scholarly journals An EOQ model for deteriorating items under supplier credits when demand is stock dependent

2010 ◽  
Vol 20 (1) ◽  
pp. 145-156
Author(s):  
Nita Shah ◽  
Poonam Mishra
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Critical Parameters ◽  
Eoq Model ◽  
Constant Rate ◽  
Cash Discount

In many circumstances retailer is not able to settle the account as soon as items are received. In that scenario supplier can offer two promotional schemes namely cash discount and /or a permissible delay to the customer. In this study, an EOQ model is developed when units in inventory deteriorate at a constant rate and demand is stock dependent. The salvage value is associated to deteriorated units. An algorithm is given to find the optimal solution. The sensitivity analysis is carried out to analyze the effect of critical parameters on optimal solution.

AN EOQ MODEL WITH LIMITED STORAGE CAPACITY UNDER TRADE CREDITS

2007 ◽  
Vol 24 (04) ◽  
pp. 575-592 ◽  
Author(s):  
LIANG-YUH OUYANG ◽  
KUN-SHAN WU ◽  
CHIH-TE YANG
Keyword(s):  
Storage Capacity ◽  
Optimal Solution ◽  
Inventory Systems ◽  
Simple Method ◽  
Eoq Model ◽  
Trade Credits ◽  
Cash Discount ◽  
Delay In Payments ◽  
Classical Economic ◽  
Theoretical Results

In the classical economic order quantity (EOQ) inventory model, it was assumed that the retailer must pay for the received items immediately. However, in practice, the supplier not only allows retailer to settle the account after a certain fixed period but also may offer a cash discount to encourage the retailer to pay for his purchases as soon as possible. On the other hand, it is common practice in most inventory systems to hold excess stocks in a rented warehouse whenever the storage capacity of the owned warehouse is insufficient. Therefore, the purpose of this paper is to establish an EOQ model with limited storage capacity, in which the supplier provides cash discount and permissible delay in payments for the retailer. In the model, we develop some useful theorems to characterize the optimal solution and provide a simple method to find the optimal replenishment cycle time and payment time. Finally, several numerical examples are given to illustrate the theoretical results and some managerial insights are also obtained.

scholarly journals The EOQ Model for Deteriorating Items with a Conditional Trade Credit Linked to Order Quantity in a Supply Chain System

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2311
Author(s):  
Kun-Jen Chung ◽  
Jui-Jung Liao ◽  
Hari Mohan Srivastava ◽  
Shih-Fang Lee ◽  
Shy-Der Lin
Keyword(s):  
Trade Credit ◽  
Analytic Solution ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Deteriorating Items ◽  
Order Quantity ◽  
Supply Chain System ◽  
Total Cost ◽  
Eoq Model ◽  
Total Cost Function

For generality, we observed that some of the optimization methods lack the mathematical rigor and some of them are based on intuitive arguments which result in the solution procedures being questionable from logical viewpoints of a mathematical analysis such as those in the work by Ouyang et al. (2009). They consider an economic order quantity model for deteriorating items with partially permissible delays in payments linked to order quantity. Basically, their inventory models are interesting, however, they ignore explorations of interrelations of functional behaviors (continuity, monotonicity properties, differentiability, et cetera) of the total cost function to locate the optimal solution, so those shortcomings will naturally influence the implementation of their considered inventory model. Consequently, the main purpose of this paper is to provide accurate and reliable mathematical analytic solution procedures for different scenarios that overcome the shortcomings of Ouyang et al.

scholarly journals The Inventory Model for Deteriorating Items under Conditions Involving Cash Discount and Trade Credit

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 596 ◽  
Author(s):  
Kun-Jen Chung ◽  
Jui-Jung Liao ◽  
Shy-Der Lin ◽  
Sheng-Tu Chuang ◽  
Hari Mohan Srivastava
Keyword(s):  
Taylor Series ◽  
Approximation Method ◽  
Optimal Solution ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Optimal Solutions ◽  
Taylor Series Approximation ◽  
Annual Total ◽  
Cash Discount ◽  
Relevant Cost

