A JOINT EOQ MODEL FOR SUPPLIER AND RETAILER WITH DETERIORATING ITEMS

2004 ◽  
Vol 21 (02) ◽  
pp. 163-178 ◽  
Author(s):  
CHINHO LIN ◽  
YIHSU LIN
Keyword(s):  
Necessary Conditions ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Solution Procedure ◽  
Sensitivity Analyses ◽  
Mutual Cooperation ◽  
Total Cost ◽  
Numerical Examples ◽  
Eoq Model ◽  
Sufficient And Necessary Conditions

The paper studies the joint inventory model between supplier and retailer relying on mutual cooperation. Unlike other studies, the deteriorated rate and partial back-ordering are consistent with assumptions for dealing with more general cases. Since it is difficult to solve this problem directly, we derived the sufficient and necessary conditions in the planning horizon, and proposed a procedure to find the optimal solution. Numerical examples and sensitivity analyses are also provided to illustrate the solution procedure. The results reveal that the extensions of the model provide a wider and reasonable situation in practice, and that they also reduce the total cost.

An EOQ model with stepwise ordering cost and the finite planning horizon under carbon cap-and-trade regulations

2021 ◽  
Vol 10 (3) ◽  
pp. 337-350
Author(s):  
Tzu-Chia Chen ◽  
Shu-Yan Yu
Keyword(s):  
Low Cost ◽  
Planning Horizon ◽  
Finite Horizon ◽  
Optimal Order ◽  
Fixed Cost ◽  
Cap And Trade ◽  
Total Cost ◽  
Eoq Model ◽  
Finite Planning Horizon ◽  
Ordering Quantity

In this study, under the carbon cap-and-trade mechanism, the ordering cost presents a stepwise function for ordering quantity, and the optimal economic ordering quantity model aims to explore the manufacturer's total cost minimization in the finite planning horizon, in combination with the actual situation that the product will produce carbon emissions during transportation and storage. The economic order quantity (EOQ) model with stepwise ordering cost is applicable to the decision environment in which goods are utilized by sea, by rail or by air (e.g., the order cost is charged in addition to the basic fixed cost, the importer of raw materials will pay an additional freight related to delivery, such as the rent for the use of container numbers.). A heuristic algorithm is also proposed to analyze the relevant properties of the optimal solution of the model and to solve the optimal order times and quantities of the manufacturer under the constraint of carbon policy.We further compared the optimal order times with the case without carbon constraint and the order times corresponding to the manufacturer's realization of the minimum carbon emission, and obtained the conditions for the manufacturer to achieve low cost and low emission under the carbon policy.Finally, the theoretical results of the model are verified by numerical examples,and the influence of relevant parameters on the inventory strategy of manufacturers is discussed. The results show that under the carbon cap-and-trade policy, there is an optimal ordering strategy that minimizes the total cost of the manufacturer in the finite horizon. When the demand of the manufacturer is under finite horizon and the carbon policy is equal to the specific multiplier of orders, the manufacturer can achieve a win-win result of low cost and low emissions.

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 On the Perron-Frobenius Theory of Mv-matrices and equivalent properties to eventually exponentially nonnegative matrices

2019 ◽  
Vol 35 ◽  
pp. 424-440
Author(s):  
Thaniporn Chaysri ◽  
Dimitrios Noutsos
Keyword(s):  
Necessary Conditions ◽  
Nonnegative Matrix ◽  
Nonnegative Matrices ◽  
Numerical Examples ◽  
Generalized Eigenvectors ◽  
Sufficient And Necessary Conditions ◽  
Left And Right ◽  
Equivalent Properties

Mv−matrix is a matrix of the form A = sI −B, where 0 ≤ ρ(B) ≤ s and B is an eventually nonnegative matrix. In this paper, Mv−matrices concerning the Perron-Frobenius theory are studied. Specifically, sufficient and necessary conditions for an Mv−matrix to have positive left and right eigenvectors corresponding to its eigenvalue with smallest real part without considering or not if index0B ≤ 1 are stated and proven. Moreover, analogous conditions for eventually nonnegative matrices or Mv−matrices to have all the non Perron eigenvectors or generalized eigenvectors not being nonnegative are studied. Then, equivalent properties of eventually exponentially nonnegative matrices and Mv−matrices are presented.  Various numerical examples are given to support our theoretical findings.

scholarly journals A study of inflation effects on an EOQ model for Weibull deteriorating/ameliorating items with ramp type of demand and shortages

2013 ◽  
Vol 23 (3) ◽  
pp. 441-455 ◽  
Author(s):  
M. Valliathal ◽  
R. Uthayakumar
Keyword(s):  
Computer Software ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Inventory Level ◽  
Decision Variable ◽  
Deterioration Rate ◽  
Eoq Model ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Ramp Type Demand

