The Minimum Cost Flow (MCF) problem is a well-known problem in the area of network optimisation. To tackle this problem, Network Simplex Algorithm (NSA) is the fastest solution method. NSA has three extensions, namely Network Simplex plus Algorithm (NSA+), Dynamic Network Simplex Algorithm (DNSA) and Dynamic Network Simplex plus Algorithm (DNSA+). The objectives of the research reported in this...

We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations and flows. The network may contain other unprescribed nodes, known as Steiner points. For concave increasing cost functions, a minimum cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characteris...

Network information flow emerged as a fertile research ground over a decade ago, with the advent of network coding that encourages information flows to be encoded when they meet within a data network. In this work, we propose the problem of space information flow — the transmission of information flows in a geometric space, instead of in a fixed, existing network topology. In this new model, in...

We consider the minimum cost network flow problem min(cx : Ax=b , x > 0) on a graph G = (V,E). First we give a minor modification of Edmonds-Karp scaling technique, and we show that it solves the minimum cost flow problem in 0((|V|'^ log 1v|)(|e| + |V| log |v|)) steps. We also provide two dual simplex algorithms that solve the minimum cost flow problem in 0(|v| log |v|) pivots and 0(|v| log |v|...

We consider a minimum-cost dynamic network-flow problem on a very special network. This network flow problem models an infinite-horizon, lot-sizing problem with deterministic demand and periodic data. We permit two different objectives: minimize long-run average-cost per period and minimize the discounted cost. In both cases we give polynomial algorithms when certain arc costs are fixed charge ...

Let G = (V, E) be a network for an assignment problem with 2n nodes and m edges, in which the largest edge cost is C. Recently the class of instances of bipartite matching problems has been shown to be in RNC provided that C is O(logk n) for some fixed k. We show how to use scaling so as to develop an improved parallel algorithm and show that bipartite matching problems are in the class RNC pro...

Cross docking is one of the options to reduce lead times and inventories and to improve customer response time in supply chains. Cross-docking centres are dynamic environments where products arrive, are regrouped, and leave the same day. In this paper we focus on the process of short-term storage of unit-loads in a cross-docking environment. The goal is to determine temporary storage locations ...

We explore here surprising links between the time-cost-tradeoff problem and the minimum cost flow problem that lead to faster, strongly polynomial, algorithms for both problems. One of the main results is a new algorithm for the unit capacity min cost flow that culminates decades of efforts to match the complexity of the fastest strongly polynomial algorithm known for the assignment problem. Th...

In this paper we use interior-point methods for linear programming, developed in t,he contest of sequential computation, to obtain a parallel algorithm for t,he bipartite matching problem. Our algorithm runs in 0*(,/E) time I. Our results extend to the weighted bipartite matching problem and to the zero-one minimum-cost flow problem, yielding O*( filog C’) algorithms?. This improvk’previous bou...

The problem to find a valid integer flow with flow multipliers on nodes or arcs is long known to be NP-complete [10]. We show that the problem is still hard when restricted to instances with a limited number of integral multipliers. To find an integer minimum cost maximal pseudoflow, respecting only the node balance constraints of the inner nodes, is also still a difficult task. Further, we dem...