16+job_shop_scheduling

16+job_shop_scheduling - Activity–on –Node...

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Unformatted text preview: Activity–on –Node Interpretation Activity–on –Node Interpretation of Job Shop Scheduling Using TOC: Creating a Feasible Gantt Chart through Project Scheduling Job Shop Scheduling Using TOC Job Shop Scheduling Using TOC Following the one machine scheduling heuristic and coming up with a sequence of jobs on each machine as indicated n the example, the next task is to load these jobs on these machines observing the sequences imposed by out solution but also not violating any imposition placed by other machines and priority of other jobs as well. To do this we need to build an activity on node network first. Job Shop Scheduling Using TOC Job Shop Scheduling Using TOC This network will have m (number of machines) layers of vertical nodes and n( number o jobs) layers of horizontal nodes totaling mn nodes.To these mn nodes we will add one start node (node S) and one finish node (node F) to make the total mn+2 nodes in all. Each horizontal layer j of nodes will be associated with job j, and each vertical layer i of nodes will be associated with machine i. Job Shop Scheduling Using TOC Job Shop Scheduling Using TOC If a job j has a machine sequence j1, j2, ….jm­1, jm, then we will draw arrows from node S to the jth copy of machine j1, an arrow from the jth copy of machine j1 to jth copy of machine j2, …, and finally an arrow from the jth copy of machine jm­1to the jth copy of machine jm. Finally, one arrow from the jth copy of job jm to the final node F. For example if for job 3 machine sequence is 4­2­ 1­3 then it will look like the partial graph below. Job Shop Scheduling Using TOC Job Shop Scheduling Using TOC The vertical arrows on this network (within a particular The vertical arrows on this network (within a particular vertical nodes layer) come from the sequencing of jobs on a machine as obtained through the applied one machine scheduling heuristic as solved in the handout. For example, on machine 3 the sequence of jobs were 6­2­5­1­4­3. Therefore we will have an arrow from 3rd copy of job node 6 in the third vertical layer to the third copy of job node 2 in the third vertical layer. This will be followed by an arrow from the third copy of job node 2 in the third vertical layer to the third copy of job node 5 in the third vertical layer, etc. Machine 3 vertical layer and the imposed job precedence arrows will look like the one shown below. Job Shop Scheduling Using TOC Job Shop Scheduling Using TOC The complete network representation of the The complete network representation of the problem is given below: Job Shop Scheduling Using TOC Job Shop Scheduling Using TOC For each node (j,i) the processing time is pji. The processing times for S­node and F­node are 0. In this activity­on­node representation all we need to do is to compute the early start time of each node. This procedure is given in the Project Management handout in class we site www.ise.ufl.edu/ein4401. Once the early start of each node, ESji, is calculated, the early finish of each node is then obtained by Job Shop Scheduling Using TOC Job Shop Scheduling Using TOC ...
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