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.

An Optimal Inventory Policy for Items Having Constant Demand and Constant Deterioration Rate with Trade Credit

2012 ◽  
Vol 5 (2) ◽  
pp. 89-95 ◽  
Author(s):  
R. P. Tripathi ◽  
S. S. Misra
Keyword(s):  
Trade Credit ◽  
Optimal Order ◽  
Order Quantity ◽  
Inventory Models ◽  
Inventory Policy ◽  
Deterioration Rate ◽  
Optimal Order Quantity ◽  
Optimal Ordering ◽  
Constant Deterioration ◽  
Ordering Quantity

In most of the classical inventory models the demand is considered as constant. In this paper the model has been framed to study the items whose demand and deterioration both are constant. The authors developed a model to determine an optimal order quantity by using calculus technique of maxima and minima. Thus, it helps a retailer to decide its optimal ordering quantity under the constraints of constant deterioration rate and constant pattern of demand.

Some Alternative Methods of Finding the Optimal Order Quantity in Inventory Models

2005 ◽  
Vol 57 (1-2) ◽  
pp. 121-128
Author(s):  
Ayan Chandra ◽  
S. P. Mukherjee
Keyword(s):  
Alternative Methods ◽  
Exceedance Probability ◽  
Optimal Order ◽  
Order Quantity ◽  
Inventory Problem ◽  
Inventory Models ◽  
Demand And Supply ◽  
Total Cost ◽  
Optimum Order ◽  
Optimal Order Quantity

We consider a purchase inventory problem where both demand and supply have been taken to be random. Several possible ways of deriving the optimum order quantity based on the distribution of total cost have been proposed. Expressions for the optimum order quantity that minimizes the mode or exceedance probability of this distribution have been worked out for some particular demand and supply distributions.

scholarly journals PENGENDALIAN PERSEDIAAN PROBABILISTIK PRODUK SUBSTITUSI DENGAN PERMINTAAN SEBAGAI FUNGSI HARGA

2021 ◽  
Vol 16 (1) ◽  
pp. 56-62
Author(s):  
Laila Nafisah ◽  
Sutrisno Sutrisno
Keyword(s):  
Sensitivity Analysis ◽  
Inventory Model ◽  
Optimal Order ◽  
Lost Sales ◽  
Business Unit ◽  
Order Quantity ◽  
Product Substitution ◽  
Inventory Models ◽  
Total Cost ◽  
Optimal Order Quantity

Kamara Living merupakan suatu unit usaha yang bergerak dalam penjualan kebutuhan sehari-hari. Salah satu produk yang populer adalah sarung bantal. Sarung bantal yang ditawarkan memiliki beberapa desain motif dan jenis yang berbeda. Permintaan akan produk sarung bantal tidak menentu antara satu desain dengan desain yang lain. Ketika desain tertentu persediaannya habis, perusahaan akan menawarkan desain lain dari jenis kain yang sama. Jika konsumen tidak bersedia maka terjadi kehilangan penjualan. Ketika persediaan berlebih, perusahaan akan memberikan harga promosi untuk mendongkrak tingkat penjualannya. Jika ini dibiarkan terus-menerus, tentu saja perusahaan akan mengalami penurunan keuntungan. Pada makalah ini dikembangkan model persediaan dengan mempertimbangkan produk substitusi dengan permintaan sebagai fungsi harga yang bertujuan untuk meminimasi total biaya persediaan. Penyelesaian model yang dilakukan mampu menghasilkan solusi kuantitas pemesanan dan titik pemesanan yang optimal. Validasi model dilakukan dengan membandingkan hasil dari model yang dikembangkan terhadap kondisi riil. Selain itu juga dilakukan analisis sensitivitas terhadap parameter-parameter yang berpengaruh. Abstract[Product-substitution Inventory Model with Demand depend on Price] Kamara Living is a business unit engaged in selling daily stuff. One popular product is pillowcases. The pillow cover offered has several different motif designs and types. The demand for pillowcases is uncertain between one design and another. When a stockout occurs for a particular design, the company will offer another design of the same type of fabric. If consumers are not willing, there will be lost sales. When there is overstock, the company will provide promotional prices to increase sales levels. If this is allowed to continue, of course the company will experience a decline in profits. In this paper, an inventory model is developed by considering substitute products with demand as a price function that aims to minimize the total cost of inventory. Completion of the model carried out is able to produce optimal order quantity and order point solutions. Model validation is done by comparing the results of the models developed against real conditions. In addition, a sensitivity analysis was carried out on the influential parameters.Keywords: Inventory Models; Product Substitution; Demand Depend on Price

scholarly journals Coping with Loss Aversion in the Newsvendor Model

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jianwu Sun ◽  
Xinsheng Xu
Keyword(s):  
Expected Utility ◽  
Loss Aversion ◽  
Confidence Level ◽  
Profit Maximization ◽  
Optimal Order ◽  
Market Demand ◽  
Newsvendor Model ◽  
Order Quantity ◽  
Decision Bias ◽  
Optimal Order Quantity

