An exact solution approach for the time-dependent traveling-salesman problem

We present an algorithm for solving the time-dependent traveling-salesman problem (TDTSP), a generalization of the classical traveling salesman problem in which the cost of travel between two cities depends on the distance between the cities and the position of the transition in the tour. The algorithm is derived by applying Benders decomposition to a mixed-integer linear programming formulation for the problem. We identify trivial TDTSPs for which a standard implementation of the algorithm requires an exponential number of iterations to converge. This motivates the development of an efficient, network-flow-based method for finding Pareto-optimal dual solutions of a highly degenerate subproblem. Preliminary computational experience demonstrates that the use of these Pareto-optimal solutions has a dramatic impact on the performance of the algorithm. © 1996 John Wiley & Sons, Inc.     

On the orbit characteristics of the M/G/ 1 retrial queue

In teletraffic applications of retrial queues only the service zone is observable. Another part of a retrial queue, the orbit, which represents the delay before repeated attempts to get service, cannot be observed. Thus, it is very important to get general results about behavior of the orbit. We investigate two characteristics of the orbit, namely, the orbit busy period and the orbit idle period, which seem to be very useful from this point of view. © 1996 John Wiley & Sons, Inc.     

Multichannel queueing systems with heterogeneous classes of arrivals

In an integrated telecommunications network, voice and data traffic compete for the same transmission facilities. Assuming Poisson arrivals and exponential service with different rates, analytic expressions are obtained for measures of performance such as blocking probability and average delay under the following operating rule: class 1 traffic behaves as a loss system while class 2 traffic is buffered when all channels are busy. In view of the inordinate amount of computational effort needed when the number of channels is large, simple approximations have been suggested.     

The conjugate gradient technique for certain quadratic network problems

We consider a class of network flow problems with pure quadratic costs and demonstrate that the conjugate gradient technique is highly effective for large-scale versions. It is shown that finding a saddle point for the Lagrangian of an m constraint, n variable network problem requires only the solution of an unconstrained quadratic programming problem with only m variables. It is demonstrated that the number of iterations for the conjugate gradient algorithm is substantially smaller than the number of variables or constraints in the (primal) network problem. Forty quadratic minimum-cost flow problems of various sizes up to 100 nodes are solved. Solution time for the largest problems (4,950 variables and 99 linear constraints) averaged 4 seconds on the CBC Cyber 70 Model 72 computer.     

Inventory models with a mixture of backorders and lost sales

This article presents several single-echelon, single-item, static demand inventory models for situations in which, during the stockout period, a fraction b of the demand is backordered and the remaining fraction 1 - b is lost forever. Both deterministic and stochastic demand are considered. although the case of stochastic demand is treated heuristically. In each situation, a mathematical model representing the average annual cost of operating the inventory system is developed. and an optimum operating policy derived. At the extremes b=1 and b=0 the models presented reduce to the usual backorders and lost sales cases, respectively.     

A queue with waiting time dependent service times

Sufficient conditions are developed for the ergodicity of a single server, first-come-first-serve queue with waiting time dependent service times.     

Sequential determination of inspection epochs for reliability systems with general lifetime distributions

The problem of determining the optimal inspection epoch is studied for reliability systems in which N components operate in parallel. Lifetime distribution is arbitrary, but known. The optimization is carried with respect to two cost factors: the cost of inspecting a component and the cost of failure. The inspection epochs are determined so that the expected cost of the whole system per time unit per cycle will be minimized. The optimization process depends in the general case on the whole failure history of the system. This dependence is characterized. The cases of Weibull lifetime distributions are elaborated and illustrated numerically. The characteristics of the optimal inspection intervals are studied theoretically.     

Decision rules for attacking targets of opportunity

Frequently in warfare, a force is required to attack a perishable enemy target system - a target system where the targets are detected seemingly at random, and if not immediately attacked, will shortly escape from detection. A conflicting situation arises when an attack element detects a target of relatively low value and has to decide whether to expend his resources on that particular target or to wait for a more lucrative one, hoping one will be found. This paper provides a decision rule giving the least valued target that should be attacked as well as the resources that should be expended as a function of the attack element's remaining mission time.     

Implicit enumeration based algorithms for postoptimizing zero-one programs

It has been shown by G. Roodman that useful postoptimization capabilities for the 0-1 integer programming problem can be obtained from an implicit enumeration algorithm modified to classify and collect all fathomed partial solutions. This paper extends the the approach as follows: 1) Improved parameter ranging formulas are obtained by higher resolution classification criteria. 2) Parameters may be changed so as to tighten the original problem, in addition to relaxing it. 3) An efficient storage structure is presented to cope with difficult data collection task implicit in this approach. 4) Finally, computer implementation is facilitated by the elaboration of a unified set of algorithms.     

On nonpreemptive strategies in stochastic scheduling

It is shown that there is an optimal strategy for a class of stochastic scheduling problems which is nonpreemptive. The results which yield this conclusion are generalizations of previous ones due to Glazebrook and Gittins. These new results also lead to an evaluation of the performance of nonpreemptive strategies in a large class of problems of practical interest.