scholarly journals An Inventory Model under Trapezoidal Type Demand, Weibull-Distributed Deterioration, and Partial Backlogging

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lianxia Zhao
Keyword(s):  
Sensitivity Analysis ◽  
Waiting Time ◽  
Optimal Solution ◽  
Inventory Model ◽  
Partial Backlogging ◽  
Inventory Models ◽  
Numerical Examples ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Theoretical Results

This paper studies an inventory model for Weibull-distributed deterioration items with trapezoidal type demand rate, in which shortages are allowed and partially backlogging depends on the waiting time for the next replenishment. The inventory models starting with no shortage is are to be discussed, and an optimal inventory replenishment policy of the model is proposed. Finally, numerical examples are provided to illustrate the theoretical results, and a sensitivity analysis of the major parameters with respect to the optimal solution is also carried out.

scholarly journals An Inventory Model with Exponential Demand Rate, Finite Production Rate and Shortages

2009 ◽  
Vol 1 (3) ◽  
pp. 473-483 ◽  
Author(s):  
R. Begum ◽  
S. K. Sahu ◽  
R. R. Sahoo
Keyword(s):  
Sensitivity Analysis ◽  
Production Rate ◽  
Average Cost ◽  
Optimal Solution ◽  
Inventory Model ◽  
Optimal Model ◽  
Numerical Examples ◽  
Demand Rate ◽  
Total Average Cost ◽  
Total Average

The paper contains an order-level inventory model having the demand rate to be a function of time. Here shortages are allowed and completely backlogged. An optimal model is developed by considering exponential demand which minimizes the total average cost. Numerical examples are used to illustrate the developed model. Sensitivity analysis of the optimal solution with respect to major parameters is carried out.  Keywords: Inventory; EOQ; Finite production; Shortages; Exponential demand. © 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.  DOI: 10.3329/jsr.v1i3.2054              J. Sci. Res. 1 (3), 473-483 (2009)     

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 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.

scholarly journals An Inventory Model for Deteriorating Items with Stock Dependent Demand and Partial Backlogging

2021 ◽  
Vol 9 (12) ◽  
pp. 296-302
Author(s):  
Vikas Kumar
Keyword(s):  
Waiting Time ◽  
Simple Algorithm ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Partial Backlogging ◽  
Numerical Examples ◽  
Proposed Model ◽  
Stock Dependent Demand ◽  
Total Profit ◽  
Dependent Demand

Abstract: In this paper, we formulate a deteriorating inventory model with stock-dependent demand Moreover, it is assumed that the shortages are allowed and partially backlogged, depending on the length of the waiting time for the next replenishment. The objective is to find the optimal replenishment to maximizing the total profit per unit time. We then provide a simple algorithm to find the optimal replenishment schedule for the proposed model. Finally, we use some numerical examples to illustrate the model. Keywords- Inventory, Deteriorating items, Stock dependent demand, Partial backlogging

scholarly journals An Inventory Model for Deteriorating Items with Quantity Dependent Permissible Delay in Payment and Partial Backlogging of Shortage

2007 ◽  
Vol 59 (3-4) ◽  
pp. 239-252
Author(s):  
Manisha Pal ◽  
Sanjoy Kumar Ghosh
Keyword(s):  
Waiting Time ◽  
Fixed Time ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Partial Backlogging ◽  
Single Item ◽  
Credit Period ◽  
Numerical Examples ◽  
Time Period ◽  
Permissible Delay In Payment

Abstract: In many inventory situations, instead of making immediate payment on receiving the consigument, the purchaser is allowed a certain fixed time period to pay for the goods bought. During this time the supplier charges no interest, but beyond this period interest is charged under the terms and condition agreed upon. As for the purchaser, he can earn interest on the revenue coolected during the credit period. This paper studies a single item inventory model for deteriorating items, when the permissible delay in payment depends on the ordered quantity and shortages are partially backlogged, assuming the backlogging rate to be inversely proportional to the waiting time for the next replenishment. An algorithm has been developed to find the optimal inventory policy. Numerical examples have been cited to illustrate the model. AMS (2000) Subject Classification: 90B05.

