This article gives an efficient algorithm for obtaining K shortest simple paths between two specified nodes in an undirected graph G with non-negative edge lengths. Letting n be the number of nodes and m be the number of edges in G, its running time is
We consider a class of n-job one-machine scheduling problems with ready time r(i), processing time p(i), and due time d(i) for each job i. Preemption is not allowed, and precedence constraints among jobs are not assumed. For this problem we show that there is a 0(n2)-time algorithm to find a schedule that minimizes the number of tardy jobs, under the assumption that r(i) < r(j) implies d(i) ≤ d(j).
This paper investigates a system whose deterioration is expressed as a continuous-time Markov process. It is assumed that the state of the system cannot be identified without inspection. This paper derives an optimal policy minimizing the expected total long-run average cost per unit time. It gives the optimal time interval between successive inspections and determines the states at which the system is to be replaced. Furthermore, under some reasonable assumptions reflecting the practical meaning of the deterioration, it is shown that the optimal policy has monotonic properties. A control limit rule holds for replacement, and the time interval between successive inspections decreases as the degree of deterioration increases.
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