Stock-dependent Demand Rate Research Articles

Joint pricing and lot-sizing policy for deteriorating items with price and stock dependent demand rate and shortage

This paper considers a joint pricing and production problem for deteriorating items with price and stock dependent demand rate, constant production rate, exponential deterioration distribution and allowing shortage. The main purpose is to determine the optimal selling price and production scheme simultaneously such that the average profit per unit time is maximised. In order to get the optimal solution, a two-stage method is proposed. In stage 1, we study the optimal solution for fixed selling price. Two cases that building inventory is profit or not are addressed. The existence and uniqueness of optimal solutions are also proved, respectively. In stage 2, we study the optimal solution for fixed production scheme and adopt Newton's method to numerically show that the solution get from the first-order necessary condition is the optimum of the problem. Based on the two-stage method, a specific iteration algorithm is presented to search the optimal solution. In the next, we conduct a numerical example to illustrate the effectiveness and practicability of model and algorithm, and verify that the result searched by the algorithm is close to the optimal solution. At last, some sensitive analyses on the main parameters are carried out and some managerial implications are put forward.

Joint pricing and lot-sizing policy for deteriorating items with price and stock dependent demand rate and shortage

Joint pricing and lot-sizing policy for deteriorating items with price and stock dependent demand rate and shortage

A two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items

In this study, we develop an inventory model for deteriorating items with stock dependent demand rate. Shortages are allowed to this model and when stock on hand is zero, then the retailer offers a price discount to customers who are willing to back-order their demands. Here, the supplier as well as the retailer adopt the trade credit policy for their customers in order to promote the market competition. The retailer can earn revenue and interest after the customer pays for the amount of purchasing cost to the retailer until the end of the trade credit period offered by the supplier. Besides this, we consider variable holding cost due to increase the stock of deteriorating items. Thereafter, we present an easy analytical closed-form solution to find the optimal order quantity so that the total cost per unit time is minimized. The results are discussed with the help of numerical examples to validate the proposed model. A sensitivity analysis of the optimal solutions for the parameters is also provided in order to stabilize our model. The paper ends with a conclusion and an outlook to possible future studies.

Economic ordering policies under credit financing for deteriorating items with stock-dependent demand rate using discounted cash flow approach

This study presents an economic ordering policy for deteriorating items with stock-level dependent demand rate in the presence of trade credit using the discounted cash flows approach. Mathematical models are derived under three different situations: instantaneous cash flows; credit only on units in stock; and a constant credit period. The main objective of this work is to minimize the present value of all future cash flows. The optimal solution is derived for finding the optimal cycle time and the present value of all future cash flows. Next, numerical examples are provided to validate the proposed models. Numerical examples show that there is significant difference in the values of optimal cycle time, order quantity, and present value of all future cash flows. Sensitivity analysis is carried out with respect to the variation of key parameters. Mathematica® 5.1 is used to find numerical results.

A Fuzzy Environment Inventory Model with Partial Backlogging under Learning Effect

this article we developed an inventory model for non- instantaneous decaying items is considered under crisp and fuzzy environment. In this study we have considered stock dependent demand rate and variable deterioration. It is supposed that shortages are allowed and partially backlogged with exponential backlogging rate. Holding cost follows the learning curve. The deterioration rate, ordering cost, shortage cost and deterioration cost are assumed as a triangular fuzzy numbers. The aim of our study is to defuzzify the total cost function by signed distance method. This model is developed in both crisp and fuzzy surroundings. A numerical experiment is given to demonstrate the developed crisp and fuzzy models. Sensitivity analysis is implemented to examine the effect of parameters. The convexity of the total cost function is shown by graphically.

Fuzzy multi-item inventory model with time varying stock dependent demand under partial backlogging

In this paper we have formulated a multi-item fuzzy inventory model with stock dependent demand rate and shortages are allowed with partial backlogging. The multi-item inventory model with demand dependent unit cost has been formulated alone with storage space constraints. The partial backlogging rate of unsatisfied demand is assumed to be decreasing exponential function for waiting time. Here the cost parameters, the objective function and constraint are imposed in fuzzy nature. The model has been solved by Fuzzy Goal Programming (FGP) method. Finally the model is expressed by numerical example.

