Finite Replenishment Rate Research Articles

Inventory optimization in a green environment with two warehouses

Recently, the environment requires more emphasis on reverse logistics in order to maintain sustainability of the human civilization. The article introduces a sustainable model for reverse logistics that is based on two storage facility. Generally speaking, the essential commodities are considered to be decaying in nature. In this model, finite replenishment rate is considered and managed by the forward as well as reverse supply chain. In the beginning, the remanufactured and newly manufactured products are stored in owned warehouses (OW) that have limited storage space and for the excess amount; suppliers hire a rented warehouses (RW) at a higher holding cost than owning warehouses. The objective of this model is to obtain the optimal production and remanufacturing strategies to minimize the total relevant costs of the system. The paper concludes with an illustration of numerical data and a sensitivity analysis. Based on the results, the practitioners are advised to reduce the cycle length if the production rate is relevantly high. Thus it will reduce the holding cost, eventually the total cost of the system.

Advance sustainable inventory management through advertisement and trade-credit policy

The concept of advanced sustainable inventory management, where demand pattern stock level and advertising dependent under trade-credit policy is taking account in this present study. Optimal credit period and cycle time are the main objective of this advanced system. A developed solution methodology is derived to show the existence of global optimality under optimum credit period and cycle time. The main concern of this advanced system is to maximize the annual total system profit of retailer with finite replenishment rate. Numerical illustration are carry forward for different cases to prove the stainability along with real impact of this model. Sensitive analysis for the key parameters is discussed in sensitivity analysis section along with some real managerial insights.

An integrated vendor–buyer replenishment policy for deteriorating items with fuzzy environment and resource constraint

Different from previous researches, our study considers a perishable item with collaborative vendor–buyer ordering policy and finite replenishment rate. Furthermore, due to the importance of inventory and capital investment in today’s fuzzy marketing environments, researches in fuzzy collaborative inventory models have become very popular research in recent decades. Therefore, in our integrated model with deteriorating inventory replenishment policy, we construct the crisp/fuzzy models with inventory investment constraints with fuzzy environments. Two different fuzzy decision-making methods are used to formulate the models. Convex fuzzy programming (CFP) method is used to maximize the weighted sum for each achievement level of the joint cost and constraints. An inverse weighted fuzzy non-linear programming (IWFNLP) is then proposed to satisfy the decision-maker’s desirable achievement level of service. A heuristic algorithm with mixed-integer hybrid differential evolution (MIHDE) is developed to solve the crisp/fuzzy models. Numerical examples and sensitivity analysis are developed to investigate the effectiveness of the proposed method in the fuzzy environment. From the numerical analysis, it can be seen that the IWFNLP method is a more efficient decision-making tool than the CFP method.

Economic ordering policy for single item inventory model over finite time horizon

This paper deals with an economic order quantity (EOQ) model for non-instantaneous deteriorating items in which the demand is a deterministic function of selling price and advertisement cost under the effect of inflation and time value of money over a finite planning horizon. In addition, a permissible delay in payment within the cycle time is offered by the supplier as an alternative to price discount. Finite replenishment rate is considered. Two different scenarios are considered here, that is, shortages are not permitted in scenario-I and shortages are permitted with partial backlogging in scenario-II. The objective of this work is to minimize the total inventory cost and to find the optimal length of replenishment and the optimal order quantity. Theoretical approaches described for the proposed scenarios are studied with the help of numerical examples. Sensitivity analysis for the major parameters of the inventory system is made and the managerial implications are given. Comparison of various results obtained for the two scenarios are studied and analyzed in detail.

An inventory model with imperfect items, stock dependent demand and permissible delay in payments under inflation

This paper develops an economic ordering quantity (EOQ) model with stock dependent demand and imperfect items under the effect of inflation and time value of money. In this model, the lifetime of a defective item follows a Weibull distribution and the imperfect items are reworked at a cost to become the perfect one. In this article, the model is considered with finite replenishment rate under progressive payment scheme within the cycle time and the retailer is allowed a trade-credit offer by the supplier to buy more items. During the credit period, the retailer can earn more by selling their products. The interest on purchasing cost is charged for the delay of payment by the retailer. The objective of this model is to minimize the total inventory cost of the retailer by finding the optimal cycle length and the optimal order quantity. Numerical examples are given to demonstrate the results. Sensitivity analysis of the model with respect to several system parameters has been carried out and the implications are discussed in detail.

An inventory model with finite replenishment, probabilistic deterioration and permissible delay in payments

This paper develops an inventory model for deteriorating items with finite replenishment rate under a progressive payment scheme within the cycle time. In this model, the deterioration function follows a probability distribution such as a (1) uniform distribution, (2) triangular distribution or (3) beta distribution. Here, the retailer is allowed a trade-credit offer by the supplier to buy more items. This model aids in minimizing the total inventory cost of the retailer by finding the optimal cycle length, the optimal time length of replenishment and the optimal order quantity. Some theorems have been framed to characterize the optimal solutions. The necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are also provided. The optimal solution of the model is illustrated with the help of numerical examples, and numerical comparisons between the three models are also given. Finally, sensitivity analysis and graphical representations are given to demonstrate the model.

