Let M be a set and F a family of its subsets. F is said by E. W. MILLER [5] to possess property B if there exists a subset K of M so that no set of the family F is contained either in K or in K (K is the complement of K in M) . HAJNAL and 1 [2] recently published a paper on the property B and its generalisations . One of the unsolved problems we state asks : What is the smallest integer in (n) ...

Commercial advertising is the main source of income for TV channels and allocation of advertising time slots for maximizing broadcasting revenues is the major problem faced by TV channel planners. In this paper, the problem of scheduling advertisements on prime-time of a TV channel is considered. The problem is formulated as a multi-unit combinatorial auction based mathematical model. This is a...

The set covering problem (SCP) is a well-known combinatorial optimization problem. This paper investigates development of a local branching approach for the SCP. This solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. The algorithm parameters are tuned by design of experiments approach. The proposed method is te...