scholarly journals A Price-Dependent Demand Model in the Single Period Inventory System with Price Adjustment

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Kamran Forghani ◽  
Abolfazl Mirzazadeh ◽  
Mehdi Rafiee
Keyword(s):  
Optimal Order ◽  
Selling Price ◽  
Inventory Problem ◽  
Demand Model ◽  
Inventory Costs ◽  
Single Period ◽  
Proposed Model ◽  
Demand Rate ◽  
Total Inventory ◽  
Dependent Demand

The previous efforts toward single period inventory problem with price-dependent demand only investigate the optimal order quantity to minimize the total inventory costs; however, there is no method in the literature to avoid unwanted costs due to the deviation between the actual demand and the previously estimated demand. To fill this gap, the present paper supposes that stochastic demand rate with normal distribution is sensitive to the selling price; this means that increasing the selling price would decrease the demand rate and vice versa. After monitoring the consumption trend within a section of the period, a new selling price is implemented to change the demand rate and reduce the shortage or salvage costs at the end of the period. Three functions were suggested to represent the demand rate as a function of selling price, and the numerical analysis was implemented to solve the proposed problem. Finally, an illustrative numerical example was solved for different configurations in order to show the advantages of the proposed model. The results revealed that there is a significant improvement in the system costs when price revision is considered.

scholarly journals Optimal Price and Lot Size for an EOQ Model with Full Backordering under Power Price and Time Dependent Demand

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1848
Author(s):  
Luis A. San-José ◽  
Joaquín Sicilia ◽  
Manuel González-de-la-Rosa ◽  
Jaime Febles-Acosta
Keyword(s):  
Lot Sizing ◽  
Optimal Solution ◽  
Selling Price ◽  
Inventory Problem ◽  
Lot Size ◽  
Power Functions ◽  
Eoq Model ◽  
Demand Rate ◽  
Parameter Values ◽  
Dependent Demand

In this paper, we address an inventory system where the demand rate multiplicatively combines the effects of time and selling price. It is assumed that the demand rate is the product of two power functions, one depending on the selling price and the other on the time elapsed since the last inventory replenishment. Shortages are allowed and fully backlogged. The aim is to obtain the lot sizing, the inventory cycle and the unit selling price that maximize the profit per unit time. To achieve this, two efficient algorithms are proposed to obtain the optimal solution to the inventory problem for all possible parameter values of the system. We solve several numerical examples to illustrate the theoretical results and the solution methodology. We also develop a numerical sensitivity analysis of the optimal inventory policy and the maximum profit with respect to the parameters of the demand function.

INVENTORY MODELS WITH STOCK-DEPENDENT DEMAND AND NONLINEAR HOLDING COSTS FOR DETERIORATING ITEMS

2004 ◽  
Vol 21 (04) ◽  
pp. 435-446 ◽  
Author(s):  
CHUN-TAO CHANG
Keyword(s):  
Deteriorating Items ◽  
Inventory Level ◽  
Order Quantity ◽  
Demand Model ◽  
Inventory Models ◽  
Holding Costs ◽  
Proposed Model ◽  
Demand Rate ◽  
Dependent Demand Rate ◽  
Dependent Demand

In this paper, we discuss why it is appropriate maximize the profits, instead of minimizing the costs, in an inventory system with an inventory-level-dependent demand rate. In addition, we restate Urban's viewpoint that the restriction of zero ending-inventory is not necessary in an inventory-level-dependent demand model. Consequently, we amend Giri and Chaudhuri's inventory model for deteriorating items by changing the objective to maximize the profits and relaxing the restriction of zero ending-inventory. Finally, we provide a couple of examples to show that both the order quantity and the profit obtained from our proposed model are significantly larger than those in Giri and Chaudhuri's model, in which the objective is to minimize the costs.

scholarly journals Inventory Modeling for Deteriorating Imperfect Quality Items with Selling Price Dependent Demand and Shortage Backordering under Credit Financing

2017 ◽  
Vol 2 (2) ◽  
pp. 110-124 ◽  
Author(s):  
Aditi Khanna ◽  
Prerna Gautam ◽  
Chandra K. Chandra K.
Keyword(s):  
Trade Credit ◽  
Optimal Order ◽  
Manufacturing Processes ◽  
Selling Price ◽  
Imperfect Quality ◽  
Inspection Process ◽  
Total Profit ◽  
Credit Financing ◽  
Fierce Competition ◽  
Dependent Demand