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.

scholarly journals Order Level Inventory Models for Deteriorating Seasonable/Fashionable Products with Time Dependent Demand and Shortages

2009 ◽  
Vol 2009 ◽  
pp. 1-24 ◽  
Author(s):  
K. Skouri ◽  
I. Konstantaras
Keyword(s):  
Inventory Model ◽  
Time Dependent ◽  
Inventory Models ◽  
Deterioration Rate ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Increasing Demand ◽  
Ramp Type Demand ◽  
Unsatisfied Demand ◽  
Dependent Demand

An order level inventory model for seasonable/fashionable products subject to a period of increasing demand followed by a period of level demand and then by a period of decreasing demand rate (three branches ramp type demand rate) is considered. The unsatisfied demand is partially backlogged with a time dependent backlogging rate. In addition, the product deteriorates with a time dependent, namely, Weibull, deterioration rate. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The optimal replenishment policy for the model is derived for both the above mentioned policies.

scholarly journals A partial backlogging inventory model for non-instantaneous deteriorating items with stock-dependent consumption rate under inflation

2010 ◽  
Vol 20 (1) ◽  
pp. 35-54 ◽  
Author(s):  
Jinh Chang ◽  
Feng Lin
Keyword(s):  
Solution Process ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Partial Backlogging ◽  
Demand Rate ◽  
Dependent Demand Rate ◽  
Dependent Demand

In this paper, we derive a partial backlogging inventory model for noninstantaneous deteriorating items with stock-dependent demand rate under inflation over a finite planning horizon. We propose a mathematical model and theorem to find minimum total relevant cost and optimal order quantity. Numerical examples are used to illustrate the developed model and the solution process. Finally, a sensitivity analysis of the optimal solution with respect to system parameters is carried out.

scholarly journals Inventory models with ramp-type demand for deteriorating items with partial backlogging and time-varing holding cost

2014 ◽  
Vol 24 (2) ◽  
pp. 249-266 ◽  
Author(s):  
Biplab Karmakar ◽  
Karabi Choudhury
Keyword(s):  
Time Varying ◽  
Partial Backlogging ◽  
Inventory Models ◽  
Two Component ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Holding Cost ◽  
Ramp Type Demand ◽  
Increasing Function ◽  
Unsatisfied Demand

In this paper, an inventory model with general ramp-type demand rate, partial backlogging of unsatisfied demand and time-varying holding cost is considered; where the ?Time-varying holding cost? means that the holding cost is a function of time, i.e. it is time dependent. The model is studied under the following different replenishment policies: (1) starting with no shortages (2) starting with shortages. Two component demand rate has been used. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The optimal replenishment policy is derived for both the above mentioned policies.

Supplier-retailer production and inventory models with defective items and inspection errors in non-cooperative and cooperative environments

2018 ◽  
Vol 52 (2) ◽  
pp. 453-471 ◽  
Author(s):  
Chih-Te Yang ◽  
Chia-Huei Ho ◽  
Hsiu-Mei Lee ◽  
Liang-Yuh Ouyang
Keyword(s):  
Sensitivity Analysis ◽  
Economies Of Scale ◽  
Transportation Costs ◽  
Equilibrium Solutions ◽  
Inventory Models ◽  
Defective Items ◽  
Numerical Examples ◽  
Inspection Errors ◽  
Mathematical Analyses ◽  
Theoretical Results

This paper proposes single-supplier single-retailer production and inventory models for maximizing the supplier and retailer’s profits in non-cooperative and cooperative environments. The effect of defective items and inspection errors are considered in the proposed models. In addition, we consider that the supplier offers the retailer a quantity threshold to absorb transportation costs for promoting the economies of scale of transport. Mathematical analyses are conducted, and optimal equilibrium production and replenishment strategies for the supplier and retailer are derived under non-cooperative and cooperative situations. Subsequently, we establish two algorithms to explain the optimal equilibrium solutions for these cases. Finally, several numerical examples and a sensitivity analysis with respect to major parameters are presented to demonstrate the theoretical results, compare the distinct solutions, and derive managerial insights.

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