Finite Replenishment Rate Research Articles

A note on “Two-warehouse inventory model with deterioration under FIFO dispatch policy”

A recently published paper by Lee [C.C. Lee, Two-warehouse inventory model with deterioration under FIFO dispatching policy, European Journal of Operational Research 174 (2006) 861–873] considers different dispatching models for the two-warehouse inventory system with deteriorating items, in which Pakkala and Achary’s LIFO (last-in–first-out) model [T.P.M. Pakkala, K.K. Achary, A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate, European Journal of Operational Research 57 (1992) 71–76] is first modified, and then the author concludes that the modified LIFO model always has a lower cost than Pakkala and Achary’s LIFO model under a particular condition specified by him. The present note points out that this conclusion is incorrect and misleading. Alternatively, we provide a new sufficient condition such that the modified LIFO model always has a lower cost than Pakkala and Achary’s model. Besides, we also compare Pakkala and Achary’s original LIFO model with Lee’s FIFO (first-in–first-out) model for the special case where the two warehouses have the same deteriorating rates. Finally, numerical examples are provided to investigate and examine the impact of corresponding parameters on policy choice. The results in this note give a much clearer picture than those at Lee’s paper about the relationships between the different dispatching policies for the two-warehouse inventory system with deterioration items.

Optimal Policy for a Deteriorating Inventory Model with Finite Replenishment Rate and with Price Dependant Demand Rate and Cycle Length Dependant Price

In this paper, an inventory model with finite and constant replenishment rate, price dependant demand rate, time value of money and inflation, finite time horizon, lead time and exponential deterioration rate and with the objective of maximizing the present worth of the total system profit is developed. Using a dynamic programming based solution algorithm, we are able to find the optimal sequence of the cycles and also to obtain different optimal selling prices, optimal order quantities and optimal maximum inventories for the cycles with unequal lengths, which have never been done before for this model. We also use a numerical example to show accuracy of the solution procedure.

Introduction to distribution logistics

Introduction to distribution logistics

EPQ Models under Permissible Payment Delay: An Algebraic Approach

The main purpose of this paper is to relax the Ouyang et al.’s model (2004) using the algebraic method to determine the optimal inventory replenishment policy for the retailer under finite replenishment rate and permissible delay in payments. Ouyang et al. (2004) assumed that the retailer would not consider paying payment until receiving all items. The purpose of this paper is to relax this assumption and establish the retailer’s inventory system as a cost minimization problem to determine the retailer’s optimal inventory cycle time. Then, an algebraic approach is provided and an easy-to-use theorem is derived to efficiently determine the optimal cycle time. Finally, numerical examples are given to illustrate the results and managerial insights are drawn.

A collaborative inventory system with permissible delay in payment for deteriorating items

A collaborative inventory system of single vendor and single buyer is developed to maximize the total profit of the whole system. However, the optimal solution for the whole system is not always beneficial to both players. To ensure mutual benefit, a negotiation factor is incorporated to share the profit between the two players according to their contributions. The permissible delay in payment is a win–win strategy for sharing profit in the collaborative system. A deteriorating inventory model with finite replenishment rate and price sensitive demand is assumed to occur in a high-tech, short life cycle and perishable electronic product. A numerical example is provided to illustrate our models. The sensitivity analysis of the demand rate, replenishment rate, deterioration factor, and other related parameters shows that the percentage extra total profit is significant when both the collaboration strategy and the deterioration factor are considered.

Retailer’s economic ordering policy with finite replenishment rate when delay in payments is permissible

This paper extends Chung et al. (2002) within the economic production quantity (EPQ) framework. In the paper of Chung et al. (2002), they modified Goyal’s model (1985) to presume that the unit selling price and the unit purchasing price are not necessarily equal to reflect the real-life situations. Furthermore, their paper proposed that at the end of the credit period, the retailer would borrow 100% purchasing cost from the bank to pay off the account. This paper will extend Chung et al. (2002) to the case that the supplier at a finite rate replenishes the units. When the supplier’s replenishment rate approaches to infinite, Chung et al. (2002) will be a special case of this paper. Two efficient theorems are developed to determine the optimal cycle time and the optimal order quantity. Numerical examples are given to illustrate these theorems.

