In this paper we consider the problem of scheduling, on a two-machine flowshop, a set ofunit-time operations subject to time delays with respect to the makespan. This problem isknown to be \hbox{${\cal NP}$}𝒩𝒫-hard in the strong sense. We propose an algorithm basedon a branch and bound enumeration scheme. This algorithm includes the implementation ofnew lower and upper bound procedures, and dominance rules. A computer simulation tomeasure the performance of the algorithm is provided for a wide range of testproblems.

The bandwidth minimization problem is of significance in network communication and related areas. Let G be a graph of n vertices. The two-dimensional bandwidth B2(G) of G is the minimum value of the maximum distance between adjacent vertices when G is embedded into an n × n grid in the plane. As a discrete optimization problem, determining B2(G) is NP-hard in general. However, exact results for this parameter can be derived for some special classes of graphs. This paper studies the “square-root rule” of the two-dimensional bandwidth, which is useful in evaluating B2(G) for some typical graphs.

Bounds obtained by Ramalhoto [1] for the variance of the busy period of an M/G/∞ queue are improved.

Some bounds for the variance of the busy period of an M/G/∞ queue are calculated as functions of parameters of the service-time distribution function. For any type of service-time distribution function, upper and lower bounds are evaluated in terms of the intensity of traffic and the coefficient of variation of the service time. Other lower and upper bounds are derived when the service time is a NBUE, DFR or IMRL random variable. The variance of the busy period is also related to the variance of the number of busy periods that are initiated in (0, t] by renewal arguments.