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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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
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.
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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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.
1,689 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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TL;DR: In this paper, the authors 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, and obtain structural monotonicity results for the optimal intensity resp, price as a function of the stock level and the length of the horizon.
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
1,537 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
TL;DR: In this paper, the authors demonstrate that analogous conclusions can be drawn for queueing models if two basic conditions are satisfied: (i) the individual car driver on making an optimal routing choice for himself-does not optimize the system at large, and (ii) the traffic load is not maximized by the individual driver.
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:
1,080 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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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.
954 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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