This paper deals with the effects of inflation and time discounting on an inventory model with general ramp type demand rate, time dependent (Weibull) deterioration rate and partial backlogging of unsatisfied demand. The model is studied under the replenishment policy, starting with shortages under two different types of backlogging rates, and their comparative study is also provided. We then use the computer software, MATLto find the optimal replenishment policies. Duration of positive inventory level is taken as the decision variable to minimize the total cost of the proposed system. Numerical examples are then taken to illustrate the solution procedure. Finally, sensitivity of the optimal solution to changes of the values of different system parameters is also studied.

scholarly journals An Integrated Vendor-Buyer Cooperative Inventory Model for Items with Imperfect Quality and Shortage Backordering

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jia-Tzer Hsu ◽  
Lie-Fern Hsu
Keyword(s):  
Probability Density Function ◽  
Cost Reduction ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Variable Number ◽  
Defective Items ◽  
Numerical Examples ◽  
Imperfect Quality ◽  
Integrated Cost ◽  
Independent Decision

We develop a model to determine an integrated vendor-buyer inventory policy for items with imperfect quality and planned backorders. The production process is imperfect and produces a certain number of defective items with a known probability density function. The vendor delivers the items to the buyer in small lots of equally sized shipments. Upon receipt of the items, the buyer will conduct a 100% inspection. Since each lot contains a variable number of defective items, shortages may occur at the buyer. We assume that shortages are permitted and are completely backordered. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. The expected total annual integrated cost is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer.

scholarly journals Controllability of Multiagent Systems with a Directed Tree

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Li Wang ◽  
Xiao Han
Keyword(s):  
Multiagent Systems ◽  
Multiagent System ◽  
Necessary Conditions ◽  
New Method ◽  
Information Communication ◽  
Controllability Problem ◽  
Directed Tree ◽  
Numerical Examples ◽  
Sufficient And Necessary Conditions ◽  
Theoretical Results

This paper addresses the controllability problem of multiagent systems with a directed tree based on the classic agreement protocol, in which the information communication topologies being a directed tree and containing a directed tree are both investigated. Different from the literatures, a new method, the star transform, is proposed to study the controllability of multiagent systems with directed topology. Some sufficient and necessary conditions are given for the controllability of such multiagent system. Numerical examples and simulations are proposed to illustrate the theoretical results.

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.

scholarly journals Optimality for E-[0,1] convex multi-objective programming

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 529-541 ◽  
Author(s):  
Tarek Emama
Keyword(s):  
Feasible Solution ◽  
Necessary Conditions ◽  
Optimal Solution ◽  
Efficient Solutions ◽  
Properly Efficient Solution ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Sufficient And Necessary Conditions ◽  
Objective Programming

In this paper, we interest with deriving the sufficient and necessary conditions for optimal solution of special classes of Programming. These classes involve generalized E-[0,1] convex functions. Characterization of efficient solutions for E-[0,1] convex multi-objective Programming are obtained. Finally, sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are derived.

scholarly journals Optimal Replenishment Policy for Weibull-Distributed Deteriorating Items with Trapezoidal Demand Rate and Partial Backlogging

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Lianxia Zhao
Keyword(s):  
Optimal Solution ◽  
Solution Procedure ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Partial Backlogging ◽  
Total Cost ◽  
Replenishment Policy ◽  
Demand Rate ◽  
The Stability ◽  
Theoretical Results

An inventory model for Weibull-distributed deteriorating items is considered so as to minimize the total cost per unit time in this paper. The model starts with shortage, allowed partial backlogging, and trapezoidal demand rate. By analyzing the model, an efficient solution procedure is proposed to determine the optimal replenishment and the optimal order quantity and the average total costs are also obtained. Finally, numerical examples are provided to illustrate the theoretical results and a sensitivity analysis of the major parameters with respect to the stability of optimal solution is also carried out.

scholarly journals Controllability of Second-Order Multiagent Systems with Multiple Leaders and General Dynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Bo Liu ◽  
Hongke Feng ◽  
Li Wang ◽  
Rong Li ◽  
Junyan Yu ◽  
...  
Keyword(s):  
Multiagent Systems ◽  
Multiagent System ◽  
Necessary Conditions ◽  
Second Order ◽  
The Other ◽  
Numerical Examples ◽  
General Dynamics ◽  
Sufficient And Necessary Conditions ◽  
Multiple Leaders ◽  
Theoretical Results

This paper proposes a new second-order discrete-time multiagent model and addresses the controllability of second-order multiagent system with multiple leaders and general dynamics. The leaders play an important role in governing the other member agents to achieve any desired configuration. Some sufficient and necessary conditions are given for the controllability of the second-order multiagent system. Moreover, the speed controllability of the second-order multiagent system with general dynamics is discussed. Particularly, it is shown that the controllability of the whole system relies on the number of leaders and the connectivity between the leaders and the members. Numerical examples illustrate the theoretical results.

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