Non-instantaneous Deterioration Research Articles

An EPQ model for non-instantaneous deteriorating item with time dependent holding cost and exponential demand rate

We consider the problem of a vendor that supplies an item to the buyer, which is a function of non-instantaneous deterioration. It is an integrated production inventory model of non-instantaneous deteriorating item in which demand rate is exponential and production rate is a function of demand rate. The holding cost varies with time. Partially deteriorated items are allowed to sale with a discount rate from original one, and the units which are completely deteriorated, are superfluous. Shortages are not allowed. The optimal cycle time is derived and the result is applied to numerical problems. A solution procedure is presented to determine an optimal replenishment cycle such that the total cost is maximised. Numerical example is cited to illustrate the results and its significant features. Finally, to study the effect of changes of demand parameters, deterioration, price discount and holding cost, on supplier a sensitivity analysis is presented numerically.

Ordering policy for non-instantaneous deteriorating items in two warehouse environment with shortages

This paper deals with non-instantaneous deteriorating items that have a shelf life and start deteriorating after a time lag. Under some special conditions, viz., attractive price discount, low storage cost, high demand, etc; the procurement of a large amount of such items at a time is decided. Because of the fixed capacity of the own warehouse (OW), a rented warehouse (RW) is used to store the excess quantity. Further, to enhance the usefulness of merchandise or goods, the first-in first-out (FIFO) dispatch policy is followed. In the present paper, a two-warehouse inventory model for non-instantaneous deteriorating items is developed under FIFO dispatch policy; shortages at OW are also allowed. The solution procedure has been illustrated with the help of a numerical example and a comprehensive sensitivity analysis is considered. Jaggi and Verma's (2010a) two-warehouse LIFO model with non-instantaneous deterioration is also compared with the proposed FIFO model.

Joint pricing and replenishment decisions for non-instantaneous deteriorating items with partial backlogging, inflation- and selling price-dependent demand and customer returns

This paper develops an Economic Order Quantity (EOQ) model for non-instantaneous deteriorating items with selling price- and inflation-induced demand under the effect of inflation and customer returns. The customer returns are assumed as a function of demand and price. Shortages are allowed and partially backlogged. The effects of time value of money are studied using the Discounted Cash Flow approach. The main objective is to determine the optimal selling price, the optimal length of time in which there is no inventory shortage, and the optimal replenishment cycle simultaneously such that the present value of total profit is maximized. An efficient algorithm is presented to find the optimal solution of the developed model. Finally, a numerical example is extracted to solve the presented inventory model using the proposed algorithm and the effects of the customer returns, inflation, and non-instantaneous deterioration are also discussed. The paper ends with a conclusion and outlook to future studies.

Joint location, inventory, and preservation decisions for non-instantaneous deterioration items under delay in payments

This study models a joint location, inventory and preservation decision-making problem for non-instantaneous deteriorating items under delay in payments. An outside supplier provides a credit period to the wholesaler which has a distribution system with distribution centres (DCs). The non-instantaneous deteriorating means no deterioration occurs in the earlier stage, which is very useful for items such as fresh food and fruits. This paper also considers that the deteriorating rate will decrease and the reservation cost will increase as the preservation effort increases. Therefore, how much preservation effort should be made is a crucial decision. The objective of this paper is to determine the optimal locations and number of DCs, the optimal replenishment cycle time at DCs, and the optimal preservation effort simultaneously such that the total network profit is maximised. The problem is formulated as piecewise nonlinear functions and has three different cases. Algorithms based on piecewise nonlinear optimisation are provided to solve the joint location and inventory problem for all cases. Computational analysis illustrates the solution procedures and the impacts of the related parameters on decisions and profits. The results of this study can serve as references for business managers or administrators.

An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and variable holding cost

Percentage of capital invested for holding the inventory of decaying item is more than that of non-decaying item. Unfortunately, most of the works done in the era of inventory controlling were and are putting forward without taking into account the aspect of variable holding cost of the deteriorating item. To bring concentrations of inventory practitioners, we present an inventory model for deteriorating item with stock-dependent demand and variable holding cost. Furthermore, non-instantaneous deteriorating approach is considered in this work. In the model, shortages are allowed and partially backlogged. The optimal policies are derived and the necessary and sufficient conditions of the existence and uniqueness of the optimal solution are theoretically carried out. As the special cases, the results of the proposed model with instantaneous and non-instantaneous deterioration rate and with and without shortages are shown. Finally, numerical examples are presented to demonstrate the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters for giving managerial insights in conclusion is carried out.

Non-Instantaneous Deterioration Inventory Model with Inflation and Stock-Dependent Demand

In this paper, an inventory model for an item is presented with inflation and stock dependent demand under non-instantaneous deterioration without allowing shortages. In real life conditions, freshness and quality ofsome products can be maintaining Here in this inventory model we assume that some products maintain originality for some time. The necessary and sufficient conditions are used to find the optimal solutions and the corresponding maximum profits for the different value sets of the given numerical data with sensitivity analyses and presented graphically.

Two-Level Credit Financing for Noninstantaneous Deterioration Items in a Supply Chain with Downstream Credit-Linked Demand

Trade credit financing is a useful tool in business today, which can be characterized as the agreement between supply chain members such as permissible delay in payments. In this study, we assume that the items have the property of noninstantaneous deterioration and the demand is a function of downstream credit. Then, an EOQ model for noninstantaneous deterioration is built based on the two-level financing policy. The purpose of this paper is to maximize the total average profit by determine the optimal downstream credit period, the optimal replenishment cycle length, and the optimal ordering quantity per cycle. Useful theorems are proposed to characterize the method of obtaining the optimal solutions. Based on the theorems, an algorithm is designed, and numerical tests and sensitive analysis are provided. Lastly, according to the sensitive analysis, managerial insights are proposed.

An optimal replenishment policy for non-instantaneous deteriorating items with two storage facilities

Deterioration has received a considerable attention in the past, and researchers have propounded a number of inventory models for the deteriorating items. It has been generally assumed that items start deteriorating as soon as they arrive in the warehouse. But in real life there are various products, like fresh fruits, vegetables, milk, meat etc., that have a shelf-life and start deteriorating after a time lag. This underlines the fact that for some initial period of time, there is no deterioration in items. This phenomenon is termed as non-instantaneous deterioration and the items are termed as non-instantaneous deteriorating items. In the present study, a two-warehouse inventory model for non-instantaneous deteriorating items has been developed. Moreover, shortage at Own Warehouse (OW) is also allowed subject to full backlogging. The solution methodology provided in this model helps to decide the feasibility of renting a warehouse. The results have been elucidated with numerical examples.

An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging

In this study, we consider a problem of determining the optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand. In the model, shortages are allowed and the backlogging rate is variable and dependent on the waiting time for the next replenishment. The necessary and sufficient conditions of the existence and uniqueness of the optimal solution are shown. As the special cases, the results for the models with instantaneous or non-instantaneous deterioration rate and with or without shortages are derived. Further, we analytically identify the best circumstance among these special cases based on the minimum total relevant cost per unit time. Sensitivity analysis of the optimal solution with respect to major parameters is carried out. Finally, four numerical examples are presented to demonstrate the developed model and the solution procedure.