chapter 11 Quality and Assurance Chapter 12 Reliability and Maintainability Appendix Tables Index

1,379 citations


Journal ArticleDOI
Abstract: SOME DISCUSSION has arisen recently as to whether the imposition of an "entrance fee" on arriving customers who wish to be serviced by a station and hence join a waiting line is a rational measure. Not much of this discussion has appeared in print; indeed this author is aware of only three short communications, representing an exchange of arguments between Leeman [1, 2] and Saaty [3]. The ideas advanced there were of qualitative character and no attempt was made to quantify the arguments. The problem under consideration is obviously analogous to one that arises in connection with the control of vehicular traffic congestion on a road network. It has been argued2 by traffic economists that the individual car driver on making an optimal routing choice for himself-does not optimize the system at large. The purpose of this communication is to demonstrate that, indeed, analogous conclusions can be drawn for queueing models if two basic conditions are satisfied:

962 citations


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

  • ...Starting with the seminal work of Naor [26], a standard assumption in the economic analysis of queues is that customers’ arrival rate to a service system is completely determined by the price and expected reward of joining the system to get served....

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  • ...Price-Regulated Demand Starting with the seminal work of Naor [26], a standard assumption in the economic analysis of queues is that customers’ arrival rate to a service system is completely determined by the price and expected reward of joining the system to get served....

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Journal ArticleDOI
TL;DR: Stochastic calculus for these stochastic processes is developed and a complete characterization of the extended generator is given; this is the main technical result of the paper.
Abstract: A general class of non-diffusion stochastic models is introduced with a view to providing a framework for studying optimization problems arising in queueing systems, inventory theory, resource allocation and other areas. The corresponding stochastic processes are Markov processes consisting of a mixture of deterministic motion and random jumps. Stochastic calculus for these processes is developed and a complete characterization of the extended generator is given; this is the main technical result of the paper. The relevance of the extended generator concept in applied problems is discussed and some recent results on optimal control of piecewise-deterministic processes are described.

881 citations


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

  • ...Since our model has nonincreasing sample paths between jumps, it must exhibit a deterministic motion between jump epochs, so that it is a piecewise-deterministic Markov process, as in [15]....

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