Flow cover inequalities are among the most effective valid inequalities for solving capacitated fixed-charge network flow problems. These valid inequalities are implications on the flow quantity on the cut arcs of a two-partitioning of the network, depending on whether some of the cut arcs are open or closed. As the implications are only on the cut arcs, flow cover inequalities can be modeled b...

This paper describes a Benders decomposition algorithm capable of efficiently solving large-scale instances of the well-known multi-commodity capacitated network design problem with demand uncertainty. The problem is important because it models many real-world applications, including telecommunications, transportation, and logistics. This problem has been tackled in the literature with meta-heu...

Many real life systems such as manufacturing, telecommunication, computers, and urban traffic systems can be modeled as capacitated-flow networks. The reliability and unreliability are two important indices to measure the quality level for a capacitated-flow network. For a multiple commodity (different types of commodity) capacitated-flow network with unreliable nodes, the arcs and nodes all ha...

We address in this paper the pickup and delivery multi-depot vehicle routing problem (PDMDVRP). In this problem, a single commodity type is collected from a set of pickup customers to be delivered to a set of delivery customers by vehicles dispatched from multiple depots. The proposed problem has many applications in practice such as distribution of money between the branches of a bank, and mov...

Minimum concave Cost Network Flow Problems (MCNFPs) arise naturally in many practical applications such as communication, transportation, distribution, and manufacturing, due to economic considerations. In addition, it has been shown that every MCNFP with general nonlinear cost functions can be transformed into a concave MCNFP on an expanded network. It must also be noted, that multiple source ...

We investigate a multi-commodity capacitated facility location problem involving sustainability concerns (e.g., restrained carbon emission). In addition, this incorporates complementarity demand function. show that incorporation can lead to superior decisions both analytically and computationally. The resultant formulation is 0–1 mixed-integer non-concave quadratic program with equilibrium cons...