this paper proposes a new mathematical model for designing and planning postal parcels carriage and postal networks. the objective of postal network designing is to determine the location, size and connection between the postal stations in a city, province or country. in this paper, a kind of multiple locations-allocations hub problem with limited capacity in collecting, distributing and broadc...

We now consider network flow problems. Such problems have some very nice properties. Specifically, we consider the minimum cost network flow problem, also known as the transshipment problem. In this problem, we are given a directed graph (V,E). The goal is to transport certain amounts of a single commodity from some vertices to others, across the edges of the graph. Specifically, each vertex v ...

We introduce a model for the computation of a multicommodity flow together with back-up flows for each commodity after any of a given set of failure states occurs in a network. We call such a total routing strategy a restorable multicommodity flow. One advantage of restorable flows over classical network protection methods, such as disjoint paths, is that the commodities may effectively share c...

The multi-commodity network flow problem (MCNF) consists in routing a set of commodities through capacitated at minimum cost and is relevant for containers liner shipping networks. As commodity transit times are often critical factor, the literature has introduced hard limits on times. In practical contexts, however, these may fail to provide sufficient flexibility since routes with even tiny d...

Spatial interaction models are frequently used to predict and explain interregional commodity flows. Studies suggest that the effects of spatial structure significantly influence spatial interaction models, often resulting in model misspecification. Competing destinations and intervening opportunities have been used to mitigate this issue. Some recent studies also show that the effects of spati...

Multiple coverings of the farthest-off points ((R,μ)-MCF codes) and the corresponding (ρ, μ)-saturating sets in projective spaces PG(N, q) are considered. We propose some methods which allow us to obtain new small (1, μ)-saturating sets and short (2, μ)-MCF codes with μ-density either equal to 1 (optimal saturating sets and almost perfect MCF-codes) or close to 1 (roughly 1+1/cq, c ≥ 1). In par...

Network flow problems with non-convex piecewise linear cost structures arise in many application areas, most notably in freight transportation and supply chain management. In the present paper, we consider mixed-integer programming (MIP) formulations of a generic multi-commodity network flow problem with piecewise linear costs. The formulations we study are based on variable disaggregation tech...

6. Lecture notes on flows and cuts 6.1 Maximum Flows Network flows deals with modelling the flow of a commodity (water, electricity, packets, gas, cars, trains, money, or any abstract object) in a network. The links in the network are capacitated and the commodity does not vanish in the network except at specified locations where we can either inject or extract some amount of commodity. The mai...