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An Optimal Inventory Policy for Items Having Constant Demand and Constant Deterioration Rate with Trade Credit
Abstract
In most of the classical inventory models the demand is considered as constant. In this paper the model has been framed to study the items whose demand and deterioration both are constant. The authors developed a model to determine an optimal order quantity by using calculus technique of maxima and minima. Thus, it helps a retailer to decide its optimal ordering quantity under the constraints of constant deterioration rate and constant pattern of demand.
In today’s competitive market, inventory management is a difficult job for every business enterprises. Objects are getting deteriorate after some period of time and result into economic loss. Keeping this in mind, this inventory model is for perishable objects where the rate of deterioration is considered to be constant with a constant demand rate. To reflect the real-life situation, the model explores a two-level trade-credit policy, i.e. the supplier offers certain credit period to the retailer and simultaneously the retailer permits a permissible delay in payment to the consumers that helps to increase the demand. If the retailer clears its entire amount during the end of first credit period, then the retailer can utilize it to earn interest. Moreover, if the retailer fails to clear the account by the end of first period, then he/she is allowed to pay off the balance after first credit period or by the end of second credit period. Here, the financial loans can be reduced through constant demand and interest earned. This paper uses a classical optimization method and calculated several numerical examples to elaborate the model. Convexity of cost function is proved through graphs. The objective of the paper is to minimize the total cost with respect to the inventory cycle time. At last, sensitivity analysis is done to study the effects of varying inventory parameters on decision variable and optimal solution.
The aim of this work is not only to give an up-to-date review of perishable inventory models, but also of the joint key topics of publications from January 2012 until December 2015 in the research area of deteriorating inventory models. The advantage of this review is the ability to quickly find papers according to given key topics. Methodically, this paper is based on the literature review of Bakker et al. (2012). However, we slightly modify the classification of inventory models of perishable goods in our work, and extend the existing key topics.
Simulation models are used to examine the effects of shelf life on the performance of three-tier automatic pipeline, variable-inventory, and order-based production control system (APVIOBPCS) supply chains with different information delays between tiers with a fixed or variable inventory constructed using SIMULINK, which provides a response to a sudden demand sales rate and a finite shelf life. This incorporates the effects of product shelf life for each tier. It is assumed that for a finite shelf life, all parties practise a first-in, first-out operation.
We show a substantial reduction in the number of discards, reducing carbon footprint and wasted resources. Fixed-inventory targets produce more discards than variable inventory, and vendor-managed inventory or electronic data transmission with discard feedback produce substantial reductions in discard.
Large number of researcher papers has been published for inventory lot-size models under trade credit financing by assuming that demand rate is constant. But demand rate is often not constant. During the growth stage of the product life cycle, the demand function increases with time. In this paper we extend the constant demand to time-dependent demand. This paper derives the problem of determining the retailer's optimal price and optimal total profit when the supplier permits delay in payments for an order of a product. In this paper demand rate is considered as a function as a function of price and time. We also provide the optimal policy for the customer to obtain its maximum annual net profit. Mathematica software is used for finding optimal price and optimal replenishment time simultaneously. Finally, numerical examples and sensitivity analysis are given to illustrate the theoretical results.
Problem statement: Demand considered in most of the classical inventory models is constant, while in most of the practical cases the demand changes with time. In this study model has been framed to study the items whose demand changes with time and deterioration rate increases with time. The effect of permissible delay is also incorporated in this study. The objective of this research is to develop an inventory model for perishable items whose perish-ability rate as well as demand increases with time. Approach: Firstly, problem is framed in the form of linear differential equation model and this model had been solved using general solution techniques of linear differential equations. The solution obtained gives the inventory level at any particular time of the cycle period. With the help of this inventory level, total as well as average inventory cost has been obtained. Results: This study developed a model to determine an optimal order quantity by using calculus technique of maxima and minima. Thus it helps retailer to decide its optimal ordering quantity under the constraints of variable deterioration rate and linear pattern of demand. Conclusion: Numerical solution of the suggested model had also been proposed, the above model can be converted into constant demand model, or for items having no deterioration. This study can further be extended for items having some other demand pattern, also time value of money and inflation can be incorporated in this model to make it more realistic and present business environment suited.
A deterministic inventory model is developed for deteriorating items for a system that allows backlogging under the condition of immediate replenishments. The model is developed for any well-oehaved probability distribution for the time to deterioration of an item. From the model developed, the earlier models developed by Ghare and Schrader and Covert and Philip can be obtained as particular cases by taking a suitable probability distribution for the time to deterioration of an item when shortage cost becomes large.