AN INVENTORY MODEL WITH DETERIORATING ITEMS UNDER PERMISSIBLE DELAY IN PAYMENTS

ABSTRACT In modern business transactions, it is a very common to allow customers some grace period before they settle the account with the supplier. The purchaser can benefit from this delay in payment due to the time value of money. Although researches with permissible delay in payment have been developed for years, most of the models considered infinite replenishment rate. However, in real-life, the replenishment rate is seldom infinite. In order to be more realistic and practical, this study develops an inventory model for deteriorating items with finite replenishment rate and shortage under permissible delay in payment. The objective of the study is to minimize the total cost by deriving the optimal ordering quantity and cycle time under permissible delay in payment. Since the derived models involve a high-order exponential function, it is not possible to solve the problem directly by classical optimization method. A computer search algorithm is developed to obtain the optimal ordering quantity and cycle time. Numerical examples are given to validate the analysis of the models.

Economic production lot size for deteriorating items taking account of the time-value of money

This study applies the discounted cash-flow approach to a deterministic inventory model of an item that deteriorates over time at a varying rate. An optimization framework is presented to derive optimal production and pricing policies to maximize the net present value of profits over a finite planning horizon. A numerical example is provided to illustrate the optimization procedure. Scope and purpose A deterministic inventory model for an item with price-dependent demand is developed in this study. It is assumed that the inventory deteriorates over time at a varying rate and shortages in inventory are allowed. The model considers a production environment with a finite replenishment rate. The time-value of money for various costs associated with the inventory system is also considered.

A simple approximation of the EMQ model with Poisson machine failures

Consideration is given to the effect of machine breakdowns on the finite replenishment rate inventory model, which is also known as the Economic Manufacturing Quality model. It is assumed that the number of failures in a production run is Poisson distributed while the repair times are random and can assume any general distribution. Upon failure, the machine will receive immediate service, and the demand will be met from inventory. Long repair times can lead to stockout situations where no backordering is allowed. With the aforementioned assumptions, a simple approximate model is developed that describes the behaviour of the problem. Specific formulations are given for the cases where the repair times are exponential and constant. The model is based on results from Poisson and regenerative processes, and when tested against simulation, it provides very good solutions.

Composite lot sizing with quantity and freight discounts

The EOQ model is aggregated into an extended composite model by including shipping costs, inspection costs, in-transit holding costs, backorder costs, finite replenishment, quality rejects, quantity discounts, and freight rate discounts in its formulation. The embellished model can be disaggregated into numerous different deterministic hybrid models by using simplified decomposition rules that apply to a variety of specific operational conditions. Optimum lot sizing formulations are derived for all non-discount situations as well as discount situations without stockouts. For these situations, efficient algorithms are used to obtain optimum lot sizes. For incremental discount situations with stockouts, efficient algorithms along with numerical analysis are required to converge upon optimum lot sizes. The simple EOQ is shown to be a special disaggregated case of its composite parent. A foundation is provided for a decision support system to deal with the variegated mix of operational conditions.

A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate

A deterministic inventory model for deteriorating items with two warehouses is developed when the replenishment rate is finite, demand is at a uniform rate, and shortages are allowed. It is assumed that the rates of deterioration of item in the two warehouses may be different. The model is analysed for the case of continuous release pattern. Several special cases are discussed and a numerical example is provided to illustrate the variation in optimum inventory level and optimum cost for varying shortage cost.

An order-level lot-size inventory model for deteriorating items with finite replenishment rate

Inventory models have been written for many systems, but most of them assumed that inventory items maintain their original value over their storage period. In actual practice, values of many items may perish over time. For example, grains decay as time progresses. For such items, the effect of decaying or deterioration should be taken into consideration. Another assumption made in many inventory models is that replenishment rate is infinite. However, when an item can be produced in-house, the replenishment rate is also the production rate, and is hence finite. This paper derives a production model for the lot-size, order-level inventory system with finite production rate, taking into consideration the effect of decay. The objective is to minimize total cost by selecting the optimal lot size and order level. The derived model cannot be solved directly; a computer search algorithm is used to obtain the optimal lot size and order level. Numerical examples are shown at the end of the paper to illustrate the derived model.

On a stochastic extension of the EOQ formula

This note considers the classical EOQ model with finite replenishment rate, under stochastic lead time. It shows that if crossover of orders is prohibited and the model's parameters are such that the system experiences each cycle both positive stock and shortage the solution is closed form and is an intuitive extension of the EOQ formula.