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 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.

scholarly journals An Inventory Model for Imperfect Quality Products with Rework, Distinct Holding Costs, and Nonlinear Demand Dependent on Price

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1362
Author(s):  
Leopoldo Eduardo Cárdenas-Barrón ◽  
María José Lea Plaza-Makowsky ◽  
María Alejandra Sevilla-Roca ◽  
José María Núñez-Baumert ◽  
Buddhadev Mandal
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Inventory System ◽  
Inventory Level ◽  
Selling Price ◽  
Lot Size ◽  
Inventory Models ◽  
Holding Costs ◽  
Imperfect Items ◽  
The Moment

Traditionally, the inventory models available in the literature assume that all articles in the purchased lot are perfect and the demand is constant. However, there are many causes that provoke the presence of defective goods and the demand is dependent on some factors. In this direction, this paper develops an economic order quantity (EOQ) inventory model for imperfect and perfect quality items, taking into account that the imperfect ones are sent as a single lot to a repair shop for reworking. After reparation, the items return to the inventory system and are inspected again. Depending on the moment at which the reworked lot arrives to the inventory system, two scenarios can occur: Case 1: The reworked lot enters when there still exists inventory; and Case 2: The reworked lot comes into when the inventory level is zero. Furthermore, it is considered that the holding costs of perfect and imperfect items are distinct. The demand of the products is nonlinear and dependent on price, which follows a polynomial function. The main goal is to optimize jointly the lot size and the selling price such that the expected total profit per unit of time is maximized. Some theoretic results are derived and algorithms are developed for determining the optimal solution for each modeled case. It is worth mentioning that the proposed inventory model is a general model due to the fact that this contains some published inventory models as particular cases. With the aim to illustrate the use of the proposed inventory model, some numerical examples are solved.

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.

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.

AN EOQ MODEL WITH CONTROLLABLE SELLING RATE

2008 ◽  
Vol 25 (02) ◽  
pp. 151-167 ◽  
Author(s):  
HORNG-JINH CHANG ◽  
PO-YU CHEN
Keyword(s):  
Distribution Function ◽  
Transaction Cost ◽  
Optimal Solution ◽  
Bivariate Distribution ◽  
Inventory Level ◽  
Selling Price ◽  
Eoq Model ◽  
Concrete Form ◽  
Demand Rate ◽  
Classical Economic

According to the marketing principle, a decision maker may control demand rate through selling price and the unit facility cost of promoting transaction. In fact, the upper bound of willing-to-pay price and the transaction cost probably depend upon the subjective judgment of individual consumer in purchasing merchandise. This study therefore attempts to construct a bivariate distribution function to simultaneously incorporate the willing-to-pay price and the transaction cost into the classical economic order quantity (EOQ) model. Through the manipulation of the constructed bivariate distribution function, the demand function faced by the supplier can be expressed as a concrete form. The proposed mathematical model mainly concerns how to determine the initial inventory level for each business cycle, so that the profit per unit time is maximized by means of the selling price and the unit-transaction cost to control the selling rate. Furthermore, the sensitivity analysis of optimal solution is performed and the implication of this extended inventory model is also discussed.

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