A hybrid CPU-GPU parallelization scheme of variable neighborhood search for inventory optimization problems

In this paper, we study various parallelization schemes for the Variable Neighborhood Search (VNS) metaheuristic on a CPU-GPU system via OpenMP and OpenACC. A hybrid parallel VNS method is applied to recent benchmark problem instances for the multi-product dynamic lot sizing problem with product returns and recovery, which appears in reverse logistics and is known to be NP-hard. We report our findings regarding these parallelization approaches and present promising computational results.Comment: 8 pages, 1 figur

A dual exterior point simplex type algorithm for the minimum cost network flow problem

A new dual simplex type algorithm for the Minimum Cost Network Flow Problem (MCNFP) is presented. The proposed algorithm belongs to a special 'exterior- point simplex type' category. Similarly to the classical network dual simplex algorithm (NDSA), this algorithm starts with a dual feasible tree-solution and reduces the primal infeasibility, iteration by iteration. However, contrary to the NDSA, the new algorithm does not always maintain a dual feasible solution. Instead, the new algorithm might reach a basic point (tree-solution) outside the dual feasible area (exterior point - dual infeasible tree)

Optimizing make-to-stock policies through a robust lot-sizing model

In this paper we consider a practical lot-sizing problem faced by an industrial company. The company plans the production for a set of products following a Make-To-Order policy. When the productive capacity is not fully used, the remaining capacity is devoted to the production of those products whose orders are typically quite below the established minimum production level. For these products the company follows a Make-To-Stock (MTS) policy since part of the production is to fulfill future estimated orders. This yields a particular lot-sizing problem aiming to decide which products should be produced and the corresponding batch sizes. These lot-sizing problems typically face uncertain demands, which we address here through the lens of robust optimization. First we provide a mixed integer formulation assuming the future demands are deterministic and we tighten the model with valid inequalities. Then, in order to account for uncertainty of the demands, we propose a robust approach where demands are assumed to belong to given intervals and the number of deviations to the nominal estimated value is limited. As the number of products can be large and some instances may not be solved to optimality, we propose two heuristics. Computational tests are conducted on a set of instances generated from real data provided by our industrial partner. The heuristics proposed are fast and provide good quality solutions for the tested instances. Moreover, since they are based on the mathematical model and use simple strategies to reduce the instances size, these heuristics could be extended to solve other multi-item lot-sizing problems where demands are uncertain.publishe

Minimum cost network flows: Problems, algorithms, and software

We present a wide range of problems concerning minimum cost network flows, and give an overview of the classic linear single-commodity Minimum Cost Network Flow Problem (MCNFP) and some other closely related problems, either tractable or intractable. We also discuss state-of-the-art algorithmic approaches and recent advances in the solution methods for the MCNFP. Finally, optimization software packages for the MCNFP are presented

Slot Machine RTP Optimization Using Variable Neighborhood Search

This work presents a Variable Neighborhood Search (VNS) approach for solving the Return-To-Player (RTP) optimization problem. A large number of software companies in the gaming industry seek to solve the RTP optimization problem in order to develop modern virtual casino gambling machines. These slot machines have a number of reels (e.g., three or more) that spin once a button is pushed. Each slot machine is required to have an RTP in a particular range according to the legislation of each country. By using a VNS framework that guides two local search operators, we show how to control the distribution of the symbols in the reels in order to achieve the desired RTP. In this study, optimization refers only to base game, the core of slot machine games, and not in bonus games, since a bonus game is triggered once two, three, or more specific symbols occur in the gaming monitor. Although other researchers have tried to solve the RTP problem in the past, this is the first time that a VNS methodology is proposed for this problem in the literature with good computational results