Dynamic Pricing and Inventory Control with Fixed Ordering Cost and Incomplete Demand Information

2021 ◽  
Author(s):  
Boxiao Chen ◽  
David Simchi-Levi ◽  
Yining Wang ◽  
Yuan Zhou
Keyword(s):  
Online Learning ◽  
Inventory Control ◽  
Dynamic Pricing ◽  
Empirical Distribution ◽  
Learning Algorithms ◽  
Pricing Strategy ◽  
Inventory Level ◽  
Demand Information ◽  
Dependent Samples ◽  
Optimal Formula

We consider the periodic review dynamic pricing and inventory control problem with fixed ordering cost. Demand is random and price dependent, and unsatisfied demand is backlogged. With complete demand information, the celebrated [Formula: see text] policy is proved to be optimal, where s and S are the reorder point and order-up-to level for ordering strategy, and [Formula: see text], a function of on-hand inventory level, characterizes the pricing strategy. In this paper, we consider incomplete demand information and develop online learning algorithms whose average profit approaches that of the optimal [Formula: see text] with a tight [Formula: see text] regret rate. A number of salient features differentiate our work from the existing online learning researches in the operations management (OM) literature. First, computing the optimal [Formula: see text] policy requires solving a dynamic programming (DP) over multiple periods involving unknown quantities, which is different from the majority of learning problems in OM that only require solving single-period optimization questions. It is hence challenging to establish stability results through DP recursions, which we accomplish by proving uniform convergence of the profit-to-go function. The necessity of analyzing action-dependent state transition over multiple periods resembles the reinforcement learning question, considerably more difficult than existing bandit learning algorithms. Second, the pricing function [Formula: see text] is of infinite dimension, and approaching it is much more challenging than approaching a finite number of parameters as seen in existing researches. The demand-price relationship is estimated based on upper confidence bound, but the confidence interval cannot be explicitly calculated due to the complexity of the DP recursion. Finally, because of the multiperiod nature of [Formula: see text] policies the actual distribution of the randomness in demand plays an important role in determining the optimal pricing strategy [Formula: see text], which is unknown to the learner a priori. In this paper, the demand randomness is approximated by an empirical distribution constructed using dependent samples, and a novel Wasserstein metric-based argument is employed to prove convergence of the empirical distribution. This paper was accepted by J. George Shanthikumar, big data analytics.

scholarly journals Inventory Control by Multiple Service Levels under Unreliable Supplying Condition

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Byungsoo Na ◽  
Jinpyo Lee ◽  
Hyung Jun Ahn
Keyword(s):  
Inventory Control ◽  
Real World ◽  
Dynamic Pricing ◽  
Threshold Level ◽  
Service Level ◽  
The Other ◽  
Inventory Level ◽  
Service Levels ◽  
Extra Charge ◽  
Threshold Price

We consider an inventory system where there is random demand from customers as well as unreliable supplying capacity from supplier. In many real-world cases, supplier might fail to satisfy the amount of order from retailers or producers so that only partial proportion of order is satisfied or even fail to deliver all of the order. Moreover, recently a concern regarding unreliable supplying capacity has been increasing since the globalization makes the retailer or producer face the extended supply network with complicated and risky supplying capacity. Also, we consider two classified customers, of which one is willing to pay extra charge for expedited delivery service but the other is not reluctant to delay the delivery without any extra charge. We show that there exists an optimal threshold for inventory and price for each service level in the following sense: if the inventory level is less than the predetermined threshold, then the retailer or producer needs to order up to the threshold level and offer threshold price corresponding to service level. Otherwise, the retailer does not need to order. The risk of stockout due to unreliable supplying capacity can be mitigated by the dynamic pricing and inventory control with multiple service levels.

Dynamic Inventory Control with Stockout Substitution and Demand Learning

2020 ◽  
Vol 66 (11) ◽  
pp. 5108-5127 ◽  
Author(s):  
Boxiao Chen ◽  
Xiuli Chao
Keyword(s):  
Inventory Control ◽  
Learning Algorithm ◽  
A Priori ◽  
Big Data Analytics ◽  
Inventory Level ◽  
Worst Case ◽  
Sales Data ◽  
Demand Learning ◽  
Demand Distribution ◽  
Demand Information

