this paper uses the l1−norm and the concept of the non-dominated vector, topropose a method to find a well-dispersed subset of non-dominated (wdsnd) vectorsof a multi-objective mixed integer linear programming (momilp) problem.the proposed method generalizes the proposed approach by tohidi and razavyan[tohidi g., s. razavyan (2014), determining a well-dispersed subset of non-dominatedvectors of...

a positive integer $n$ is called a clt number if every group of order $n$ satisfies the converse of lagrange's theorem‎. ‎in this note‎, ‎we find all clt and supersolvable numbers up to $1000$‎. ‎we also formulate some questions about the distribution of these numbers‎.

vehicle routing problem (vrp) is one of the major problems in the transportation and distribution planning. in the most previous studies, the objective of vrp models was distance and vehicle related costs. however in many industrial cases along with routing distance, vehicle loading amount is a factor of cost function. in this paper, we formulate a mixed integer non-linear programming (minlp) m...

this paper uses the weighted l$_1-$norm to propose an algorithm for finding a well-dispersed subset of non-dominated solutions of multiple objective mixed integer linear programming problem. when all variables are integer it finds the whole set of efficient solutions. in each iteration of the proposed method only a mixed integer linear programming problem is solved and its optimal solutions gen...

In this paper, bi-level programming is proposed for designing a competitive supply chain network. A two-stage stochastic programming approach has been developed for a multi-product supply chain comprising a capacitated supplier, several distribution centers, retailers and some resellers in the market. The proposed model considers demand’s uncertainty and disruption in distribution centers and t...

This paper presents a three-level supply chain model which includes single supplier, several distribution centers and sets of retailers. For this purpose, by adopting the queuing approach, a mixed nonlinear integer programming model is formulated. The proposed model follows minimizing the total cost of the system by determining: 1) the number and location of distribution centers between candida...

Although several papers have studied no-idle scheduling problems, they all focus on flow shops, assuming one processor at each working stage. But, companies commonly extend to hybrid flow shops by duplicating machines in parallel in stages. This paper considers the problem of scheduling no-idle hybrid flow shops. A mixed integer linear programming model is first developed to mathematically form...

In this research, a single batch processing machine scheduling problem with minimization of total earliness and tardiness as the objective function is investigated.We first formulate the problem as a mixed integer linear programming model. Since the research problem is shown to be NP-hard, an improved memetic algorithmis proposed to efficiently solve the problem. To further enhance the memetic ...

This paper proposes a bi-objective model for the facility location problem under a congestion system. The idea of the model is motivated by applications of locating servers in bank automated teller machines (ATMS), communication networks, and so on. This model can be specifically considered for situations in which fixed service facilities are congested by stochastic demand within queueing frame...