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 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 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 Multi objective fuzzy inventory model with deterioration, price and time dependent demand and time dependent holding cost

2020 ◽  
Vol 11 (3) ◽  
pp. 928
Author(s):  
Satya Kumar Das ◽  
Sahidul Islam
Keyword(s):  
Graphical Representation ◽  
Fuzzy Programming ◽  
Inventory Model ◽  
Time Dependent ◽  
Selling Price ◽  
Multi Objective ◽  
Holding Cost ◽  
Fuzzy Inventory ◽  
Cost Parameters ◽  
Dependent Demand

In this paper, we have formulated an inventory model with time dependent holding cost, selling price as well as time dependent demand. Multi-item inventory model has been considered under limitation on storage space. Due to uncertainty all the require cost parameters are taken as generalized trapezoidal fuzzy number. Our proposed multi-objective inventory model has been solved by using fuzzy programming techniques which are FNLP, FAGP, WFNLP and WFAGP methods. A numerical example is provided to demonstrate the application of the model. Finally to illustrate the model and sensitivity analysis and graphical representation have been shown. 

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