We consider an inventory control problem with multiple products and stockout substitution. The firm knows neither the primary demand distribution for each product nor the customers’ substitution probabilities between products a priori, and it needs to learn such information from sales data on the fly. One challenge in this problem is that the firm cannot distinguish between primary demand and substitution (overflow) demand from the sales data of any product, and lost sales are not observable. To circumvent these difficulties, we construct learning stages with each stage consisting of a cyclic exploration scheme and a benchmark exploration interval. The benchmark interval allows us to isolate the primary demand information from the sales data, and then this information is used against the sales data from the cyclic exploration intervals to estimate substitution probabilities. Because raising the inventory level helps obtain primary demand information but hinders substitution demand information, inventory decisions have to be carefully balanced to learn them together. We show that our learning algorithm admits a worst-case regret rate that (almost) matches the theoretical lower bound, and numerical experiments demonstrate that the algorithm performs very well. This paper was accepted by J. George Shanthikumar, big data analytics.

scholarly journals Dynamic Pricing and Optimal Control for a Stochastic Inventory System with Non-Instantaneous Deteriorating Items and Partial Backlogging

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 906
Author(s):  
Xuxiang Luo ◽  
Zaiming Liu ◽  
Jinbiao Wu
Keyword(s):  
Optimal Control ◽  
Inventory Control ◽  
Dynamic Pricing ◽  
Hjb Equation ◽  
Exact Expression ◽  
Deteriorating Items ◽  
Dynamic Programming Principle ◽  
Inventory Level ◽  
Total Profit ◽  
Replenishment Cycle

In this paper, we consider a problem of the dynamic pricing and inventory control for non-instantaneous deteriorating items with uncertain demand, in which the demand is price-sensitive and governed by a diffusion process. Shortages and remains are permitted, and the backlogging rate is variable and dependent on the waiting time for the next replenishment. In order to maximize the expected total profit, the problem of dynamic pricing and inventory control is described as a stochastic optimal control problem. Based on the dynamic programming principle, the stochastic control model is transformed into a Hamilton-Jacobi-Bellman (HJB) equation. Then, an exact expression for the optimal dynamic pricing strategy is obtained via solving the HJB equation. Moreover, the optimal initial inventory level, the optimal selling pricing, the optimal replenishment cycle and the optimal expected total profit are achieved when the replenishment cycle starts at time 0. Finally, some numerical simulations are presented to demonstrate the analytical results, and the sensitivities analysis on system parameters are carried out to provide some suggestions for managers.

scholarly journals SOL: A library for scalable online learning algorithms

2017 ◽  
Vol 260 ◽  
pp. 9-12 ◽  
Author(s):  
Yue Wu ◽  
Steven C.H. Hoi ◽  
Chenghao Liu ◽  
Jing Lu ◽  
Doyen Sahoo ◽  
...  
Keyword(s):  
Online Learning ◽  
Learning Algorithms ◽  
Online Learning Algorithms

Multi-objective particle swarm optimisation approach for production-inventory control systems

2018 ◽  
Vol 13 (4) ◽  
pp. 1037-1056 ◽  
Author(s):  
Huthaifa AL-Khazraji ◽  
Colin Cole ◽  
William Guo
Keyword(s):  
Control System ◽  
Control Systems ◽  
Inventory Control ◽  
Dynamic Performance ◽  
Particle Swarm ◽  
Particle Swarm Optimisation ◽  
Inventory Level ◽  
Content Type ◽  
Multi Objective ◽  
Production Inventory

Purpose This paper aims to optimise the dynamic performance of production–inventory control systems in terms of minimisation variance ratio between the order rate and the consumption, and minimisation the integral of absolute error between the actual and the target level of inventory by incorporating the Pareto optimality into particle swarm optimisation (PSO). Design/method/approach The production–inventory control system is modelled and optimised via control theory and simulations. The dynamics of a production–inventory control system are modelled through continuous time differential equations and Laplace transformations. The simulation design is conducted by using the state–space model of the system. The results of multi-objective particle swarm optimisation (MOPSO) are compared with published results obtained from weighted genetic algorithm (WGA) optimisation. Findings The results obtained from the MOPSO optimisation process ensure that the performance is systematically better than the WGA in terms of reducing the order variability (bullwhip effect) and improving the inventory responsiveness (customer service level) under the same operational conditions. Research limitations/implications This research is limited to optimising the dynamics of a single product, single-retailer single-manufacturer process with zero desired inventory level. Originality/value PSO is widely used and popular in many industrial applications. This research shows a unique application of PSO in optimising the dynamic performance of production–inventory control systems.

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