scholarly journals Analysis of Inventory Model with Time Dependent Quadratic Demand Function Including Time Variable Deterioration Rate without Shortage

2021 ◽  
pp. 97-109
Author(s):  
Md. Atiqur Rahman ◽  
Mohammed Forhad Uddin
Keyword(s):  
Demand Function ◽  
Optimal Solution ◽  
Quadratic Function ◽  
Inventory Model ◽  
Time Dependent ◽  
Inventory Cost ◽  
Total Cost ◽  
Deterioration Rate ◽  
Total Inventory ◽  
Dependent Demand

This paper deals with an inventory model for deteriorating items along with time dependent demand which is quadratic function of time. In this model, the deterioration rate follows deterministic deterioration which is quadratic function of time. Here shortages are not allowed. The main purpose of this paper is to investigate minimum total cost per unit time of the inventory model. The result are validated with the help of numerical example. The sensitivity analysis of the optimal solution with respect to various parameters is carried out. Finally the behavior of the relation between parameters and total inventory cost have been shown using figure.

scholarly journals Controllable deterioration rate for time-dependent demand and time-varying holding cost

2014 ◽  
Vol 24 (1) ◽  
pp. 87-98 ◽  
Author(s):  
Vinod Mishra
Keyword(s):  
Linear Function ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Inventory Cost ◽  
Deterioration Rate ◽  
Preservation Technology ◽  
Demand Rate ◽  
Holding Cost ◽  
Total Inventory ◽  
Dependent Demand

In this paper, we develop an inventory model for non-instantaneous deteriorating items under the consideration of the facts: deterioration rate can be controlled by using the preservation technology (PT) during deteriorating period, and holding cost and demand rate both are linear function of time, which was treated as constant in most of the deteriorating inventory models. So in this paper, we developed a deterministic inventory model for non-instantaneous deteriorating items in which both demand rate and holding cost are a linear function of time, deterioration rate is constant, backlogging rate is variable and depend on the length of the next replenishment, shortages are allowed and partially backlogged. The model is solved analytically by minimizing the total cost of the inventory system. The model can be applied to optimizing the total inventory cost of non-instantaneous deteriorating items inventory for the business enterprises, where the preservation technology is used to control the deterioration rate, and demand & holding cost both are a linear function of time.

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.

An Optimal Policy with Three-Parameter Weibull Distribution Deterioration, Quadratic Demand, and Salvage Value Under Partial Backlogging

2018 ◽  
Vol 5 (1) ◽  
pp. 79-98
Author(s):  
Trailokyanath Singh ◽  
Hadibandhu Pattanayak ◽  
Ameeya Kumar Nayak ◽  
Nirakar Niranjan Sethy
Keyword(s):  
Weibull Distribution ◽  
Quadratic Function ◽  
Deteriorating Items ◽  
Partial Backlogging ◽  
Order Quantity ◽  
Inventory Cost ◽  
Deterioration Rate ◽  
Replenishment Policy ◽  
Total Inventory ◽  
Weibull Distribution Deterioration

This paper deals with an EOQ (Economic Order Quantity) model for deteriorating items having the following characteristics: 1) Deteriorating items follow a three-parameter Weibull distribution deterioration rate; 2) Shortages are allowed and are partially backlogged; 3) Salvage value of items is incorporated; 4) Demand is deterministic and a time-dependent quadratic function of time. The principal objective of the introduced model is to minimize the average total inventory cost by finding an optimal replenishment policy. The effectiveness of the model is validated with a numerical example and the sensitivity analysis of the optimal solutions to changes in the values of the various parameters associated with the model has been performed.

scholarly journals Inventory Model for Three–parameter Weibull Deterioration and Partial Backlogging

2019 ◽  
pp. 1-9
Author(s):  
Naresh Kumar Kaliraman
Keyword(s):  
Inventory Model ◽  
Time Dependent ◽  
Order Quantity ◽  
Inventory Cost ◽  
Numerical Illustration ◽  
Decision Variables ◽  
Demand Rate ◽  
Optimum Order ◽  
Total Inventory ◽  
Total Average Cost

This paper develops an economic order quantity inventory model for time dependent three parameters Weibull deterioration. Partially backlogged shortages are considered. The demand rate is deterministic and time dependent. The rate of deterioration is time dependent. We have derived the most favorable order quantity model by minimizing the entire inventory cost. A numerical illustration has been carried out to evaluate the result of parameters on decision variables and the total average cost of the model. The research focus of this paper is to derive the optimum order quantity by minimizing the total inventory cost.