Partial Trade-Credit Policy of Retailer with Exponentially Deteriorating Items

This model considers the strategy that supplier offers retailer a full trade-credit policy whereas retailer offers their customers a partial trade-credit policy. For such assumption, retailer can earn more profits. In this supplier–retailer model, deterioration of products is assumed as exponential. The main purpose is to minimize the retailer’s annual total cost with finite replenishment rate. Graphical representations are given under different circumstances. The analytical derivation of the model is given to obtain the minimum cost. Some numerical examples for different cases are provided to illustrate the model.

An inventory model for defective items with trade credit and inflation

This paper develops an inventory model with imperfect items under the effect of inflation and time value of money in which demand is a deterministic function of selling price and advertisement cost. In this process, a certain fraction of purchased items are defective. These non-conforming items are reworked or refunded if they reach the customer. In this article, the model is considered with finite replenishment rate under progressive payment scheme within the cycle time. Here, the retailer is allowed a trade credit offer by the supplier to buy more items. This model aids in minimizing the total inventory cost by finding the optimal cycle length, the optimal time length of replenishment, and the optimal order quantity. As a particular case, the results of the perfect system (i.e. the system without defective items) are obtained. The optimal solution of the model is illustrated with the help of numerical examples. Also, the effect of changes in the different parameters on the optimal total cost is graphically presented.

The EPQ model under conditions of two levels of trade credit and limited storage capacity in supply chain management

An inventory problem involves a lot of factors influencing inventory decisions. To understand it, the traditional economic production quantity (EPQ) model plays rather important role for inventory analysis. Although the traditional EPQ models are still widely used in industry, practitioners frequently question validities of assumptions of these models such that their use encounters challenges and difficulties. So, this article tries to present a new inventory model by considering two levels of trade credit, finite replenishment rate and limited storage capacity together to relax the basic assumptions of the traditional EPQ model to improve the environment of the use of it. Keeping in mind cost-minimisation strategy, four easy-to-use theorems are developed to characterise the optimal solution. Finally, the sensitivity analyses are executed to investigate the effects of the various parameters on ordering policies and the annual total relevant costs of the inventory system.

An Inventory Model with Finite Replenishment Rate, Trade Credit Policy and Price-Discount Offer

When some suppliers offer trade credit periods and price discounts to retailers in order to increase the demand of their products, retailers have to face different types of discount offers and credits within which they have to take a decision which is the best offer for them to make more profit. The retailers try to buy perfect-quality items at a reasonable price, and also they try to invest returns obtained by selling those items in such a manner that their business is not hampered. In this point of view, we consider an economic order quantity (EOQ) model for various types of time-dependent demand when delay in payment and price discount are permitted by suppliers to retailers. The models of various demand patterns are discussed analytically. Some numerical examples and graphical representations are considered to illustrate the model.

A two-warehouse inventory model with increasing demand and time varying deterioration

In this paper, an inventory model of two-warehouse is considered with quadratically increasing demand and time varying deterioration. Comparing to the existing literature, the model is derived with finite replenishment rate and unequal length of the cycle time. The associated cost of the system is minimized. A numerical example, the graphical representation and sensitivity analysis are provided to illustrate the model.

A production–inventory model incorporating the effect of preservation technology investment when demand is fluctuating with time

In most of the inventory models in the literature, the rate of deterioration of goods is viewed as an exogenous variable, which is not subject to control. In the real market, firms can reduce the rate of deterioration of products by means of effective capital investment in preservation technology. In this research, we formulate a production–inventory model for deteriorating items with time-varying demand and finite replenishment rate by allowing preservation technology cost as a decision variable in conjunction with production policy. The objective is to find the optimal production and preservation technology investment strategies while minimizing the total cost over the planning horizon. A traditional particle swarm optimization is coded and used to solve the mixed-integer nonlinear programming problem. Some numerical examples are used to illustrate the features of the proposed model.

An EPQ model under two levels of trade credit and limited storage space

A B S T R A C T In this article, a production inventory model is developed to determine the retailer's optimal replenishment decisions under two levels of trade credit and limited storage space. Two levels of trade credit refers that the supplier provides to his/her retailer a permissible delay period to settle the account and the retailer also in turn provides a delay period to his/her customer for paying of purchasing goods. The retailer's credit period M offered by supplier is greater than customers credit period N provides by the retailer. This paper investigates retailer optimal replenishment policy under finite replenishment rate by minimizing the total annual inventory cost. Three theorems are developed to determine optimal cycle time, optimal relevant cost and optimal order quantity for retailers accurate and rapidly. A numerical example is used to analyze the validity of propose model, Sensitive analysis shows managerial decisions for retailer.

An EOQ model with delay in payments and stock dependent demand in the presence of imperfect production

In real life situation, supplier generally offers a delay period to the retailer to buy more. In this connection, a mathematical model is considered to investigate the retailer’s optimal replenishment policy under permissible delay in payment with stock dependent demand within the EOQ (Economic Order Quantity) framework. Most of the EOQ models are considered with infinite replenishment rate. In this article, the model is considered with finite replenishment rate under progressive payment scheme with the production of defective items within the cycle time. The mathematical models have been derived for obtaining the optimal cycle time so that the annual total relevant cost is minimized. Numerical examples along with graphical representation and sensitivity analysis are provided to illustrate the model.