We introduce loss aversion into the decision framework of the newsvendor model. By introducing the loss aversion coefficientλ, we propose a novel utility function for the loss-averse newsvendor. First, we obtain the optimal order quantity to maximize the expected utility for the loss-averse newsvendor who is risk-neutral. It is found that this optimal order quantity is smaller than the expected profit maximization order quantity in the classical newsvendor model, which may help to explain the decision bias in the classical newsvendor model. Then, to reduce the risk which originates from the fluctuation in the market demand, we achieve the optimal order quantity to maximize CVaR about utility for the loss-averse newsvendor who is risk-averse. We find that this optimal order quantity is smaller than the optimal order quantity to maximize the expected utility above and is decreasing in the confidence levelα. Further, it is proved that the expected utility under this optimal order quantity is decreasing in the confidence levelα, which verifies that low risk implies low return. Finally, a numerical example is given to illustrate the obtained results and some management insights are suggested for the loss-averse newsvendor model.

scholarly journals Coordination of Supply Chain with One Supplier and Two Competing Risk-Averse Retailers under an Option Contract

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Rui Wang ◽  
Shiji Song ◽  
Cheng Wu
Keyword(s):  
Supply Chain ◽  
Conditional Value At Risk ◽  
Optimal Order ◽  
Pareto Optimum ◽  
Risk Averse ◽  
Order Quantity ◽  
Supply Chain System ◽  
Chain System ◽  
Option Contract ◽  
Optimal Order Quantity

This paper studies an option contract for coordinating a supply chain comprising one risk-neutral supplier and two risk-averse retailers engaged in promotion competition in the selling season. For a given option contract, in decentralized case, each risk-averse retailer decides the optimal order quantity and the promotion policy by maximizing the conditional value-at-risk of profit. Based on the retailers’ decision, the supplier derives the optimal production policy by maximizing expected profit. In centralized case, the optimal decision of the supply chain system is obtained. Based on the decentralized and centralized decision, we find the coordination conditions of the supply chain system, which can optimize the supply chain system profit and make the profits of the supply chain members achieve Pareto optimum. As for the subchain, we also find the coordination conditions, which generalize the results of the supply chain with one supplier and one retailer. Our analysis and numerical experiments show that there exists a unique Nash equilibrium between two retailers, and the optimal order quantity of each retailer increases (decreases) with its own (competitor’s) promotion level.

scholarly journals Trade Credit with Barter in a Capital-Constrained Supply Chain

2021 ◽  
Vol 13 (20) ◽  
pp. 11361
Author(s):  
Yangyang Huang ◽  
Zhenyang Pi ◽  
Weiguo Fang
Keyword(s):  
Supply Chain ◽  
Trade Credit ◽  
Wholesale Price ◽  
Uncertain Demand ◽  
Equilibrium Strategy ◽  
Optimal Order ◽  
Order Quantity ◽  
Supply Rate ◽  
Optimal Order Quantity ◽  
And Performance

Barter has emerged to alleviate capital pressure, maximize the circulation of goods, and facilitate the disposal of excess inventory. This study considers a two-level supply chain consisting of a manufacturer and a capital-constrained retailer with trade credit, in which the retailer exchanges unsold products for needed subsidiary products on a barter platform. The retailer’s optimal order quantity and the manufacturer’s wholesale price are derived, and the influences of barter and other factors on the equilibrium strategy and performance of the supply chain are examined; these results are verified and supplemented by numerical simulation. We find that the retailer can increase profit by bartering when facing highly uncertain demand, that the retailer’s optimal order quantity increases with the supply rate and demand for subsidiary products, and that both manufacturer and retailer benefit from the high supply rate of subsidiary products. However, barter induces the manufacturer to raise the wholesale price to prevent its profit from being harmed. In addition, the manufacturer suffers from the retailer’s initial capital.

scholarly journals Inventory Models with Defective Units and Sub-Lot Inspection

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1038
Author(s):  
Han-Wen Tuan ◽  
Gino K. Yang ◽  
Kuo-Chen Hung
Keyword(s):  
Lower Bound ◽  
Optimal Solution ◽  
Upper Bounds ◽  
Interior Solution ◽  
Order Quantity ◽  
Inventory Models ◽  
Defective Items ◽  
Numerical Examples ◽  
Counter Example ◽  
Analytical Foundation

Inventory models must consider the probability of sub-optimal manufacturing and careless shipping to prevent the delivery of defective products to retailers. Retailers seeking to preserve a reputation of quality must also perform inspections of all items prior to sale. Inventory models that include sub-lot sampling inspections provide reasonable conditions by which to establish a lower bound and a pair of upper bounds in terms of order quantity. This should make it possible to determine the conditions of an optimal solution, which includes a unique interior solution to the problem of an order quantity satisfying the first partial derivative. The approach proposed in this paper can be used to solve the boundary. These study findings provide the analytical foundation for an inventory model that accounts for defective items and sub-lot sampling inspections. The numerical examples presented in a previous paper are used to demonstrate the derivation of an optimal solution. A counter-example is constructed to illustrate how existing iterative methods do not necessarily converge to the optimal solution.

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