A Hybrid Multi-Objective Programming Framework for Modeling and Optimization of Supply Chain Problems

Abstract

Abstract-This paper presents a hybrid programming framework for solving multi-objective optimization problems in supply chain. The proposed approach consists of the integration and hybridization of two modeling and solving environments, i.e., constraint logic programming and mathematical programming, to obtain a programming framework that offers significant advantages over the classical approach derived from operational research. The strongest points of both components are combined in the hybrid framework, which by introducing transformation allows a significant reduction in size of a problem and the optimal solution is found a lot faster. This is particularly important in the multi-objective optimization where problems have to be solved over and over again to find a set of Pareto-optimal solutions. An over two thousand-fold reduction in size was obtained for the illustrative examples together with a few hundred-fold reduction in the speed of finding the solution in relation to the mathematical programming method. In addition, the proposed framework allows the introduction of logical constraints that are difficult or impossible to model in operational research environments.

Lecturers' competences configuration model for the timetabling problem

“…As part of further works, research is planned on modeling and solving UCTP integrated with the configuration model (Chapter B) and additional logic constraints are to be introduced [12,13] related to lecturers' preferences as to the times and forms of the curses, halls etc. It is also planned to apply the method of hybrid modeling and solving to the above-mentioned problem [14][15][16]. wsp=1.25; A=100; B=3; EndData Min=@sum(pom_1(i,k):Y(i,k)); @for(pom_1(i,k): X(i,k)<=(G(i,k)+Y(i,k))*A); @for(subjects(i): @sum(lecturers(k):X(i,k))=h(i)); @for(lecturers(k): @sum(subjects(i):l(i)*X(i,k))>=s(k)); @for(lecturers(k)|z(k)#EQ#0: @sum(subjects(i):l(i)*X(i,k))<=s(k)*wsp); @sum(pom_1(i,k):Y(i,k))<=B; @for(pom_1(i,k):@GIN(X(i,k))); @for(pom_1(i,k):@BIN(Y(i,k))); @for(pom_1(i,k)|G(i,k)#EQ#1:Y(i,k)=0); end…”

Maximizing the Supply Chain Profit in Multimodal Transportation Problem with Transfer Part using Two-Echelon Genetic Algorithm

“…The transfer component of multimodal transport incurs both costs and transfer time. While many multimodal studies primarily focus on reducing overall costs, often neglecting specific transportation expenses such as transfer costs [7][8], this study seeks to fill that gap and provide a comprehensive analysis. This paper implements a mathematical programming model based on the previous study for distribution network design with a time window in the form of Mixed-Integer Nonlinear Programming (MINLP) model.…”