scholarly journals Bartering: Price-Setting Newsvendor Problem with Barter Exchange

2021 ◽  
Vol 13 (12) ◽  
pp. 6684
Author(s):  
Milena Bieniek
Keyword(s):  
Demand Function ◽  
Social Economic ◽  
Optimal Solution ◽  
Newsvendor Problem ◽  
Optimal Order ◽  
Price Setting ◽  
Order Quantity ◽  
Economic Uncertainty ◽  
Optimal Price ◽  
Dependent Demand

Barter exchange is a system of swapping goods or services for other goods or services in a moneyless and direct manner. Barter has become an effective model of a circular economy because it reduces the consumption impact. Bartering maximizes the utility of assets and existing resources, and can unleash the unspent social, economic, and environmental value of underutilized assets. The present article analyzes the price-setting newsvendor problem with a barter exchange option. The retailer facing a stochastic price-dependent demand sells a product on the market and, additionally, needs another product for its own purposes. Therefore, first, the retailer trades the unsold product for the product it needs by means of barter, and next disposes of the unsold product at a discounted price at the end of the selling season. The retailer’s optimal order quantity and optimal price are derived assuming additive uncertainty in demand. This type of demand function has special characteristics, for example, the actual demand may attain negative values in times of economic uncertainty. The possibility of negative demand realizations is taken into consideration in the study. It proves that, in certain cases, the optimal solution belongs to the set of high barter prices which implies that the actual demand may be negative.

EOQ Model with Stock-Level Dependent Demand and Different Holding Cost Functions

2017 ◽  
Vol 8 (4) ◽  
pp. 59-75 ◽  
Author(s):  
H.S. Shukla ◽  
R.P. Tripathi ◽  
Neha Sang
Keyword(s):  
Order Approximation ◽  
Optimal Solution ◽  
Optimal Order ◽  
Order Quantity ◽  
Inventory Cost ◽  
Stock Level ◽  
Numerical Examples ◽  
Eoq Model ◽  
Holding Cost ◽  
Dependent Demand

This paper presents EOQ (Economic Order Quantity) model with stock- level dependent demand and different types of holding cost function. We show that the total relevant inventory cost per unit time is convex with respect to cycle time. Mathematical models are established to determine optimal order quantity and total relevant inventory cost. Numerical examples are provided for two different models i.e. (i): Instantaneous replenishment with inventory dependent holding cost and (ii) Instantaneous replenishment with quadratic time dependent carrying cost. Numerical examples are provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. The second order approximation is used for finding closed form optimal solution. Mathematica 5.2 software is used to find numerical results.

Dominance Relationship Among the Retailer’s Strategies Under the Semi-Stackelberg Newsvendor Situation with Quantity Discounts

2016 ◽  
Vol 33 (02) ◽  
pp. 1650014
Author(s):  
Youkyung Won
Keyword(s):  
Probability Distribution ◽  
Demand Function ◽  
Dominant Strategy ◽  
Optimal Order ◽  
Quantity Discounts ◽  
Order Quantity ◽  
Dominance Relationship ◽  
Optimal Order Quantity ◽  
Dependent Demand ◽  
Stackelberg Leader

In this paper, we investigate the retailer’s behavior under the supplier-driven semi-Stackelberg newsvendor situation in which (i) the supplier plays as a semi-Stackelberg leader with or without his discounts schedule being offered to the retailer, (ii) the retailer plays as a Stackelberg follower with or without her discounts schedule being offered to the end customer, and (iii) neither party has perfect information on the endogenous price-dependent demand function or exogenous probability distribution of demand. In this situation, the retailer’s concern is identifying the dominant strategy by which she can safely implement her own scheme for customer discounts regardless of the order quantity rather than finding the best strategy yielding the optimal order quantity that maximizes her expected profit. We show that a consistent dominance relationship exists among the retailer’s strategies when the newsvendor chooses to offer progressive multiple discounts to customers regardless of the supplier’s strategy of offering the retailer either all-units discounts or no-discounts.

scholarly journals Hedging Risks in the Loss-Averse Newsvendor Problem with Backlogging

