this paper presents a mathematical model for a flow shop scheduling problem consisting of m machine and n jobs with fuzzy processing times that can be estimated as independent stochastic or fuzzy numbers. in the traditional flow shop scheduling problem, the typical objective is to minimize the makespan). however,, two significant criteria for each schedule in stochastic models are: expectable m...

Open-shop scheduling problem (OSSP) is a well-known topic with wide industrial applications which belongs to one of the vital issues in field engineering. This paper deals two-stage open shop processing time jobs allied probabilities. The concept string two job blocks are disjoint nature considered so that first block covers fixed route and second an arbitrary path. Further, weights also introd...

In this paper we consider the open shop scheduling problem where the jobs have delivery times. The minimization criterion is the maximum lateness of the jobs. This problem is known to be NP-hard, even restricted to only 2 machines. We establish that any list scheduling algorithm has a performance ratio of 2. For a fixed number of machines, we design a polynomial time approximation scheme (PTAS)...

oftware companies face many challenges in growing their businesses. Product lines must evolve—new products and add-ons to existing products are essential to bring in new incremental revenue. Product quality must be monitored and improved. Engineering must support current and older releases while still driving innovation. Employees must be motivated by interesting opportunities and more than sta...

Scheduling is a scientific domain concerning the allocation of limited tasks over time. The goal of scheduling is to maximize (or minimize) different criteria of a facility as makespan, occupation rate of a machine, total tardiness ... In this area, scientific community usually group the problem with, on one hand the system studied, defining the number of machines (one machine, parallel machine...

The sparse linear method can reduce or expanse the solution range of integer programming problem by using former enumeration method lists all solution space, and then constraining them into a scale, after that picking up optimal solution form this scale. Calculation time will be reduced by using a revised integer programming model based on sparse linear, which can help reduce the number of solu...

This paper addresses a multiprocessor generalization of the preemptive open-shop scheduling problem. The set of processors is partitioned into two groups and the operations of the jobs may require either single processors in either group or simultaneously all processors from the same group. We consider two variants depending on whether preemptions are allowed at any fractional time point or onl...

This paper addresses the application of AI techniques in a practical OR problem , i.e. scheduling. Scheduling is a scientific domain concerning the allocation of tasks to a limited set of resources over time. The goal of scheduling is to maximize (or minimize) different optimization criteria such as the makespan (i.e. the completion time of the last operation in the schedule), the occupation ra...