We present a column generation algorithm for solving the bi-objective multicommodity minimum cost flow problem. This method is based on the biobjective simplex method and Dantzig-Wolfe decomposition. The method is initialised by optimising the problem with respect to the first objective, a single objective multi-commodity flow problem, which is solved using DantzigWolfe decomposition. Then, sim...

Context: The Next Release Problem involves determining the set of requirements to implement in the next release of a software project. When the problem was first formulated in 2001, Integer Linear Programming, an exact method, was found to be impractical because of large execution times. Since then, the problem has mainly been addressed by employing metaheuristic techniques. Objective: In this ...

Environmental and economic objective functions are used simultaneously to select the operating conditions of a steam and power plant. Different methodologies to solve bi objective optimization problems were implemented successfully. The life cycle potential environmental impact and the operating cost of the utility plant are minimized simultaneously. A methodology is presented to estimate the p...

In order to solve the two-sided matching problem based on uncertain score information, a new method is presented. Firstly, the description of the two-sided matching problem with uncertain scores is given. Secondly, the satisfaction degrees of each agent towards the agents on the other side are calculated. A multi-objective optimization model to maximize the satisfaction degrees of agents is set...

This paper presents a novel bi-objective multi-product capacitated vehicle routing problem with uncertainty in demand of retailers and volume of products (UCVRP) and heterogeneous vehicle fleets. The first of two conflict fuzzy objective functions is to minimize the cost of the used vehicles, fuel consumption for full loaded vehicles and shortage of products. The second ...

In this paper, the strategic planning of a supply chain under a static chain-to-chain competition on the plane is addressed. It is assumed that each retailer has a coverage area called the radius of influence. The demand of each demand zone is divided equally between the retailers which can cover that market. However, the demand of distant customers who are not in the retailers’ radius of influ...

Nowadays, researches pay more attention to environmental concerns consisted of various communities. This study proposes a multi-echelon, multi-period closed-loop supply chain (CLSC). A comprehensive model considers the selection of selection of technology and environmental effects. The supply chain is under a build-to-order (BTO) environment. So, there is not a final product inventory. Also, th...

Let A be a prime *-algebra. In this paper, we suppose that ? : satisfies ?(A B) = ?(A) B + ?(B) where A*B B*A for all A, A. Then, is an additive *-derivation.

______________________ Abstract: Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define multi-level programs with any number of levels. Supply...