The production processes throughout the world aim at improving quality by introducing latest technologies so as to perform well in fierce competition. Despite this due to various unavoidable factors, most of the manufacturing processes end up with certain imperfections. Hence, all the items produced are not of perfect quality. The condition tends to be more susceptible while dealing with items of deteriorating quality; therefore an inspection process is must for screening good quality items from the ordered lot. Demand is assumed to be price dependent and it is represented by a constant price elasticity function. Also to endure with the rapid growth and turbulent markets, the suppliers try to engage and attract retailers through various gimmicks and one such contrivance is offering trade credit, which is proved to be an influential strategy for attracting new customers. In view of this, the present paper develops an inventory model for items of imperfect quality with deterioration under trade-credit policies with price dependent demand. Shortages are allowed and fully backlogged. A mathematical model is developed to depict this scenario. The aim of the study is to optimize the optimal order level, backorder level and selling price so as to maximize the retailer’s total profit. Findings are validated quantitatively by using numerical analysis. Sensitivity analysis is also performed so as to cater some important decision-making insights.

scholarly journals Dynamic Pricing Policy Using Preservation Technology with Stock and Price Sensitive Demand

2020 ◽  
Vol 26 (3) ◽  
pp. 266-274
Author(s):  
Uttam Kumar Khedlekar ◽  
Priyanka Singh ◽  
Neelesh Gupta
Keyword(s):  
Dynamic Pricing ◽  
Policy Decision ◽  
Pricing Strategy ◽  
Selling Price ◽  
Market Demand ◽  
Pricing Policy ◽  
Preservation Technology ◽  
Proposed Model ◽  
Stock Policy ◽  
Dependent Demand

This paper aims to develop a dynamic pricing policy for deteriorating items with price and stock dependent demand. In declining market demand of items decreases with respect to time and also after a duration items get outdated. In this situation it needs a pricing policy to sale the items before end season. The proposed dynamic pricing policy is applicable for a limited period to clease the stock. Policy decision regarding the selling price could aggressively attracts the costumers. Objectives are to maximize the prot/revenue, pricing strategy and economic order level for such a stock dependent and price sensitive items. We are giving numerical example and simulation to illustrate the proposed model.

Ordering Policy in a Two-Warehouse Environment for Deteriorating Items under Inflationary Conditions

2014 ◽  
pp. 320-338
Author(s):  
Chandra K. Jaggi ◽  
Sarla Pareek ◽  
Aditi Khanna ◽  
Ritu Sharma
Keyword(s):  
Global Economy ◽  
Aggregate Demand ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Inventory Problem ◽  
Inventory Costs ◽  
Ordering Policy ◽  
Demand Rate ◽  
Warehousing Systems ◽  
The Cost

In this chapter, the two-warehouse inventory problem is considered for deteriorating items with constant demand rate and shortages under inflationary conditions. In today’s unstable global economy, the effects of inflation and time value of money cannot be ignored as it increases the cost of goods. To safeguard from the rising prices, during the inflation regime, the organization prefers to keep a higher inventory, thereby increasing the aggregate demand. This additional inventory needs additional storage space that is facilitated by a rented warehouse. Further ahead, in the real business world, to retain the freshness of the commodity, most of the organizations adopt the First-In-First-Out (FIFO) dispatching policy. FIFO policy yields fresh and good conditioned stock thereby resulting in customer satisfaction, especially when items are deteriorating in nature. However, the two warehousing systems usually assume that the holding cost of items is more in Rental Warehouse (RW) than the Owned Warehouse (OW) due to modern preserving techniques. Therefore, to reduce the inventory costs, it is economical to consume the goods of RW at the earliest. This approach is termed the Last-In-First-Out (LIFO) approach. The objective of the present chapter is to develop a two warehouse inventory model with FIFO and LIFO dispatching policies under inflationary conditions. Further, comparison between FIFO and LIFO policies has been exhibited with the help of a numerical example. Sensitivity analysis has also been performed to study the impact of various parameters on the optimal solution.

A Bi-objective Multi-Product Multi-Constraint EPQ Model in a Stochastic Environment and Partial Shortage

2020 ◽  
Vol 19 (03) ◽  
pp. 567-587
Author(s):  
Seyedeh Sanaz Mirkhorsandi ◽  
Seyed Hamid Reza Pasandideh
Keyword(s):  
Goal Attainment ◽  
Programming Model ◽  
Multi Objective ◽  
Holding Costs ◽  
Inventory Costs ◽  
Economic Production ◽  
Proposed Model ◽  
Demand Rate ◽  
Nonlinear Programming Model ◽  
Epq Model

One of the classical models for inventory control is economic production quantity (EPQ), which is widely used in industry. In this paper, an EPQ model with partial shortage is developed by considering the real world conditions, and costs related to the backorder demand are taken as fixed and time-dependent. In the proposed model, determination of the inventory cycle length, the length of positive inventory cycle and backordered demand rate are considered in shortage period. The aim of the presented research is to minimize the total inventory costs and the space required for storage products so that the stochastic and classic constraints including holding costs, lost sales, backorder, budget, total number of productions and average shortage times should be satisfied while optimizing the multi-objective problem. Presented model is a bi-objective nonlinear programming model. Then, to solve the proposed model, three multi-objective decision-making methods including Lp-metric, goal programming and goal attainment are used. Besides, numerical examples are executed in small, medium and large scales by use of GAMS software, and the performance of the methods is compared in terms of objective functions and required CPU time. Finally, sensitivity analysis is done to determine the effect of change in the main parameters of the model on the objective function value.

