This paper addresses the globally optimal solution of the network-constrained unit commitment (NCUC) problem incorporating a nonlinear alternating current (AC) model of the transmission network. We formulate the NCUC as a mixed-integer quadratically constrained quadratic programming (MIQCQP) problem. A global optimization algorithm is developed based on a multi-tree approach that iterates betwe...

 We consider a generalization of the classical quadratic assignment problem, where coordinates of locations are uncertain and only upper and lower bounds are known for each coordinate. We develop a mixed integer linear programming model as a robust counterpart of the proposed uncertain model. A key challenge is that, since the uncertain model involves nonlinear objective function of the ...

Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation Pareto front challenging. The present article shows that certain algorithms were originally devised for continuous can be successfully adapted to approximate integer, and mixed-integer, multi-objective problems. Relationships amongst variou...

in this paper, a multi-product single machine scheduling problem with the possibility of producing defected jobs, is considered. we concern rework in the scheduling environment and propose a mixed-integer programming (mip) model for the problem.  based on the philosophy of just-in-time production, minimization of the sum of earliness and tardiness costs is taken into account as the objective fu...

This study introduces a green location, routing and inventory problem with customer satisfaction, backup distribution centers and risk of routes in the form of a non-linear mixed integer programming model. In this regard, time window is considered to increase the customer satisfaction of the model and transportation risks is taken into account for the reliability of the system. In addition, dif...

one of important problems in supply chains management is supplier selection. in a company, there are massive data from various departments so that extracting knowledge from the company’s data is too complicated. many researchers have solved this problem by some methods like fuzzy set theory, goal programming, multi objective programming, the liner programming, mixed integer programming, analyti...

the environmental rules of reverse logistic networks have caused important economic growth in the past decades. to integrate forward logistic networks with reverse logistics networks a helpful method is to design both networks simultaneously. considering more retrieval choices in modeling reverse logistic systems can be very critical. this article contains a mixed integer linear programming mod...