This paper develops an MILP model, named Satisfactory-Green Vehicle Routing Problem. It consists of routing a heterogeneous fleet of vehicles in order to serve a set of customers within predefined time windows. In this model in addition to the traditional objective of the VRP, both the pollution and customers’ satisfaction have been taken into account. Meanwhile, the introduced model prepares a...

The aim of this study is to propose a new mixed integer linear programming (MILP) model to find the minimum required number of yard cranes, Rubber tyred gantry cranes (RTGCs), for completion the total amount of works at the end of planning horizon. In other word, we find the optimal number of yard cranes in a container terminal which completes the total amount of works. The paper supports the p...

This paper discussed the scheduling problem of outpatients in a radiology center with an emphasis on priority. To more compatibility to real-world conditions, we assume that the elapsed times in different stages to be uncertain that follow from the specific distribution function. The objective is to minimize outpatients’ total spent time in a radiology center. The problem is formulated as a fle...

In this paper, a mathematical programming model is presented for integrated problem of closed loop supply chain network design and supplier selection. The suppliers  propose discount policy based on purchase amount and loyalty of buyers which are both taken from the elements of RFM (Recency, Frequency and Monetary) technique. The main objective of this paper which is formulated by a mixed-integ...

This paper considers a bi-objective mathematical model for locations of landfills, transfer stations and material recovery facilities (MRFs) in order to serve the entire regions and simultaneously identify the capacities of landfills. This is a mixed-integer programming (MIP) model, whose objectives are to minimize the total cost and pollution simultaneously. To validate the model, a numerical ...

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...