Single machine stochastic JIT scheduling problem subject to machine breakdowns

In this paper we research the single machine stochastic JIT scheduling problem subject to the machine breakdowns for preemptive-resume and preemptive-repeat.The objective function of the problem is the sum of squared deviations of the job-expected completion times from the due date.For preemptive-resume,we show that the optimal sequence of the SSDE problem is V-shaped with respect to expected processing times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.We discuss the difference between the SSDE problem and the ESSD problem and show that the optimal solution of the SSDE problem is a good approximate optimal solution of the ESSD problem,and the optimal solution of the SSDE problem is an optimal solution of the ESSD problem under some conditions.For preemptive-repeat,the stochastic JIT scheduling problem has not been solved since the variances of the completion times cannot be computed.We replace the ESSD problem by the SSDE problem.We show that the optimal sequence of the SSDE problem is V-shaped with respect to the expected occupying times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.A new thought is advanced for the research of the preemptive-repeat stochastic JIT scheduling problem.

Production Control of a Manufacturing System with Random Machine Breakdowns

We consider a serial production system with machine breakdowns, where the machine at each station alternates between up and down states with exponential up and down time distributions. To obtain insight about the optimal production strategy, we focus on one production station. Its production process (output) and that of the previous station (input) are modeled by point processes with stochastic intensities. Our objectives is to control both input and output intensities such that expected discounted profit is maximized. We show that the optimal control policy is of a threshold type which is characterized by two threshold values.When each station in the serial system has reliable machines, the well known Kanban production strategy, which was first developed in Toyota Motor Co. of Japan, is usually used to control the production process at each station. Our result in this paper implies that, among other things, the traditional Kanban control rule has to be modified if the production environment is random.

Monitoring the Heavy Element of Cr in Agricultural Soils Using a Mobile Laser-Induced Breakdown Spectroscopy System with Support Vector Machine

Due to its complicated matrix effects, rapid quantitative analysis of chromium in agricultural soils is difficult without the concentration gradient samples by laser-induced breakdown spectroscopy. To improve the analysis speed and accuracy, two calibration models are built with the support vector machine method： one considering the whole spectra and the other based on the segmental spectra input. Considering the results of the multiple linear regression analysis, three segmental spectra are chosen as the input variables of the support vector regression （SVR） model. Compared with the results of the SVR model with the whole spectra input, the relative standard error of prediction is reduced from 3.18% to 2.61% and the running time is saved due to the decrease in the number of input variables, showing the robustness in rapid soil analysis without the concentration gradient samples.