scholarly journals A Deterministic Inventory Model of Deteriorating Items with Two Rates of Production, Shortages, and Variable Production Cycle

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Jhuma Bhowmick ◽  
G. P. Samanta
Keyword(s):  
Production Control ◽  
Continuous Production ◽  
Decision Rules ◽  
Optimal Solution ◽  
Inventory Model ◽  
Optimal Decision ◽  
Inventory Level ◽  
Production Cycle ◽  
Demand Rate ◽  
Variable Production

A Continuous production control inventory model is developed for a deteriorating item having shortages and variable production cycle. It is assumed that the production rate is changed to another at a time when the inventory level reaches a prefixed level and continued until the inventory level reaches the level . The demand rate is assumed to be constant, and the production cycle T is taken as variable. The production is started again at a time when the shortage level reaches a prefixed quantity . For this model, the total cost per unit time as a function of , , S, and T is derived. The optimal decision rules for , , S, and T are computed. The sensitivity of the optimal solution towards changes in the values of different system parameters is also studied. Results are illustrated by numerical examples.

scholarly journals A production inventory model with deteriorating items and shortages

2004 ◽  
Vol 14 (2) ◽  
pp. 219-230 ◽  
Author(s):  
G.P. Samanta ◽  
Ajanta Roy
Keyword(s):  
Cycle Time ◽  
Production Control ◽  
Continuous Production ◽  
Optimal Solution ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Production Cycle ◽  
Stock Level ◽  
Deterioration Rate ◽  
Time Sensitivity

A continuous production control inventory model for deteriorating items with shortages is developed. A number of structural properties of the inventory system are studied analytically. The formulae for the optimal average system cost, stock level, backlog level and production cycle time are derived when the deterioration rate is very small. Numerical examples are taken to illustrate the procedure of finding the optimal total inventory cost, stock level, backlog level and production cycle time. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system.

On Optimal Inventory Model for Obsolescence Perishable Products under Unpermitted-Stockout

2011 ◽  
Vol 201-203 ◽  
pp. 1292-1295
Author(s):  
Xiao Liang Xie
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Economic Order Quantity ◽  
Inventory Level ◽  
Order Quantity ◽  
Short Life ◽  
Numerical Examples ◽  
Fast Change ◽  
Demand Rate ◽  
Long Life

With the advancement of science and technology and the fast change of buyer requirements, the short-life products have been shortened at large, some formerly long-life products gradually turn to value deterioration products. The ratio of value deterioration products to modern products is getting higher and higher. This paper develops a deterministic economic order quantity EOQ inventory model, where the demand rate depends on the on-hand inventory when inventory level exceeds certain quantity , otherwise the demand rate is constant. The effects of obsolescence are taken into account, for it is related to the demand rate. The results are discussed through two numerical examples. A sensitivity analysis of the optimal solution with respect to parameters of the system is carried out.

AN EOQ MODEL WITH CONTROLLABLE SELLING RATE

2008 ◽  
Vol 25 (02) ◽  
pp. 151-167 ◽  
Author(s):  
HORNG-JINH CHANG ◽  
PO-YU CHEN
Keyword(s):  
Distribution Function ◽  
Transaction Cost ◽  
Optimal Solution ◽  
Bivariate Distribution ◽  
Inventory Level ◽  
Selling Price ◽  
Eoq Model ◽  
Concrete Form ◽  
Demand Rate ◽  
Classical Economic

According to the marketing principle, a decision maker may control demand rate through selling price and the unit facility cost of promoting transaction. In fact, the upper bound of willing-to-pay price and the transaction cost probably depend upon the subjective judgment of individual consumer in purchasing merchandise. This study therefore attempts to construct a bivariate distribution function to simultaneously incorporate the willing-to-pay price and the transaction cost into the classical economic order quantity (EOQ) model. Through the manipulation of the constructed bivariate distribution function, the demand function faced by the supplier can be expressed as a concrete form. The proposed mathematical model mainly concerns how to determine the initial inventory level for each business cycle, so that the profit per unit time is maximized by means of the selling price and the unit-transaction cost to control the selling rate. Furthermore, the sensitivity analysis of optimal solution is performed and the implication of this extended inventory model is also discussed.