An Inventory Model for Maximum Life Time Products under the Price and Stock Dependent Demand Rate

An Inventory Model for Maximum Life Time Products under the Price and Stock Dependent Demand Rate

주문량 종속 신용거래 하에서 재고 종속형 제품수요를 갖는 퇴화성제품의 공급체인 재고모형

본 연구는 공급자(supplier), 중간공급자(distributor) 그리고 고객(customer)으로 구성된 2 단계 공급사슬에서 퇴화성 제품(deteriorating products)에 대한 중간공급자의 재고모형을 분석하였다. 문제 분석을 위해 공급자는 중간공급자의 수요 증대를 목적으로 중간공급자의 주문 크기에 따라 차별적으로 외상 기간을 허용하고, 최종 고객의 수요는 중간공급자의 재고 수준에 따라 선형적(linearly)으로 증가한다는 가정 하에 모형을 분석하였다. 중간공급자의 이익을 최대화하는 경제적 주문량 결정 방법을 제시하였고, 예제를 통하여 그 해법의 타당성을 보였으며, 민감도 분석을 통하여 퇴화율이 재고정책에 미치는 영향을 분석하였다.

Cost Analysis for a Supplier in an Inflationary Environment with Stock Dependent Demand Rate for Perishable Items

The present study is concerned with the cost modeling of an inventory system with perishable multi-items having stock dependent demand rates under an inflationary environment of the market. The concept of permissible delay is taken into account. The study provides the cost analysis of inventory system under the decision criteria of time value of money, inflation, deterioration, and stock dependent demand. Numerical illustrations are derived from the quantitative model to validate the results. The cost of inventory and optimal time are also computed by varying different system parameters. The comparison of these results is facilitated by computing the results with neurofuzzy results.

A Note on Non-linear Profit-Maximization Entropic Order Quantity (EnOQ) Model for Deteriorating Items with Stock Dependent Demand Rate

A Note on Non-linear Profit-Maximization Entropic Order Quantity (EnOQ) Model for Deteriorating Items with Stock Dependent Demand Rate

An inventory model with both stock-dependent demand rate and stock-dependent holding cost rate

In this paper, we develop an inventory model under a stock-dependent demand rate and stock-dependent holding cost rate with relaxed terminal conditions. Shortages are allowed and partially backlogged in the model. The purpose of this study is to determine the optimal order quantity and the ending inventory level such that the total profit per unit time is maximized for the retailer. We first establish a proper model for a mathematical formulation. Then we develop several theoretical results and provide the decision-maker with an algorithm to determine the optimal solution. Finally, numerical examples are provided to illustrate the solution procedure, and a sensitivity analysis of the optimal solution with respect to major parameters is carried out.

Effect of salvage value on a two-warehouse inventory model for deteriorating items with stock-dependent demand rate and partial backlogging

In this study, an EOQ model with two level of storage is developed when units in inventory deteriorate at a constant rate and demand is stock dependent. The salvage value is allied to deteriorated units. When stock level exceeds the capability of own warehouse (OW), it is to be kept in additional rented warehouse (RW) with higher holding cost than OW. The inventory held in RW is transferred to OW in continuous release pattern till the stock in RW gets exhausted. In developing the model it is assumed that shortages are allowed and partially backlogged. An algorithm is given to find the optimal solution. The sensitivity analysis is voted for out to analyse the effect of critical parameters on optimal solution by using MATHEMATICA–5.2 for the feasibility and applicability of our model.

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.

An inventory model of price and stock dependent demand rate with deterioration under inflation and delay in payment

This paper deals with the economic order quantity model for deteriorating items with price and stock dependent demand rate, where deterioration is constant. We have noticed the effect of shortage under inflation and taken into consideration the condition of permissible delay in payment. In first case, the credit period is less than or equal to the cycle time for settling the account and secondly the credit period is greater than the cycle time for settling the account. Then we have obtained the condition for minimizing the total cost. Finally, the results are illustrated by a numerical example for different cases and sensitivity analysis is carried out to analyze the effect of the parameters on the optimal solution.

Optimal Inventory Model for Time Dependent Decaying Items with Stock Dependent Demand Rate and Shortages

This paper deals with in developing an inventory model for time dependent decaying items as bread, food stuff, green vegetables and medicine etc. The rate of deterioration is time dependent and considers a linear function of time. Demand rate is stock dependent in linear form. It is a common phenomenon observed in the super market that a large pile of goods attracts more customers. Shortages are allowed and shortages are completely backlogged. The numerical example is given to illustrate the model developed. The model is solved analytically by maximizing the total profit.