An EOQ model with delay in payments and time varying deterioration rate

This article deals with an EOQ ( Economic Order Quantity) model for finite replenishment rate where demand and deterioration rate are both time-dependent. In this model, the retailers are allowed a trade-credit offer by the suppliers to buy more items with different discount rates on the purchasing costs. During the credit period, the retailers can earn more by selling their products. The interest on purchasing cost is charged for the delay of payment by the retailers. Some of the items may deteriorate in the course of time. In this regard, the author develops an EOQ model for time varying deterioration rate. The profit function of the model is maximized. Finally, a numerical example and graphical illustrations are used to illustrate the model.

A two-warehouse inventory model under trade credit in the supply chain management

The traditional EOQ (Economic Ordering Quantity) inventory model has three basic assumptions (A), (B) and (C) to be summarized as follows: (A) The retailer must be paid for the items as soon as the items are received; (B) The replenishment rate is infinite; (C) The inventories are stored by a single warehouse with unlimited capacity. Few inventory models with generalizing assumptions (A), (B) and (C) together have been found in the literature. This paper tries to incorporate the above concepts to consider the inventory model with the trade credit, finite replenishment rate and limited storage capacity to relax assumptions (A), (B) and (C) simultaneously to establish a new economic production quantity model. The mathematical model and the solution procedure are developed and numerical examples are provided to illustrate them. Key words: Economic ordering quantity, permissible delay in payments, trade credit, limited storage capacity, finite replenishment rate.

A Stock Dependent Economic Order Quantity Model for Perishable Items Under Inflationary Conditions

Problem statement: In most of the earlier inventory models, effect of inflation has been ignored, which is playing pilot role in present environment. In this article, we have proposed an economic order quantity model for deteriorating items having stock dependent demand (whose demand varies with the stock) under the effect of inflation. Approach: Firstly, problem is framed in the form of linear differential equation model and then this model has been solved with general solution technique of linear differential equations. Using the solution the expression for total cost of inventory has been obtained. Results: Using total cost equation an optimal order quantity is obtained and convexity of various costs is also studied. This model helps retailer to decide his economic order quantity for deteriorating items having stock dependent demand. The consideration of effect of inflation makes this model more relevant for present business environment. Conclusion: The convexity of various costs proves the validity of this model. The effect of inflation with two different rates is also studied in tables below considering both constant as well as stock dependent demand. The graph of these tables shows that the optimal inventory cost increases with increase in number of cycles it increases rapidly in starting but becomes stable for large number of cycles. The proposed model can be extended in several ways. For instance, we may generalize the model to allow for shortages, quantity discounts, time value of money, finite replenishment rate, permissible delay in payments and others.

A two-warehouse production model for deteriorating inventory items with time-dependent demands

A two-warehouse inventory model for deteriorating items with time-dependent demand has been developed. Compared with previous models, the model involves a free form time-dependent demand and a finite replenishment rate within a finite planning horizon. Rather than the heuristic approach of equal production cycle times adopted by Lee and Ma, an approach which permits variation in production cycle times is adopted to determine the number of production cycles and the times for replenishment during a finite planning horizon. Numerical examples are provided to illustrate the application of the model and the results indicate that the performance of the proposed approach is superior to that of the heuristic approach of Lee and Ma.

An inventory model under uncertain inflationary conditions, finite production rate and inflation-dependent demand rate for deteriorating items with shortages

In the existing literature, inventory models under inflationary conditions are usually developed under the assumption of certain inflation rates and constant, time-varying or stock-dependent demand rate. In many real-life situations, the practical experiences reveal that the inflation is non-deterministic and a variable. Meanwhile, the demand rate can be related to the inflation rates. The theoretical contribution of this article is to consider stochastic inflationary conditions with variable probability density functions (pdfs) over the time horizon, and the demand rate is dependent to the inflation rates (any arbitrary pdfs can be used). The developed model, also, implicates to finite replenishment rate, finite time horizon and deteriorating items with shortages. The objective is minimisation of the expected present value of costs over the time horizon. The numerical example and case study have been provided for evaluation and validation of the theoretical results and some special cases of the model are discussed.

The optimal ordering policy with trade credit under two different payment methods

Suppliers’ offering delay payment terms to retailers can be regarded as a type of price reduction. In today’s ever competitive marketplace, offering delay payments has become a commonly adopted method to suppliers. Most of the inventory models with permissible delay in payments assumed that the entire lot size is delivered at the same time. However, in practice, goods ordered are usually arrived overtime in separate batches. In this study, we discuss an inventory problem with a finite replenishment rate under trade credit for two payment methods. We establish a theorem to find the optimal solution for each payment method. Numerical examples are also given to illustrate the solution procedure. Finally, to investigate the effect of changes of some main parameter values on the optimal solution, a sensitivity analysis is performed and some management interpretations are proposed.