Minimizing makespan on a single machine subject to random breakdowns

We investigate optimal sequencing policies for the expected makespan problem with an unreliable machine, where jobs have to be reprocessed in their entirety if preemptions occur because of breakdowns. We identify a class of uptime distributions under which LPT minimizes expected makespan.     

Parallel computation of the flow of integral viscoelastic fluids on a heterogeneous network of workstations

We consider the parallel computation of flows of integral viscoelastic fluids on a heterogeneous network of workstations. The proposed methodology is relevant to computational mechanics problems which involve a compute-intensive treatment of internal variables (e.g. fibre suspension flow and deformation of viscoplastic solids). The main parallel computing issue in such applications is that of load balancing. Both static and dynamic allocation of work to processors are considered in the present paper. The proposed parallel algorithms have been implemented in an experimental, parallel version of the commercial POLYFLOW package developed in Louvain-la-Neuve. The implementation uses the public domain PVM software library (Parallel Virtual Machine), which we have extended in order to ease porting to heterogeneous networks. We describe parallel efficiency results obtained with three PVM configurations, involving up to seven workstations with maximum relative processing speeds of five. The physical problems are the stick/slip and abrupt contraction flows of a K.B.K.Z. integral fluid. Using static allocation, parallel efficiencies in the range 67%–85% were obtained on a PVM network with four workstations having relative speeds of 2:1:1:1. Parallel efficiencies higher than 90% were obtained on the three PVM configurations using the dynamic load-balancing schemes.     

Synchronized abandonments in a single server unreliable queue

We consider a single server unreliable queue represented by a 2-dimensional continuous-time Markov chain. At failure times, the present customers leave the system. Moreover, customers become impatient and perform synchronized abandonments, as long as the server is down. We analyze this model and derive the main performance measures using results from the basic q-hypergeometric series.     

Rating the raters in a mixed model: An approach to deciphering the rater reliability

Rating the raters has attracted extensive attention in recent years. Ratings are quite complex in that the subjective assessment and a number of criteria are involved in a rating system. Whenever the human judgment is a part of ratings, the inconsistency of ratings is the source of variance in scores, and it is therefore quite natural for people to verify the trustworthiness of ratings. Accordingly, estimation of the rater reliability will be of great interest and an appealing issue. To facilitate the evaluation of the rater reliability in a rating system, we propose a mixed model where the scores of the ratees offered by a rater are described with the fixed effects determined by the ability of the ratees and the random effects produced by the disagreement of the raters. In such a mixed model, for the rater random effects, we derive its posterior distribution for the prediction of random effects. To quantitatively make a decision in revealing the unreliable raters, the predictive influence function (PIF) serves as a criterion which compares the posterior distributions of random effects between the full data and rater-deleted data sets. The benchmark for this criterion is also discussed. This proposed methodology of deciphering the rater reliability is investigated in the multiple simulated and two real data sets.     

Inverse stochastic resonance induced by synaptic background activity with unreliable synapses

Inverse stochastic resonance (ISR) is a recently pronounced phenomenon that is the minimum occurrence in mean firing rate of a rhythmically firing neuron as noise level varies. Here, by using a realistic modeling approach for the noise, we investigate the ISR with concrete biophysical mechanisms. It is shown that mean firing rate of a single neuron subjected to synaptic bombardment exhibits a minimum as the spike transmission probability varies. We also demonstrate that the occurrence of ISR strongly depends on the synaptic input regime, where it is most prominent in the balanced state of excitatory and inhibitory inputs.     

A polling model with an autonomous server

This paper considers polling systems with an autonomous server that remains at a queue for an exponential amount of time before moving to a next queue incurring a generally distributed switch-over time. The server remains at a queue until the exponential visit time expires, also when the queue becomes empty. If the queue is not empty when the visit time expires, service is preempted upon server departure, and repeated when the server returns to the queue. The paper first presents a necessary and sufficient condition for stability, and subsequently analyzes the joint queue-length distribution via an embedded Markov chain approach. As the autonomous exponential visit times may seem to result in a system that closely resembles a system of independent queues, we explicitly investigate the approximation of our system via a system of independent vacation queues. This approximation is accurate for short visit times only.      

Exact analysis of a two-workstation one-buffer flow line with parallel unreliable machines

This paper examines a model of a serial flow line with two workstations and an intermediate buffer. Each workstation consists of multiple unreliable parallel machines which are not necessarily identical, viz., the processing times, failure times and repair times of the parallel machines at each workstation are assumed to be exponentially distributed with non-identical mean rates. The system under consideration is solved via exact Markovian analysis. More specifically, a recursive algorithm that generates the transition matrix for any value of the intermediate buffer capacity is developed and all possible transition equations are derived and solved analytically. Once the transition equations are solved the performance measures of the model under consideration can be easily evaluated. This model may be used as a decomposition block for solving larger flow lines with parallel unreliable machines at each workstation.     

Production control of an unreliable manufacturing system under the assumption of no backlog

This paper deals with an unreliable manufacturing system in which no backlog is allowed. The hedging point policy is used to control production. This paper's objective is to find the optimum hedging point so as to minimize the average inventory cost. Firstly, for a tentative hedging point, we derive the limiting distribution of the inventory level. This derivation is accomplished by comparison between this system and a finite storage-production system. Based on it we calculate the average inventory cost and find the optimum hedging point.This research was supported in part by the National Natural Science Foundation of China. Bin Liu was partially supported by ITDC, contract No. 105-82150.     

On solving the discrete location problems when the facilities are prone to failure

The classical discrete location problem is extended here, where the candidate facilities are subject to failure. The unreliable location problem is defined by introducing the probability that a facility may become inactive. The formulation and the solution procedure have been motivated by an application to model and solve a large size problem for locating base stations in a cellular communication network. We formulate the unreliable discrete location problems as 0–1 integer programming models, and implement an enhanced dual-based solution method to determine locations of these facilities to minimize the sum of fixed cost and expected operating (transportation) cost. Computational tests of some well-known problems have shown that the heuristic is efficient and effective for solving these unreliable location problems.     

极大化提前完工总量平行机排序问题的LPT算法

研究带有共同交货期的三台平行机排序问题。工件在加工过程中不允许中断, 目标是极大化所有工件的提前完工量, 即在交货期前所加工工件(或部分) 的总加工时长。由于该问题是NP-难问题, 本文应用经典LPT算法来解决该问题。我们证明了LPT算法求解该问题的最坏情况界至多为$\frac{15}{13}$, 并给出实例说明最坏情况界的下界为$\frac{27}{25}$。