Supply chain coordination with stock-dependent demand rate and credit incentives

In this paper, we consider a supply chain which consists of a single manufacturer and a single retailer with a single product type. Demand is assumed to be dependent on the retailer's stock level. Without coordination, the retailer determines its order quantity to maximize its own profit, which is usually smaller than the manufacturer's economic production quantity. Three coordination policies are presented to coordinate the manufacturer's and the retailer's decisions. First, the credit period policy and the quantity discount policy are developed and the total profits under the two policies are compared. Then we develop a centralized supply chain policy and show that there is a unique optimal order quantity to achieve a perfect coordination. The centralized supply chain can get higher or equal channel profit while the credit period policy and the quantity discount policy are easier to achieve. Numerical examples are provided to illustrate the proposed policies.

Ordering policy for stock-dependent demand rate under progressive payment scheme: a comment

In a recent paper, Soni and Shah developed a model for finding the optimal ordering policy for a retailer facing stock-dependent demand and a supplier offering a progressive payment scheme. In this comment, we correct several errors in the formulation of the models of Soni and Shah and modify some assumptions to increase the model's applicability. Numerical examples illustrate the benefits of our modifications.

Dilemma of rented warehouse and shelf for inventory systems with displayed stock level dependent demand

Impact of display stock has been extensively discussed in literature in terms of stock dependent demand rate. In some recent papers a three-component inventory level dependent demand (as displayed stock level (DSL)) has been proposed. It has been assumed that demand is independent of instantaneous inventory level if inventory is above a certain level in a shelf. As the demand is independent of instantaneous inventory level, a retailer is always in dilemma whether inventory additional to that level will be kept in the shelf or to rent a new storage. In this paper we focus on this by developing three mathematical models. We show that the problem in choosing rented storage or shelf to keep additional inventory can always be eliminated (a) without the knowledge of optimal stocking points or (b) with the knowledge of any one optimal stocking point. Also, if there is enough opportunity to have an extra storage and a mild limit on inventory holding cost in the shelf is satisfied, then there is no need to display inventory in the shelf above the certain level. The results are illustrated by numerical examples and sensitivity analysis is carried out.

Optimal policy for profit maximising in an EOQ model under non-linear holding cost and stock-dependent demand rate

In this article, we integrate a non-linear holding cost with a stock-dependent demand rate in a maximising profit per unit time model, extending several inventory models studied by other authors. After giving the mathematical formulation of the inventory system, we prove the existence and uniqueness of the optimal policy. Relying on this result, we can obtain the optimal solution using different numerical algorithms. Moreover, we provide a necessary and sufficient condition to determine whether a system is profitable, and we establish a rule to check when a given order quantity is the optimal lot size of the inventory model. The results are illustrated through numerical examples and the sensitivity of the optimal solution with respect to changes in some values of the parameters is assessed.

Optimal ordering policy for deteriorating items with power-form stock dependent demand under two-warehouse storage facility

In realistic world, there usually exist various factors that induce the retailer to order more items than the capacity of his Own-warehouse (OW). Therefore, for the retailer, it is very practical to determine whether or not to rent other warehouse and what order policy to adopt if other warehouse is indeed needed. For the stock dependent demand pattern, retailer has his own warehouse to display the items and may hire another warehouse of the larger capacity, treated as rented warehouse (RW) to storage the excess inventory. In this paper, an inventory model with power form stock-dependent demand rate is developed. The demand rate is assumed to be a polynomial form of current inventory level in Own-warehouse. It is also assumed that retailer first fulfills the demand (depending upon the stock displayed in the OW) directly from the RW until the inventory level in the RW reaches to the zero level, after that, demand is fulfilled from OW. As a consequence, no item is transferred from RW to OW, therefore no transfer cost (neither fixed nor variable) is considered between RW and OW. It is considered that the deterioration rate per unit items in the RW and OW are different due to different preservation environments, as a consequence the holding costs per unit item in RW and OW are also different. Proposed model is illustrated with some numerical example along with some sensitivity analysis of parameters.