scholarly journals An Inventory Model with Stock-Dependent Demand Rate and Maximization of the Return on Investment

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 844
Author(s):  
Valentín Pando ◽  
Luis A. San-José ◽  
Joaquín Sicilia
Keyword(s):  
Optimal Policy ◽  
Return On Investment ◽  
Global Optimum ◽  
Inventory Model ◽  
Selling Price ◽  
Fixed Costs ◽  
Lot Size ◽  
Inventory Cost ◽  
Purchasing Cost ◽  
Demand Rate

This work presents an inventory model for a single item where the demand rate is stock-dependent. Three fixed costs are considered in the model: purchasing cost, ordering cost and holding cost. A new approach focused on maximizing the return on investment (ROI) is used to determine the optimal policy. It is proved that maximizing profitability is equivalent to minimizing the average inventory cost per item. The global optimum of the objective function is obtained, proving that the zero ending policy at the final of a cycle is optimal. Closed expressions for the lot size and the maximum ROI are determined. The optimal policy for minimizing the inventory cost per unit time is also obtained with a zero-order point, but the optimal lot size is different. Both solutions are not equal to the one that provides the maximum profit per unit time. The optimal lot size for the maximum ROI policy does not change if the purchasing cost or the selling price vary. A sensitivity analysis for the optimal values regarding the initial parameters is performed by using partial derivatives. The maximum ROI is more sensitive regarding the selling price or the purchasing cost than regarding the other parameters. Some useful managerial insights are deduced for decision-makers. Numerical examples are solved to illustrate the obtained results.

scholarly journals Profitability Index Maximization in an Inventory Model with a Price- and Stock-Dependent Demand Rate in a Power-Form

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1157
Author(s):  
Valentín Pando ◽  
Luis A. San-José ◽  
Joaquín Sicilia ◽  
David Alcaide-López-de-Pablo
Keyword(s):  
Cycle Time ◽  
Optimal Policy ◽  
Inventory Model ◽  
Selling Price ◽  
Lot Size ◽  
Financial Investment ◽  
Demand Rate ◽  
Holding Cost ◽  
Optimal Values ◽  
Dependent Demand

This paper presents the optimal policy for an inventory model where the demand rate potentially depends on both selling price and stock level. The goal is the maximization of the profitability index, defined as the ratio income/expense. A numerical algorithm is proposed to calculate the optimal selling price. The optimal values for the depletion time, the cycle time, the maximum profitability index, and the lot size are evaluated from the selling price. The solution shows that the inventory must be replenished when the stock is depleted, i.e., the depletion time is always equal to the cycle time. The optimal policy is obtained with a suitable balance between ordering cost and holding cost. A condition that ensures the profitability of the financial investment in the inventory is established from the initial parameters. Profitability thresholds for several parameters, including the scale and the non-centrality parameters, keeping all the others fixed, are evaluated. The model with an isoelastic price-dependent demand is solved as a particular case. In this last model, all the optimal values are given in a closed form, and a sensitivity analysis is performed for several parameters, including the scale parameter. The results are illustrated with numerical examples.

Two phases inventory model with variable cycle length under discount policy

2020 ◽  
Vol 54 (1) ◽  
pp. 1-18
Author(s):  
Brojeswar Pal ◽  
Subhankar Adhikari
Keyword(s):  
Optimality Criteria ◽  
Inventory Model ◽  
Linear Functions ◽  
Inventory Level ◽  
Second Phase ◽  
Selling Price ◽  
Lot Size ◽  
Power Functions ◽  
Demand Rate ◽  
Two Phases

This study deals with single stage inventory model where two phases are involved in an inventory cycle. In the first phase of the cycle, demand depends on both of inventory level and selling price while in the second, the demand depends on price only. Discount policy in selling price is offered in the second phase and inventory level at the end of the cycle is taken to be zero. Two models have been constructed on infinite time horizon. In the first model the demand rate is taken as the sum of two linear functions of inventory level and selling price and, in the second model, it is taken as a product of two power functions of inventory level and selling price. Our objective is to maximize average profit by considering ordering lot size and selling price as decision variables. Numerical examples of each model have been provided. The optimality criteria for the solutions are also checked by both graphically and numerically. Sensitivity analysis for different parameters in both models has been discussed in details to check the feasibility of the models.

