This paper considers a two-unit paralleled system with general failure time and repair time distributions. The equations governing the behaviour of the system, without using regenerative (or cyclic) nature, have been derived by employing the method of supplementary variable. Then the problems of calculating the Laplace transform of the reliability of the system and the mean time to the first sy...

We propose and analyze a generic mathematical model for dynamic vehicle routing problems, which we call the dynamic traveling repairman problem (DTRP). The model is motivated by applications in which the objective is minimizing the wait for service in a stochastic and dynamically changing environment. This is a departure from traditional vehicle routing problems which seek to minimize total tra...

In this paper we study online algorithms for the online Traveling Repairman Problem (TRP) with precedence constraints. We show that, under general stochastic structures for the problem data, unknown and unused by the online algorithm, many online algorithms for this problem are almost surely asymptotically optimal. We also provide computational results for special cases that show that the conve...

In this paper, we propose a general framework for online scheduling problems in which each machine has multiple states that lead to different processing times. For these problems, in addition to deciding how to assign jobs to machines, we also need to set the states of the machines each time they are assigned jobs. For a wide range of machine environments, job processing characteristics and con...

This paper analyses the reliability of a cold standby system consisting of two repairable units, a switch and a repairman. At any time, one of the two units is operating while the other is on cold standby. The repairman may not always at the job site, or take vacation. We assume that shocks can attack the operating unit. The arrival times of the shocks follow a homogeneous Poisson process and t...

Abstract In this paper, we study the multi-depot k -traveling repairman problem. This problem extends traditional traveling to case. Its objective, similar single depot variant, is minimization of sum arrival times customers. We propose two distinct formulations model problem, obtained on layered graphs. order find feasible solutions for largest instances, a hybrid genetic algorithm where initi...

Refrigeration repair workers may be intermittently exposed to fluorocarbons and their thermal decomposition products. A case of peripheral neuropathy (distal axonopathy) in a commercial refrigeration repairman prompted an epidemiological investigation of the health of refrigeration repair workers. No additional cases of peripheral neuropathy were identified among the 27 refrigeration repair wor...

We consider an extension of the classical machine-repair model. As opposed to the classical model, we assume that the machines, apart from receiving service from the repairman, also supply service themselves to queues of products. The extended model can be viewed as a layered queueing network (LQN), where the first layer consists of two separate queues of products. Each of these queues is serve...