In this study, we consider stationary waiting times in a Poisson driven single-server m-node queues in series. We assume that service times at nodes are independent, and are either deterministic or non-overlapped. Each node excluding the first node has a finite waiting line and every node is operated under a FIFO service discipline and a communication blocking policy (blocking before service). By applying (max, +)-algebra to a corresponding stochastic event graph, a special case of timed Petri nets, we derive the explicit expressions for stationary waiting times at all areas, which are functions of finite buffer capacities. These expressions allow us to compute the performance measures of interest such as mean, higher moments, or tail probability of waiting time. Moreover, as applications of these results, we introduce optimization problems which determine either the biggest arrival rate or the smallest buffer capacities satisfying probabilistic constraints on waiting times. These results can be also applied to bounds of waiting times in more general systems. Numerical examples are also provided.

We discuss the problem of selecting profitable customer orders arriving at a company providing two classes of services. For an arriving customer order for the first class, the company 1) makes a decision whether to accept or reject it (admission control), or 2) decides a price of the order to offer to an arriving customer (pricing control). The customer order undergoing processing in the system may be cancelled owing to unavoidable circumstances with the customer. The second class of service is provided as a sideline, which prevents the server from being idle when all the customer orders for the first class are completed and delivered. This yields the sideline profit. We discuss both admission control and pricing control problems in an identical framework as well as examine the structure of the optimal policies maximizing the total expected present discounted net profit gained over an infinite planning horizon.

In this paper, we have considered the multicriteria quadratic plant location problem. In addition to the allocation costs, the maintenance costs of the plants are also considered. The objective functions considered in this paper are quadratic in nature. The given problem is reduced to the problem with linear objective function. The method of Fernandez and Puerto (2003) is applied to solve the reduced problem. It is illustrated with help of examples. The effect of the change in the allocation and maintenance costs on allocation of plants to the clients has also been discussed.

We show that when a max-cut problem is allowed native-weight edges, to decide if the problem has a cut of a positive weight is NP-hard. This implies that there is no polynomial time algorithm which guarantees a cut whose objective value is no less than $1/p(<I>)$ times the optimum for any polynomially computable polynomial p, where denotes the encoding length of an instance I.