scholarly journals A Joint Return Policy for a Multi-Item Perishable Inventory Model with Deterministic Demands, Return and All-Units Discount

2020 ◽  
Vol 5 (3) ◽  
pp. 416-431
Author(s):  
Dharma Lesmono ◽  
Taufik Limansyah ◽  
Neilshan Loedy
Keyword(s):  
Optimal Solution ◽  
Return Time ◽  
Inventory Model ◽  
Inventory Cost ◽  
Perishable Inventory ◽  
Numerical Examples ◽  
Joint Return ◽  
Total Inventory ◽  
The Individual ◽  
Parameter Values

In this paper, we develop a multi-item perishable inventory model with deterministic demands, return and all-units discount. We consider a situation where a retailer sells several products to the customer and orders the products from one supplier. Demands are assumed to be deterministic following an inventory-dependent demand, and the supplier offers all-units discount to the retailer who has an opportunity to return unsold or deteriorated products to the supplier at a certain cost. In order to minimize the total cost for the retailer, the decision variables are the optimal return time and the optimal ordering quantity. Considering a multi-item case as an extension of the model by Setiawan et al. (2018) is the main contribution of this paper. We also develop an algorithm to find the optimal solution of the model. Numerical examples for three items are given to illustrate the model and a sensitivity analysis is performed to study the effect of the changes in parameter values on the optimal solution. We consider two scenarios, one with all-units discount and one with no discount. Within these two scenarios, we consider conditions of individual or joint return time for these three items. It is found that the individual return time with no discount gives the least total inventory cost in the numerical examples. Also, in general increasing the value of holding cost, deteriorating rate, return cost per unit and backorder cost will increase the total inventory cost in all scenarios.

scholarly journals Purchasing Inventory Models for Deteriorating Items with Quadratic Demand

2019 ◽  
Vol 20 (2) ◽  
pp. 204
Author(s):  
C. K. Sivashankari
Keyword(s):  
Optimal Solution ◽  
Deteriorating Items ◽  
Time Dependent ◽  
Lot Size ◽  
Inventory Cost ◽  
Replenishment Policy ◽  
Parameter Values ◽  
Visual Basic 6.0 ◽  
Production Lot Size ◽  
Dependent Demand

This paper deals with purchasing inventory replenishment policy for deteriorating items consider with the time-dependent quadratic demand and time-dependent backlogging. Two models were formulated and solved. First, it is for deteriorating items with quadratically time-dependent demand for deteriorating items. Second, quadratically time-dependent demand for deteriorating items and shortages. A mathematical model is developed to the fourth-order equation for each model, and the optimal production lot size, which minimizes the total cost is derived. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system. Numerical examples are taken to illustrate the procedure of finding the optimal inventory cost, cycle time, and optimal lot size. The numerical experiment in this model was coded in Microsoft Visual Basic 6.0.

scholarly journals Effect of Inflation on Two Storage Inventory Model with Time Dependent Deteriorating Items and Stock Dependent Demand

2020 ◽  
Vol 5 (3) ◽  
pp. 544-555
Author(s):  
Preeti Sharma ◽  
Sanjay Sharma ◽  
B. B. Singh ◽  
Anand Tyagi
Keyword(s):  
Inventory Control ◽  
Present Model ◽  
Control Model ◽  
Inventory Model ◽  
Time Dependent ◽  
Deterioration Rate ◽  
Production Inventory ◽  
Stock Dependent Demand ◽  
Inventory Control Model ◽  
Dependent Demand

For deteriorating product, there always be a pressure on the company to maximize the profit. In the present model, an effort is made to develop a production inventory control model having two separate warehouses. In most of the study, the demand is assumed as time dependent which is not appropriate; but here authors have considered stock based demand. An approach is taken into consideration that deterioration rate different for different warehouses.

INVENTORY MODEL OF DETERIORATING ITEMS FOR LINEAR HOLDING COST WITH TIME DEPENDENT DEMAND

2015 ◽  
Vol 4 (1) ◽  
pp. 29-36
Author(s):  
N Mishra ◽  
SP Mishra ◽  
Srichandan Mishra ◽  
J Panda ◽  
UK Misra
Keyword(s):  
Inventory Model ◽  
Deteriorating Items ◽  
Time Dependent ◽  
Holding Cost ◽  
Dependent Demand
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