A deterministic production and transportation planning problem is considered over a finite time horizon for two products that can be produced in each of two regions. Each region uses its own facility to supply the demands for two products. Demands for product 2 in one region can be satisfied either by its own production or by transportation from other region, while no transportation between two regions is allowed for product 1. Production, inventory and transportation costs are assumed to be non-decreasing and concave. The objective is to find the schedule of production and transportation in each region by which the total cost over the horizon is minimized. Using a network flow approach, we develop a dynamic programming algorithm that can find an optimal policy.

We propose an efficient heuristic algorithm for two-stage hybrid flowshop scheduling with sequence-dependent setup times. In the past, metaheuristic approaches, which usually need long time, have been mostly used for the problem. In this study, due to practical reasons of the application that we consider, we need to obtain the solution of the problem within a reasonably short computational time, even for large-sized problems. In this study, we devise the proposed algorithm as a hybrid of two methods, that is, the beam search and NEH method, and we compare the performances with other existing local search methods. The results of the computational experiments show that the proposed algorithm solves the problems in a relatively shorter computation time, while the scheduling performances are superior to the existing methods.

This paper considers an optimal base station clustering problem for designing a mobile (wireless) communication network. For a given network with a set of nodes (base stations), the problem is to optimally partition the set of nodes into subsets (each called a cluster) such that the associated inter-cluster traffic is minimized under certain topological constraints and cluster capacity constraints. In the problem analysis, the problem is formulated as an integer programming problem. The integer programming problem is then transformed into a binary integer programming problem, for which the associated linear programming relaxation is solved in a column generation approach assisted by a branch-and-bound procedure. For the column generation, both a heuristic algorithm and a valid inequality approach are exploited.Various numerical examples are solved to evaluate the effectiveness of the LP (Linear Programming) based branch-and-bound algorithm.

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