In this paper we consider the problem of scheduling precedence task graphs inparallel processing where there can be disturbances in computation andcommunication times. Such a phenomenon often occurs in practice, due to ourinability to exactly predict the time because of system intrusion like cache miss and packet transmission time in mediums like ethernet etc. We propose a method based on the addition of some extra edges to protect the initial scheduling from performing badly due to such changes and provide an upper bound on theperformance guarantee for the scheduling algorithms. Moreover, this construction guarantees a result at least as goodas the result obtained for the initial static scheduling.We also show that this construction is a minimal set in context of partially on-line scheduling.

In this paper we consider a like-queue production system in which server startupand breakdowns are possible. The server is turned on (i.e. begins startup)when N units are accumulated in the system and off when the system is empty.We model this system by an M[x]/M/1 queue withserver breakdowns and startup time under the N policy. The arrival rate varies according to the server's status:off, startup, busy, or breakdown.While the server is working, he is subject tobreakdowns according to a Poisson process. When the server breaks down, he requires repairat a repair facility, where the repair time follows the negative exponential distribution.We study the steady-state behaviour of the system size distribution atstationary point of time as well as the queue size distribution at departure point of timeand obtain some useful results.The total expected cost function per unit time is developed to determine the optimal operatingpolicy at a minimum cost. This paper provides the minimum expected cost and the optimal operatingpolicy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided.

In this paper, we study the problem of computing a minimum cost Steiner tree subject to a weight constraint in a Halin graph where each edge has a nonnegative integer cost and a nonnegative integer weight. We prove the NP-hardness of this problem and present a fully polynomial time approximation scheme for this NP-hard problem.

This paper studies the issue of well-posednessfor vector optimization. It is shown thatcoercivity implies well-posedness without any convexity assumptionson problem data.For convex vector optimization problems,solution sets of such problems are non-convex in general,but they are highly structured. By exploring such structures carefully via convex analysis,we are able to obtaina number of positive results, including a criterion for well-posedness in terms of that of associated scalar problems.In particularwe show that a well-known relative interiority conditioncan be used as a sufficient condition for well-posedness in convexvector optimization.