scholarly journals Inventory Policies for Price-Sensitive Stock-Dependent Demand and Quantity Discounts

2018 ◽  
Vol 3 (3) ◽  
pp. 245-257 ◽  
Author(s):  
Nita H. Shah ◽  
Monika K. Naik
Keyword(s):  
Selling Price ◽  
Quantity Discounts ◽  
Market Demand ◽  
Inventory Problem ◽  
Purchasing Cost ◽  
Decision Variables ◽  
Demand Rate ◽  
Total Profit ◽  
Holding Cost ◽  
Optimum Solution

It was usually observed in typical EOQ inventory models that the holding cost, the purchasing cost and the demand rate are constant and the purchasing cost is irrespective of the order size. But practically, the demand rate is based on various factors including sale price, seasonality and availability. Due to the lengthening of shortage periods, the holding cost per unit item increases. Also with the inclusion of quantity discounts, the unit purchasing cost is usually decreased for higher order sizes. This article addresses jointly with the inconsistency of the rate of demand, unit purchasing cost and unit holding cost for deteriorating items. This paper proposes a model based on an inventory problem including selling price of products and stock-dependent market demand rate, holding cost based on storage time and purchasing cost is influenced by order size by offering all units quantity discounts. An algorithm for estimating the optimum solution of decision variables by maximizing total profit and minimizing the overall cost of the model is developed in this paper. Validation of the developed model is confirmed with the help of a numerical example along with the sensitivity-analysis of decision variables by varying various inventory parameters.

scholarly journals Controllable deterioration rate for time-dependent demand and time-varying holding cost

2014 ◽  
Vol 24 (1) ◽  
pp. 87-98 ◽  
Author(s):  
Vinod Mishra
Keyword(s):  
Linear Function ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Inventory Cost ◽  
Deterioration Rate ◽  
Preservation Technology ◽  
Demand Rate ◽  
Holding Cost ◽  
Total Inventory ◽  
Dependent Demand

In this paper, we develop an inventory model for non-instantaneous deteriorating items under the consideration of the facts: deterioration rate can be controlled by using the preservation technology (PT) during deteriorating period, and holding cost and demand rate both are linear function of time, which was treated as constant in most of the deteriorating inventory models. So in this paper, we developed a deterministic inventory model for non-instantaneous deteriorating items in which both demand rate and holding cost are a linear function of time, deterioration rate is constant, backlogging rate is variable and depend on the length of the next replenishment, shortages are allowed and partially backlogged. The model is solved analytically by minimizing the total cost of the inventory system. The model can be applied to optimizing the total inventory cost of non-instantaneous deteriorating items inventory for the business enterprises, where the preservation technology is used to control the deterioration rate, and demand & holding cost both are a linear function of time.

scholarly journals A Two-Period Newsvendor Model with Product Extension and Shortage-Making Strategy

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Kuo-Hsien Wang ◽  
Che-Tsung Tung ◽  
Yuan-Chih Huang
Keyword(s):  
Optimal Order ◽  
Ripple Effect ◽  
Newsvendor Model ◽  
Numerical Examples ◽  
Deterministic Demand ◽  
Proposed Model ◽  
Demand Rate ◽  
Order Quantities ◽  
Second Period ◽  
Product Extension

This study deals with a two-period newsvendor setting in which the item in the second period is a product extension of the item in the first period. A shortage strategy toward the first item is intentionally made so as to stimulate more sales amounts of the second item. The stochastic demand of these two items is assumed to be a linear-additive pattern comprising a deterministic demand and an error demand, where the deterministic demand consists of a primary demand and a consumer price elasticity, and the error demand is hypothesized to be exponentially distributed. The objective of this study is to optimize system's overall expected profit by jointly determining the optimal order quantities and selling prices of these two items. We first compare our proposed model with the classical newsvendor model in light of profit performances, and it reveals that a higher shifting demand rate makes our model a more profitable setting. Impact on profit performances caused by an increasing primary demand of the second item is then demonstrated by numerical examples that an unthought-of ripple effect of an increasing error demand of the second item also occurs.

scholarly journals An Inventory Model with Price and Quality Dependent Demand Where Some Items Produced Are Defective

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Tapan Kumar Datta
Keyword(s):  
Quality Index ◽  
Unit Price ◽  
Model Parameters ◽  
Selling Price ◽  
Defective Items ◽  
Joint Determination ◽  
Demand Rate ◽  
Dependent Demand

This paper analyzes an inventory system for joint determination of product quality and selling price where a fraction of items produced are defective. It is assumed that only a fraction of defective items can be repaired/reworked. The demand rate depends upon both the quality and the selling price of the product. The production rate, unit price, and carrying cost depend upon the quality of the items produced. Quality index is used to determine the quality of the product. An algorithm is provided to solve the model with given values of model parameters. Sensitivity analysis has also been performed.

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