scholarly journals Mathematical Modeling for Risk Averse Firm Facing Loss Averse Customer’s Stochastic Uncertainty

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Seungbeom Kim ◽  
Jinpyo Lee ◽  
Minjae Park
Keyword(s):  
Programming Model ◽  
Choice Model ◽  
Planning Horizon ◽  
Risk Averse ◽  
Base Stock Policy ◽  
Multinomial Choice ◽  
Joint Pricing ◽  
Stock Policy ◽  
Finite Planning Horizon ◽  
Actual Price

To optimize the firm’s profit during a finite planning horizon, a dynamic programming model is used to make joint pricing and inventory replenishment decision assuming that customers are loss averse and the firm is risk averse. We model the loss averse customer’s demand using the multinomial choice model. In this choice model, we consider the acquisition and transition utilities widely used by a mental accounting theory which also incorporate the reference price and actual price. Then, we show that there is an optimal inventory policy which is base-stock policy depending on the accumulated wealth in each period.

scholarly journals Integrating Dynamic Pricing and Inventory Control for Fresh Agriproduct under Multinomial Logit Choice

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Xiong-zhi Wang ◽  
Wenliang Zhou
Keyword(s):  
Dynamic Pricing ◽  
Programming Model ◽  
Choice Model ◽  
Multinomial Logit ◽  
Linear Ordering ◽  
Stochastic Dynamic ◽  
Inventory Problem ◽  
Numerical Illustration ◽  
Dynamic Stochastic ◽  
Joint Pricing

In this article, we investigate a joint pricing and inventory problem for a retailer selling fresh agriproducts (FAPs) with two-period shelf lifetime in a dynamic stochastic setting, where new and old FAPs are on sale simultaneously. At the beginning of each period the retailer makes ordering decision for new FAP and sets regular and discount price for new and old inventories, respectively. After demand realization, the expired leftover is disposed and unexpired inventory is carried to the next period, continuing selling. Unmet demand of all FAPs is backordered. The objective is to maximize the total expected discount profit over the whole planning horizon. We present a price-dependent, stochastic dynamic programming model taking into account zero lead time, linear ordering costs, inventory holding, and backlogging costs, as well as disposal cost. Considering the influence of the perishability, we integrate a Multinomial Logit (MNL) choice model to describe the consumer behavior on purchasing fresh or nonfresh product. By way of the inverse of the price vector, the original formulation can be transferred to be jointly concave and tractable. Finally we characterize the optimal policy and develop effective methods to solve the problem and conduct a simple numerical illustration.

scholarly journals Joint Pricing and Inventory Replenishment Decisions with Returns and Expediting under Reference Price Effects

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Yuan Li ◽  
Yumei Hou
Keyword(s):  
Reference Price ◽  
Base Stock ◽  
List Price ◽  
Optimal Pricing ◽  
Threshold Policy ◽  
Inventory Replenishment ◽  
Base Stock Policy ◽  
Price Effects ◽  
Joint Pricing ◽  
Stock Policy

This paper considers a single-item joint pricing and inventory replenishment problem under reference price effects in consecutive T periods. Demands in consecutive periods are sensitive to price and reference price with general demand distribution. At the end of each period, after the demand realization, a firm can return excess stocks to a supplier or place an expediting order to reduce the loss by shortage. Unfilled demands are fully backlogged. In order to maximize the total expected discounted profit with reference price effects the optimal pricing and inventory replenishment policies for regular order and the inventory adjustment decisions for returning/expediting are derived. The optimal replenishment policy for regular order is a base-stock policy, the optimal pricing policy is a base-stock-list-price policy, and the optimal policy for returning/expediting inventory adjustment follows a dual-threshold policy. Furthermore, the analysis of the operational impacts (from the perspective of adding returning/expediting and reference price effects, respectively) is researched. Numerical results also show that considering both returning/expediting and reference price effects is more profitable than considering only one of them.

Optimizing preventive maintenance over a finite planning horizon in a semi-Markov framework

2020 ◽  
Author(s):  
Antonio Sánchez Herguedas ◽  
Adolfo Crespo Márquez ◽  
Francisco Rodrigo Muñoz
Keyword(s):  
Preventive Maintenance ◽  
Recurrence Relations ◽  
Direct Calculation ◽  
Planning Horizon ◽  
Practical Implementation ◽  
Practical Application ◽  
Mathematical Solution ◽  
Accumulated Reward ◽  
Finite Planning Horizon

Abstract This paper describes the optimization of preventive maintenance (PM) over a finite planning horizon in a semi-Markov framework. In this framework, the asset may be operating, and providing income for the asset owner, or not operating and undergoing PM, or not operating and undergoing corrective maintenance following failure. PM is triggered when the asset has been operating for τ time units. A number m of transitions specifies the finite horizon. This system is described with a set of recurrence relations, and their z-transform is used to determine the value of τ that maximizes the average accumulated reward over the horizon. We study under what conditions a solution can be found, and for those specific cases the solution τ* is calculated. Despite the complexity of the mathematical solution, the result obtained allows the analyst to provide a quick and easy-to-use tool for practical application in many real-world cases. To demonstrate this, the method has been implemented for a case study, and its accuracy and practical implementation were tested using Monte Carlo simulation and direct calculation.

Optimality of Base Stock Policy under Unknown Demand Distributions: New Results and a New Method

2021 ◽  
Author(s):  
Alain Bensoussan ◽  
Suresh Sethi ◽  
Abdoulaye Thiam ◽  
Janos Turi
Keyword(s):  
Base Stock ◽  
New Method ◽  
Base Stock Policy ◽  
Stock Policy

scholarly journals Validating Virtual Safety Stock Effectiveness through Simulation

10.5772/56859 ◽  
2013 ◽  
Vol 5 ◽  
pp. 41 ◽  
Author(s):  
Maria Elena Nenni ◽  
Massimiliano M. Schiraldi
Keyword(s):  
Service Level ◽  
Inventory System ◽  
Time Interval ◽  
Common Condition ◽  
Simple Method ◽  
Safety Stock ◽  
Safety Stocks ◽  
Base Stock Policy ◽  
Stock Policy ◽  
Business To Business

As a means of avoiding stock-outs, safety stocks play an important role in achieving customer satisfaction and retention. However, traditional safety stock theory is based on the assumption of the immediate delivery of the ordered products, which is not a common condition in business-to-business contexts. Virtual safety stock theory was conceived to raise the service level by exploiting the potential time interval in the order-to-delivery process. Nevertheless, its mathematical complexity prevented this technique from being widely adopted in the industrial world. In this paper, we present a simple method to test virtual safety stock effectiveness through simulation in an inventory system using a base stock policy with periodic reviews and backorders. This approach can be useful for researchers as well as practitioners who want to model the behaviour of an inventory system under uncertain conditions and verify the opportunity for setting up a virtual safety stock on top of, or instead of, the traditional physical safety stock.

Sign in / Sign up

Export Citation Format

Share Document