In the year 2004, Chang and Teng investigated an inventory model for deteriorating items in which the supplier not only provides a cash discount, but also allows a permissible delay in payments. The main purpose of the present investigation is three-fold, as follows. First, it is found herein that Theorem 1 of Chang and Teng (2004) has notable shortcomings in terms of their determination of the optimal solution of the annual total relevant cost Z ( T ) by adopting the Taylor-series approximation method. Theorem 1 in this paper does not make use of the Taylor-series approximation method in order to overcome the shortcomings in Chang and Teng (2004) and alternatively derives all the optimal solutions of the annual total relevant cost Z ( T ) . Secondly, this paper systematically revisits the annual total relevant cost Z ( T ) in Chang and Teng (2004) and presents in detail the mathematically correct ways for the derivations of Z ( T ) . Thirdly, this paper not only shows that Theorem 1 of Chang and Teng (2004) is not necessarily true for finding the optimal solution of the annual total relevant cost Z ( T ) , but it also demonstrates how Theorem 1 in this paper can locate all of the optimal solutions of Z ( T ) . The mathematical analytic investigation presented in this paper is believed to be useful for correct managerial considerations and managerial decisions.

scholarly journals Robustness of the Multi-Attribute Utility Model for Bridge Maintenance Planning

2018 ◽  
Vol 13 (4) ◽  
pp. 404-415 ◽  
Author(s):  
Zaharah Allah Bukhsh ◽  
Irina Stipanovic ◽  
Sandra Skaric Palic ◽  
Giel Klanker
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Risk Tolerance ◽  
Critical Parameters ◽  
Maintenance Planning ◽  
Bridge Management ◽  
Utility Model ◽  
Attribute Weights ◽  
Multi Attribute Utility Theory ◽  
Decision Making Model

Optimisation of maintenance planning is an essential part of bridge management. With the purpose to support maintenance planning, a multi- objective decision-making model is introduced in this paper. The model is based on multi-attribute utility theory, which is used for the optimisation process when multiple performance goals have to be taken into account. In the model, there are several parameters, which are freely chosen by the decision maker. The model is applied to the inventory of 22 bridges, where four Key Performance Indicators were determined for four performance aspects:  reliability, availability, costs and environment. A sensitivity analysis is performed by changing risk tolerance parameter and attribute weights to determine the robustness of the model. The Multi-Attribute Utility model and sensitivity analysis presented in this paper will help decision-makers to examine the robustness of the optimal solution by dynamically changing the critical parameters.

scholarly journals Inventory models with stock- and price-dependent demand for deteriorating items based on limited shelf space

2010 ◽  
Vol 20 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Chun-Tao Chang ◽  
Yi-Ju Chen ◽  
Tzong-Ru Tsai ◽  
Wu Shuo-Jye
Keyword(s):  
Optimal Solution ◽  
Deteriorating Items ◽  
Selling Price ◽  
Order Quantity ◽  
Shelf Space ◽  
Stock Level ◽  
Eoq Model ◽  
Eoq Models ◽  
Demand Rate ◽  
Dependent Demand

This paper deals with the problem of determining the optimal selling price and order quantity simultaneously under EOQ model for deteriorating items. It is assumed that the demand rate depends not only on the on-display stock level but also the selling price per unit, as well as the amount of shelf/display space is limited. We formulate two types of mathematical models to manifest the extended EOQ models for maximizing profits and derive the algorithms to find the optimal solution. Numerical examples are presented to illustrate the models developed and sensitivity analysis is reported.

scholarly journals EOQ Model for Deteriorating Items with Stock-Level-Dependent Demand Rate and Order-Quantity-Dependent Trade Credit

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Jie Min ◽  
Jian Ou ◽  
Yuan-Guang Zhong ◽  
Xin-Bao Liu
Keyword(s):  
Trade Credit ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Order Quantity ◽  
Eoq Model ◽  
Demand Rate ◽  
Delay In Payments ◽  
Dependent Demand Rate ◽  
Dependent Demand

