An EOQ model with stock dependent demand and imperfect quality items

This paper deals with an economic order quantity model where demand is stock dependent. Items received are not of perfect quality and each lot received contains percentage defective imperfect quality items, which follow a probability distribution. Two cases are considered. 1) Imperfect quality items are held in stock and sold in a single batch after a 100 percent screening process. 2) A hundred percent screening process is performed but the imperfect quality items are sold as soon as they are detected. Approximate optimal solutions are derived in both cases. A numerical example is provided in order to illustrate the development of the model. Sensitivity analysis is also presented, indicating the effects of percentage imperfect quality items on the optimal order quantity and total profit

Deterministic and stochastic optimal inventory control with logistic stock-dependent demand rate

It has been suggested by many supply chain practitioners that in certain cases inventory can have a stimulating effect on the demand. In mathematical terms this amounts to the demand being a function of the inventory level alone. In this work we propose a logistic growth model for the inventory dependent demand rate and solve first the continuous time deterministic optimal control problem of maximising the present value of the total net profit over an infinite horizon. It is shown that under a strict condition there is a unique optimal stock level which the inventory planner should maintain in order to satisfy demand. The stochastic version of the optimal control problem is considered next. A bang-bang type of optimal control problem is formulated and the associated Hamilton-Jacobi-Bellman equation is solved. The inventory level that signifies a switch in the ordering strategy is worked out in the stochastic case. Copyright © 2014 Inderscience Enterprises Ltd

A periodic review inventory model with stock dependent demand, permissible delay in payment and price discount on backorders

In this paper we study a periodic review inventory model with stock dependent demand. When stock on hand is zero, the inventory manager offers a price discount to customers who are willing to backorder their demand. Permissible delay in payments allowed to the inventory manager is also taken into account. Numerical examples are cited to illustrate the model

A Two Warehouse Inventory Model with Stock-Dependent Demand and variable deterioration rate

In this paper we discuss a two warehouses inventory model for non-instantaneous deteriorating items. Throughout last so many years, mostly researchers have consideration to the situation where the demand rate is dependent on the level of the on-hand inventory. For inventory systems, such as fashionable commodities, the length of the waiting time for the next replenishment would determine whether the backlogging will be accepted or not. In real life situation, enterprises usually buy more goods than can be stored in their own warehouses (OW) for future production or sales. The surplus quantities are frequently stored in an extra storage space, represented by rented warehouses (RW).The rented warehouse is considered to charge high unit holding cost than the own warehouse. The necessary and sufficient conditions of the existence and uniqueness of the optimal solution are shown. We determine the optimal replenishment policy for non-instantaneous deteriorating items with partial backlogging and stock-dependent demand

Two Warehouse Inventory Model for Deteriorating Products with Stock Dependent Demand and Shortages

In this paper a deterministic inventory model for two warehouses has been developed. In two warehouses the first is the owned warehouse with a fixed capacity of W units and the other one is rented warehouse with unlimited stocking capacity. The deterioration occurs in both the warehouses. First the demand is fulfilled from the inventory in rented warehouse and after thatthe inventory in owned warehouse has been used. The shortages are allowed in owned warehouse only and the excess demand is partially backlogged. For the generality of the model we presented the equations for total cost of the system. A numerical example and sensitivity analysis with respect to different associated parameters has also been presented to illustrate the model

A comprehensive extension of optimal ordering policy for stock-dependent demand under progressive payment scheme

[[abstract]]In a recent paper, Soni and Shah (2008) presented an inventory model with a stock-dependent demand under progressive payment scheme, assuming zero ending-inventory and adopting a cost-minimization objective. However, with a stock-dependent demand a non-zero ending stock may increase profits resulting from the increased demand. This work is motivated by Soni and Shah’s (2008) paper extending their model to allow for: (1) a non-zero ending-inventory, (2) a profit-maximization objective, (3) a limited inventory capacity and (4) deteriorating items with a constant deterioration rate. For the resulted model sufficient conditions for the existence and uniqueness of the optimal solution are provided. Finally, several economic interpretations of the theoretical results are also given.[[incitationindex]]SCI[[booktype]]紙

A DETERIORATING INVENTORY MODEL WITH LIMITED VEHICLE CAPACITY, STOCK DEPENDENT DEMAND AND UNAVAILABILITY SUPPLY

Inventory model is one research topic that has been given attention intensively in the supply chain. There are two main costs for inventory, which are transport cost and inventory cost. Therefore, some buyers would like to apply a Vendor Managed Inventory (VMI) system where vendors handle the transportation and manage stocks at the buyer’s hand. The problem is complex for some items, such as fruits and vegetables, in which the items deteriorate. The need for fruits and vegetables tends to be higher as the stock is high. Deteriorating inventory models have been developed in many years, however, only a few models considering vehicle capacity, carbon emission, deteriorating items, stock dependent demand, and unavailability supply. In this study, a deteriorating inventory model for multi items in one distribution with stock dependent demand is improved. On the other hand, fruits and vegetable stock are not consistently available, so lost sales costs should be examined. Environmental issues have been studied by many researchers. Therefore, we further consider the carbon emission yield in this model. Since the closed-loop solution can not be obtained, we employ a simple heuristic solution in Maple. A sensitivity analysis is employed to obtain some management insight. The sensitivity analysis indicates that the carbon emission tax rate can encourage decision-makers to increase order quantity and reduce carbon emission, but the policy should deal with many features that are recognized by decision-makers to make it usefu

An Inventory Model for Perishable Products with Stock-Dependent Demand and Trade Credit under Inflation

We consider an inventory model for perishable products with stock-dependent demand under inflation. It is assumed that the supplier offers a credit period to the retailer, and the length of credit period is dependent on the order quantity. The retailer does not need to pay the purchasing cost until the end of credit period. If the revenue earned by the end of credit period is enough to pay the purchasing cost or there is budget, the balance is settled and the supplier does not charge any interest. Otherwise, the supplier charges interest for unpaid balance after credit period, and the interest and the remaining payments are made at the end of the replenishment cycle. The objective is to minimize the retailer’s (net) present value of cost. We show that there is an optimal cycle length to minimize the present value of cost; furthermore, a solution procedure is given to find the optimal solution. Numerical experiments are provided to illustrate the proposed model

A note on: Optimal ordering policy for stock-dependent demand under progressive payment scheme

In a recent paper, Soni and Shah [Soni, H., Shah, N. H. (2008). Optimal ordering policy for stock-dependent demand under progressive payment scheme. European Journal of Operational Research 184(1), 91–100] developed a model to find the optimal ordering policy for a retailer with stock-dependent demand and a supplier offering a progressive payment scheme to the retailer. This note corrects some errors in the formulation of the model of Soni and Shah. It also extends their work by assuming that the credit interest rate of the retailer may exceed the interest rate charged by the supplier. Numerical examples illustrate the benefits of these modifications