Profit maximization in an inventory system with time-varying demand, partial backordering and discrete inventory cycle

In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into acco...

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Bibliographic Details
Published in:Annals of operations research 2022-09, Vol.316 (2), p.763-783
Main Authors: San-José, Luis A., Sicilia, Joaquín, González-de-la-Rosa, Manuel, Febles-Acosta, Jaime
Format: Article
Language:English
Subjects:
Algorithms
Business and Management
Combinatorics
Costs
Integers
Inventory
Inventory control
Inventory management
Mathematical programming
Nonlinear programming
Operations research
Operations Research/Decision Theory
Optimization
Order quantity
Parameter sensitivity
Profitability
Profits
Purchasing
Replenishment
S.i. : Claio 2018
Sensitivity analysis
Theory of Computation
Time dependence
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Summary:In this paper, an inventory problem where the inventory cycle must be an integer multiple of a known basic period is considered. Furthermore, the demand rate in each basic period is a power time-dependent function. Shortages are allowed but, taking necessities or interests of the customers into account, only a fixed proportion of the demand during the stock-out period is satisfied with the arrival of the next replenishment. The costs related to the management of the inventory system are the ordering cost, the purchasing cost, the holding cost, the backordering cost and the lost sale cost. The problem is to determine the best inventory policy that maximizes the profit per unit time, which is the difference between the income obtained from the sales of the product and the sum of the previous costs. The modeling of the inventory problem leads to an integer nonlinear mathematical programming problem. To solve this problem, a new and efficient algorithm to calculate the optimal inventory cycle and the economic order quantity is proposed. Numerical examples are presented to illustrate how the algorithm works to determine the best inventory policies. A sensitivity analysis of the optimal policy with respect to some parameters of the inventory system is developed. Finally, conclusions and suggestions for future research lines are given.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-021-04161-6