Answer set programming is a programming paradigm where a given problem is formalized as a logic program whose answer sets correspond to the solutions to the problem. In this paper, we link answer set programming with another widely applied paradigm, viz. mixed integer programming. As a theoretical result, we establish translations from non-disjunctive logic programs to linear constraints used i...

‎this paper proposes a multi-supplier multi-product inventory model in which the suppliers have unlimited production capacity, allow delayed payment, and offer either an all-unit or incremental discount. the retailer can delay payment until after they have sold all the units of the purchased product. the retailer’s warehouse is limited, but the surplus can be stored in a rented warehouse at a...

logistic network design is one of the most important strategic decisions in supply chain management that has recently attracted the attention of many researchers. transportation network design is then one of the most important fields of logistic network. this study is concerned with designing a multi-stage and multi-product logistic network. at first, a mixed integer nonlinear programming model...

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 design of closed-loop logistics (forward and reverse logistics) has attracted growing attention with the stringent pressures of customer expectations, environmental concerns and economic factors. This paper considers a multi-product, multi-period and multi-objective closed-loop logistics network model with regard to facility expansion as a facility location–allocation problem, which more cl...

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...

Abstract This paper proposes a multi-objective mixed-integer linear programming to model cold chain with complementary operations on hierarchical hub network. Central hubs are linked each other in the first level of network and star lower-level hubs. As for case study, different levels provide various refreshing or freezing keep perishable goods fresh along Disruption is formulated by considera...