This paper develops a generalized inventory model for exponentially deteriorating items with current-stock-dependent demand rate and permissible delay in payments. In the model, the payment for the item must be made immediately if the order quantity is less than the predetermined quantity; otherwise, a fixed trade credit period is permitted. The maximization of the average profit per unit of time is taken as the inventory system’s objective. The necessary and sufficient conditions and some properties of the optimal solution to the model are developed. Simple solution procedures are proposed to efficiently determine the optimal ordering policies of the considered problem. Numerical example is also presented to illustrate the solution procedures obtained.

scholarly journals An inventory model for deteriorating items with exponential declining demand and partial backlogging

2005 ◽  
Vol 15 (2) ◽  
pp. 277-288 ◽  
Author(s):  
Liang-Yuh Ouyang ◽  
Kun-Shan Wu ◽  
Mei-Chuan Cheng
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Cost Function ◽  
Waiting Time ◽  
Optimal Solution ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Partial Backlogging ◽  
Numerical Example ◽  
Declining Demand

This study proposes an EOQ inventory mathematical model for deteriorating items with exponentially decreasing demand. In the model, the shortages are allowed and partially backordered. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Further, we show that the minimized objective cost function is jointly convex and derive the optimal solution. A numerical example is presented to illustrate the model and the sensitivity analysis is also studied.

Aplikasi Metode Hungarian Dalam Optimalisasi Waktu Penugasan Karyawan dan Keuntungan Produksi Home Industry

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Empya Charlie ◽  
Siti Rusdiana ◽  
Rini Oktavia
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Optimal Scheduling ◽  
Total Work ◽  
Work Time ◽  
Hungarian Method ◽  
Total Work Time

Penelitian ini bertujuan untuk mengoptimalkan penjadwalan karyawan di CV. Karya Indah Bordir dalam melakukan tugas-tugas tertentu menggunakan metode Hungaria, serta menganalisis sensitivitas solusi optimal jika ada pengurangan waktu karyawan untuk menyelesaikan tugas-tugas. Metode Hongaria diterapkan pada proses bordir yang melibatkan 11 karyawan dan 10 tugas. Hasil penjadwalan yang optimal meminimalkan waktu produksi bordir perusahaan. Hasil penjadwalan optimal yang ditemukan adalah: karyawan 1 mengerjakan tas Mambo, karyawan 2 mengerjakan tas Elli, karyawan 3 mengerjakan tas Lonjong, karyawan 4 mengerjakan tas Tampang bunga, karyawan 6 mengerjakan tas Ransel, karyawan 7 mengerjakan tas Tima, karyawan 8 mengerjakan tas Keong, karyawan 9 mengerjakan tas Alexa, karyawan 10 mengerjakan tas Luna, dan karyawan 11 mengerjakan tas Mikha, dengan total waktu kerja adalah 13,7 jam. Setelah metode Hongaria diterapkan, CV. Karya Indah Bordir mendapat peningkatan pendapatan sebanyak 9,09%. Analisis sensitivitas dilakukan dengan mengurangi waktu karyawan dalam menyulam tas. Hasil analisis sensitivitas adalah beberapa batasan untuk variabel basis dan non basis untuk mempertahankan solusi optimal.   This research has a purpose to optimize the scheduling of employees in CV. Karya Indah Bordir in doing certain tasks using Hungarian method, as well as analyzing the sensitivity of the optimal solution if there is a reduction on the employees time to finish the tasks. The Hungarian method was applied on the embroidery process involving 11 employees and 10 tasks. The optimal scheduling result minimize the time of the embroidery production of the company. The optimal scheduling result found is: employee 1 does the Mambo bag, employee 2 does the Elli bag, employee 3 does the Lonjong bag, employee 4 does the Tampang bunga bag, employee 6 does the Ransel, employee 7 does the Tima bag, employee 8 does the Keong bag, employee 9 does the Alexa bag, employees 10 does the Luna bag, and employee 11 does the Mikha bag, with the total work time is 13,7 hours. After the Hungarian method was applied, CV. Karya Indah Bordir got the increasing revenue as much as 9,09 %. The sensitivity analysis was conducted by reducing the time of the employees take in embroidery the bags. The results of the sensitivity analysis are some boundaries for basis and non basis variables to maintain the optimal solution. 

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