A vector x⋴R^n is weakly k-majorized by a vector q⋴R^k if the sum of r largest components of x is less than or equal to the sum of r largest components of q for r=1, 2, …, k and k≤n. In this paper we extend the components of x to their absolute values in the above description and generalize some results in [2] and [3] by G. Dahl and F. Margot.

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In this paper, we develop a branch-and-bound algorithm to solve a network flow problem of optimizing production and transportation simultaneously. The production cost is assumed to be a concave function in light of scale economy. The proposed algorithm generates a globally optimal solution to this nonconvex minimization problem in finite time, without assuming the separability of the production-cost function unlike existing algorithms. We also report some computational results, which indicate that the algorithm is fairly promising for practical use.

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In this paper, we give the series expansion for the stationary probabilities π_n of the queue length of an M/D/1 queue based on analytic properties of the probability generating function π(z). We determine the poles and their associated residues of π(z), then give the partial fraction expansion of π(z). The series expansion of π_n are given by the poles and residues. We also give an upper bound and a lower bound for π_n.

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While travel cost in urban areas is generally best modeled using network distances, continuous distance measures are mostly used for location problems in rural environments. Combining both is not only interesting from a modeling perspective, but has also computational advantages since it combines reduced storage requirements for the network data with a high accuracy of the approximated distances. In this paper, Weber problems with combined distance measures are discussed. If continuous distances are measured using block norm distances, the resulting Weber problems can be represented by bilinear programming formulations. Theoretical properties of this model are discussed, and two possible solution strategies are suggested.

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We consider the problem of locating a single new facility in the plane in the presence of a bounded region, where the distance measures are different in the interior and exterior of this region. This is, in fact, an extension of previous work for unbounded regions separated by a line (Brimberg et al. [2]). We explore the properties of the problem, propose exact and approximate solution procedures, and examine a special case.

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A single facility has to be located in the plane in competition with fixed existing facilities, some belonging to the same chain, the others to competing chains. Demand points patronise the facility to which they are most attracted. Attraction is increasing with the quality of the facility and decreasing with its distance to demand. We study the lexicographic optimisation problem with primary objective to maximise the total market share of the chain, and secondarily to minimise the market losses of friendly facilities and/or the risk that competing facilities would raise their current quality in order to gain back lost customers.

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We consider a hub network design model based on the Stackelberg hub location model, where two firms compete with each other to maximize their own profit. The firm as a leader first locates p hubs and decides which OD pairs should be in services on the condition that the other firm as a follower locates q hubs and decides its strategies in a similar way after that. To avoid the possibility of unprofitable services, we incorporate flow threshold constraints into the model. We formulate the leader's problem as a bilevel programming problem with the follower's problem as a lower level problem. We solve the problem with the complete enumeration method and a greedy heuristic. The main objective is to make it clear how the network structure can be affected by the flow threshold constraints and the competitor's strategies.

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