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 429 ◽  
Author(s):  
Xiaoqing Liu ◽  
Felix T. S. Chan ◽  
Xinsheng Xu
Keyword(s):  
Value At Risk ◽  
Profit Maximization ◽  
Newsvendor Problem ◽  
Sensitivity Analyses ◽  
Conditional Value At Risk ◽  
Optimal Order ◽  
Newsvendor Model ◽  
Order Quantity ◽  
Decision Bias ◽  
Optimal Order Quantity

This paper studies the optimal order decisions for the loss-averse newsvendor problem with backordering and contributes to the risk hedging issue in the newsvendor model. The Conditional Value-at-Risk (CVaR) measure is applied to quantify the potential risks for the loss-averse newsvendor in a backordering setting, and we obtain the optimal order quantity for a loss-averse newsvendor to maximize the CVaR of utility. It is found that the optimal order quantity to maximize the CVaR objective could be bigger or smaller than the expected profit maximization (EPM) order quantity, which provides an alternative explanation on decision bias in the newsvendor model. This study also reveals that the optimal order quantity for a loss-averse newsvendor to maximize expected utility with backordering is smaller than the EPM order quantity, which implies that backordering encourages the loss-averse newsvendor to order fewer items. Sensitivity analyses are performed to investigate the properties of the optimal order quantities and managerial insights are suggested. This paper provides a novel method for the risk management of the loss-averse newsvendor model and presents several new ordering policies for the retailers in practice.

scholarly journals Replenishment Model with Entropic Order Quantity for Deteriorating Items under Inflation

2021 ◽  
pp. 34-47
Author(s):  
P. K. Tripathy ◽  
Anima Bag
Keyword(s):  
Cost Minimization ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Selling Price ◽  
Order Quantity ◽  
Total Cost ◽  
Purchase Cost ◽  
Holding Cost ◽  
Special Approach

The purpose of the current paper is to determine an optimal order quantity so as to minimize the total cost of the inventory system of a business enterprise. The model is developed for deteriorating items with stock and selling price dependent demand under inflation without permitting shortage. Optimal solution is achieved by cost minimization strategy considering replenishment cost, purchase cost, holding cost and deterioration cost with a special approach to entropy cost for bulk size purchasing units. The effectiveness of the proposed model has been avowed through empirical investigation. Sensitivity analysis has been accomplished to deduce managerial insights. Findings suggest that an increased inflationary effect results in increment in the system total cost. The paper can be extended by allowing shortage. The model can be utilized in the business firms dealing with bulk purchasing units of electric equipments, semiconductor devices, photographic films and many more.

scholarly journals An EOQ model with stock dependent demand and imperfect quality items

2010 ◽  
Vol 20 (2) ◽  
pp. 237-247 ◽  
Author(s):  
Shibaji Panda
Keyword(s):  
Optimal Order ◽  
Optimal Solutions ◽  
Order Quantity ◽  
Screening Process ◽  
Imperfect Quality ◽  
Eoq Model ◽  
Total Profit ◽  
Approximate Optimal Solutions ◽  
Single Batch ◽  
Dependent Demand

This paper deals with an economic order quantity model where demand is stock dependent. Items received are not of perfect quality and each lot received contains percentage defective imperfect quality items, which follow a probability distribution. Two cases are considered. 1) Imperfect quality items are held in stock and sold in a single batch after a 100 percent screening process. 2) A hundred percent screening process is performed but the imperfect quality items are sold as soon as they are detected. Approximate optimal solutions are derived in both cases. A numerical example is provided in order to illustrate the development of the model. Sensitivity analysis is also presented, indicating the effects of percentage imperfect quality items on the optimal order quantity and total profit.

scholarly journals The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 484 ◽  
Author(s):  
Ting-Chen Hu ◽  
Kuo-Chen Hung ◽  
Kuo-Lung Yang
Keyword(s):  
Iterative Method ◽  
Optimal Solution ◽  
Threshold Value ◽  
Optimal Order ◽  
Order Quantity ◽  
Inventory Models ◽  
Worst Case ◽  
Distribution Free ◽  
Second Moments ◽  
Optimal Order Quantity

