Optimizing multi-item multi-period inventory control system with discounted cash flow and inflation: Two calibrated meta-heuristic algorithms

https://paginas.fe.up.pt/~niadr/PUBLICATIONS/LIACC_publications_2011_12/pdf/OR_16_A_hybrid_method_of_fuzzy_Shafii.pdf

A hybrid method of fuzzy simulation and genetic algorithm to optimize constrained inventory control systems with stochastic replenishments and fuzzy demand

There are two main assumptions in multiperiodic inventory control problems. The first is the continuous review, where, depending on the inventory level, orders can happen at any time, and the other is the periodic review, where orders can only happen at the beginning of each period. In this paper, these assumptions are relaxed, and the periods between two replenishments are assumed independent and identically distributed random variables. Furthermore, the decision variables are assumed integer-type and that there are two kinds of space and budget constraints. The incremental discounts to purchase products are considered, and a combination of backorder and lost sales are taken into account for the shortages. The model of this problem is shown to be a mixed integer-nonlinear programming type, and in order to solve it, both genetic algorithm and simulated annealing approaches are employed. At the end, two numerical examples are given to demonstrate the applicability of the proposed methodologies in which genetic algorithm method performs better than simulated annealing in terms of objective function values.

A genetic algorithm to optimize multiproduct multiconstraint inventory control systems with stochastic replenishment intervals and discount

A fuzzy vendor managed inventory of multi-item economic order quantity model under shortage: An ant colony optimization algorithm

As one of the classical problems in the economic market, the newsvendor problem aims to make maximal profit by determining the optimal order quantity of products. However, the previous newsvendor models assume that the selling price of a product is a predefined constant and only regard the order quantity as a decision variable, which may result in an unreasonable investment decision. In this article, a new newsvendor model is first proposed, which involves of both order quantity and selling price as decision variables. In this way, the newsvendor problem is reformulated as a mixed-variable nonlinear programming problem, rather than an integer linear programming problem as in previous investigations. In order to solve the mixed-variable newsvendor problem, a histogram model-based estimation of distribution algorithm (EDA) called ${\mathrm{ EDA}}_{mvn}$ is developed, in which an adaptive-width histogram model is used to deal with the continuous variables and a learning-based histogram model is applied to deal with the discrete variables. The performance of ${\mathrm{ EDA}}_{mvn}$ was assessed on a test suite with eight representative instances generated by the orthogonal experiment design method and a real-world instance generated from real market data of Alibaba. The experimental results show that, ${\mathrm{ EDA}}_{mvn}$ outperforms not only the state-of-the-art mixed-variable evolutionary algorithms, but also a commercial software, i.e., Lingo.

An Estimation of Distribution Algorithm for Mixed-Variable Newsvendor Problems

This article points out the real-world prevalence of the multiple-product, multiple-constraint newsboy problem with two objectives—the ‘newsstand problem’—in which there are total and incremental discounts on purchasing prices. The constraints are the warehouse capacity and the batch forms of the order placements. The first objective of this problem is to find the order quantities that maximize expected profit, and the second objective is maximizing the service rate. It is assumed that the holding and shortage costs, modelled by a quadratic function, occur at the end of the period. Moreover, the decision variables are integer. A formulation of the problem is presented and shown to be an integer nonlinear programming model. Finally, an efficient hybrid algorithm is provided to solve the model and the results are illustrated with a numerical example.

Optimizing the multi-product, multi-constraint, bi-objective newsboy problem with discount by a hybrid method of goal programming and genetic algorithm

Vahid Hoseini

Papers

Optimizing the multi-product, multi-constraint, bi-objective newsboy problem with discount by a hybrid method of goal programming and genetic algorithm