scholarly journals Inventory Model with Partial Backordering When Backordered Customers Delay Purchase after Stockout-Restoration

2016 ◽  
Vol 2016 ◽  
pp. 1-16
Author(s):  
Ren-Qian Zhang ◽  
Yan-Liang Wu ◽  
Wei-Guo Fang ◽  
Wen-Hui Zhou
Keyword(s):  
Layer Structure ◽  
Inventory Model ◽  
Inventory Cost ◽  
Cost Component ◽  
Lipschitz Optimization ◽  
Partial Backordering ◽  
Demand Rate ◽  
Holding Cost ◽  
Total Inventory ◽  
Inventory Holding

Many inventory models with partial backordering assume that the backordered demand must be filled instantly after stockout restoration. In practice, however, the backordered customers may successively revisit the store because of the purchase delay behavior, producing a limited backorder demand rate and resulting in an extra inventory holding cost. Hence, in this paper we formulate the inventory model with partial backordering considering the purchase delay of the backordered customers and assuming that the backorder demand rate is proportional to the remaining backordered demand. Particularly, we model the problem by introducing a new inventory cost component of holding the backordered items, which has not been considered in the existing models. We propose an algorithm with a two-layer structure based on Lipschitz Optimization (LO) to minimize the total inventory cost. Numerical experiments show that the proposed algorithm outperforms two benchmarks in both optimality and efficiency. We also observe that the earlier the backordered customer revisits the store, the smaller the inventory cost and the fill rate are, but the longer the order cycle is. In addition, if the backordered customers revisit the store without too much delay, the basic EOQ with partial backordering approximates our model very well.

scholarly journals Two warehouse inventory model for deteriorating item with exponential demand rate and permissible delay in payment

2017 ◽  
Vol 27 (1) ◽  
pp. 109-124 ◽  
Author(s):  
Naresh Kaliraman ◽  
Ritu Raj ◽  
Shalini Chandra ◽  
Harish Chaudhary
Keyword(s):  
Sensitivity Analysis ◽  
Inventory Model ◽  
Deteriorating Items ◽  
The Other ◽  
Inventory Cost ◽  
Numerical Illustration ◽  
Deterioration Rate ◽  
Permissible Delay In Payment ◽  
Demand Rate

A two warehouse inventory model for deteriorating items is considered with exponential demand rate and permissible delay in payment. Shortage is not allowed and deterioration rate is constant. In the model, one warehouse is rented and the other is owned. The rented warehouse is provided with better facility for the stock than the owned warehouse, but is charged more. The objective of this model is to find the best replenishment policies for minimizing the total appropriate inventory cost. A numerical illustration and sensitivity analysis is provided.

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.

Deteriorating Inventory Model under Permissible Delay in Payments and Fuzzy Environment

2016 ◽  
pp. 77-99 ◽  
Author(s):  
Nita H. Shah ◽  
Sarla Pareek ◽  
Isha Sangal
Keyword(s):  
Solution Procedure ◽  
Inventory Model ◽  
Variable Cost ◽  
Selling Price ◽  
Gravity Method ◽  
Deterioration Rate ◽  
Eoq Model ◽  
Fuzzy Environment ◽  
Demand Rate ◽  
Delay In Payments

This paper deals with the problem of determining the EOQ model for deteriorating items in the fuzzy sense where delay in payments is permissible. The demand rate, ordering cost, selling price per item and deterioration rate are taken as fuzzy numbers. The total variable cost in fuzzy sense is de-fuzzified using the centre of gravity method. The solution procedure has been explained with the help of numerical example.

Sign in / Sign up

Export Citation Format

Share Document