For inventory models with unknown distribution demand, during shortages, researchers used the first and the second moments to derive an upper bound for the worst case, that is the min-max distribution-free procedure for inventory models. They applied an iterative method to generate a sequence to obtain the optimal order quantity. A researcher developed a three-sequence proof for the convergence of the order quantity sequence. We directly provide proof for the original order quantity sequence. Under our proof, we can construct an increasing sequence and a decreasing sequence that both converge to the optimal order quantity such that we can obtain the optimal solution within the predesigned threshold value.

scholarly journals PARTIAL BACKORDERING INVENTORY MODEL WITH LIMITED STORAGE CAPACITY UNDER ORDER-SIZE DEPENDENT TRADE CREDIT

2021 ◽  
Vol 0 (0) ◽  
pp. 1-32
Author(s):  
Wen-Hui Jiang ◽  
Ling Xu ◽  
Zhen-Song Chen ◽  
Witold Pedrycz ◽  
Kwai-Sang Chin
Keyword(s):  
Trade Credit ◽  
Storage Capacity ◽  
Optimal Solution ◽  
Capacity Constraints ◽  
Inventory Model ◽  
Optimal Order ◽  
Model Parameters ◽  
Order Quantity ◽  
Size Dependent ◽  
Partial Backordering

This study formulates an inventory model with limited storage capacity under the condition of order-size dependent trade credit. Shortages are allowed and partially backlogged. The objective of this study is to determine the optimal replenishment cycle length, the optimal fraction of no shortage, and whether retailers should choose to rent an extra warehouse to store more items, such that retailers’ total annual profit is maximized. We prove the global optimally of objective functions and derive the closed-form optimal solution. Some numerical examples are presented to illustrate the applicability of the proposed model. Sensitivity analysis is carried out and managerial insights are obtained. We find that if retailers’ own warehouse capacity is relatively small, they always benefit from enlarging order quantity and renting an extra warehouse; meanwhile, suppliers further prolong the credit period is beneficial for both parties. On the contrary, as retailers’ own warehouse capacity increases and exceeds the optimal order quantity under that of without capacity constraints, adopting the same replenishment strategy as that without capacity constraints is profitable for retailers. Our results also reveal that other model parameters (e.g., ordering cost, inventory holding cost, shortages cost, backordering rate, etc.) have a significant impact on retailers’ optimal decisions.

scholarly journals Optimal order policy for deteriorating items in response to temporary price discount linked to order quantity

2009 ◽  
Vol 40 (4) ◽  
pp. 383-400 ◽  
Author(s):  
Liang-Yuh Ouyang ◽  
Chih-Te Yang ◽  
Hsiu-Feng Yen
Keyword(s):  
Cost Saving ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Market Demand ◽  
Order Quantity ◽  
Price Discount ◽  
Total Cost ◽  
Holding Cost ◽  
Special Order

This paper investigates the possible effects of a temporary price discount offered by a supplier on a retailer's replenishment policy for deteriorating items, whereby the price discount rate depends on the order quantity. The purpose of this study is to develop a decision process for retailers to assist in determining whether to adopt a regular or special order policy. Furthermore, the optimal quantity of a special order policy for a selected case is determined by maximizing the total cost saving between special and regular orders for the duration of the depletion time. This research establishes an algorithm to determine the optimal solution and utilizes several numerical examples to illustrate the theoretical results and subsequently conducts a sensitivity analysis of the optimal solution with respect to the main parameters. Finally, the results reveal that (1) the optimal special order quantity is determined by trading off the benefits of the price discount against the additional holding cost, (2) the retailer benefits in terms of total cost saving if the remnant inventory is as low as possible when adopting a special order policy, (3) for the retailer it is preferable to adopt the special order policy if the unit purchase cost, market demand rate and/or ordering cost increase, and (4) the retailer will order a lower quantity and the total cost saving will decrease when either the holding cost rate or deterioration rate is high. Thus, this study provides the basis for enterprises to make inventory decisions.

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