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.

An Optimal Inventory Model Based on the Effect of Time-Limited Free Back-Orders

2011 ◽  
Vol 474-476 ◽  
pp. 1338-1344
Author(s):  
Biao Zhang ◽  
Di Zhang
Keyword(s):  
Inventory Model ◽  
Inventory Level ◽  
Mathematical Software ◽  
Model Based ◽  
The Status ◽  
Demand Rate ◽  
Optimal Ordering ◽  
Back Order

An optimal inventory model is proposed in this paper. Firstly, the prerequisite of this model is given out. Under the supposed condition of deterioration, the demand rate of articles depends on the inventory level, meanwhile the status of shortage and partial back-order. The optimal inventory model of fixed free back orders is on this basis. With those numerical values in this model, the optimal ordering cycle and ordering batch of stock system are counted out and the sensitivity is analyzed by using the mathematical software Mathmatica 7.0.

scholarly journals An Inventory Model for Imperfect Quality Products with Rework, Distinct Holding Costs, and Nonlinear Demand Dependent on Price

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1362
Author(s):  
Leopoldo Eduardo Cárdenas-Barrón ◽  
María José Lea Plaza-Makowsky ◽  
María Alejandra Sevilla-Roca ◽  
José María Núñez-Baumert ◽  
Buddhadev Mandal
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Inventory System ◽  
Inventory Level ◽  
Selling Price ◽  
Lot Size ◽  
Inventory Models ◽  
Holding Costs ◽  
Imperfect Items ◽  
The Moment

Traditionally, the inventory models available in the literature assume that all articles in the purchased lot are perfect and the demand is constant. However, there are many causes that provoke the presence of defective goods and the demand is dependent on some factors. In this direction, this paper develops an economic order quantity (EOQ) inventory model for imperfect and perfect quality items, taking into account that the imperfect ones are sent as a single lot to a repair shop for reworking. After reparation, the items return to the inventory system and are inspected again. Depending on the moment at which the reworked lot arrives to the inventory system, two scenarios can occur: Case 1: The reworked lot enters when there still exists inventory; and Case 2: The reworked lot comes into when the inventory level is zero. Furthermore, it is considered that the holding costs of perfect and imperfect items are distinct. The demand of the products is nonlinear and dependent on price, which follows a polynomial function. The main goal is to optimize jointly the lot size and the selling price such that the expected total profit per unit of time is maximized. Some theoretic results are derived and algorithms are developed for determining the optimal solution for each modeled case. It is worth mentioning that the proposed inventory model is a general model due to the fact that this contains some published inventory models as particular cases. With the aim to illustrate the use of the proposed inventory model, some numerical examples are solved.

scholarly journals Production inventory model for controllable deterioration rate with shortages

2019 ◽  
Author(s):  
Umakanta Mishra ◽  
Jacobo Tijerina-Aguilera ◽  
Sunil Tiwari ◽  
Leopoldo Eduardo Cárdenas-Barrón
Keyword(s):  
Optimal Solution ◽  
Solution Procedure ◽  
Inventory Model ◽  
Production Cycle ◽  
Proper Solution ◽  
Deterioration Rate ◽  
Preservation Technology ◽  
Production Policy ◽  
Production Inventory ◽  
Theoretical Results

This paper deals with an economic production quantity (EPQ) inventory model for deteriorating items under preservation technology. The preservation technology is used to protect the items from deterioration. Three different production levels are considered. It is assumed that initially the production rate is at lower rate and it increases gradually over the period. This is just in order to reduce the holding cost by avoiding the larger stock quantity in the beginning of production cycle. The shortages are permitted and fully backordered. The objective of the production inventory model is to determine optimal production policy which minimizes the manufacturer’s total cost. Theoretical results are established in order to demonstrate the existence of the optimal solution and a proper solution procedure is presented. A numerical example and a sensitivity analysis are presented to validate the theoretical results. Also, some managerial insights are provided.

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