Chapter 16 Scheduling McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc All Rights Reserved Chapter 16: Learning Objectives • You should be able to: – Explain what scheduling involves and the importance of good scheduling – Discuss scheduling needs in high-volume and intermediate-volume systems – Discuss scheduling needs in job shops – Use and interpret Gantt charts, and use the assignment method for loading – Discuss and give example of commonly used priority rules – Describe some of the unique problems encountered in service systems, and describe some of the approaches used for scheduling service systems 16-2 Scheduling • Scheduling: – Establishing the timing of the use of equipment, facilities and human activities in an organization – Effective scheduling can yield – Cost savings – Increases in productivity 16-3 Processing Systems • Flow System – High-volume system with standardized equipment and activities • Intermediate-Volume System – Output fall between the standardized-type output of highvolume systems and the make-to-order output of job shops • Low-Volume System – Scheduling for low-volume systems with many variations in requirements 16-4 Hungarian Method Row reduction: subtract the smallest number in each row from every number in the row a Enter the result in a new table Column reduction: subtract the smallest number in each column from every number in the column a Enter the result in a new table Test whether an optimum assignment can be made a Determine the minimum number of lines needed to cross out all zeros b If the number of lines equals the number of rows, an optimum assignment is possible Go to step c Else, go to step 16-5 Hungarian Method (contd.) If the number of lines is less than the number of rows, modify the table: a b c Subtract the smallest number from every uncovered number in the table Add the smallest uncovered number to the numbers at intersections of cross-out lines Numbers crossed out but not at intersections of cross-out lines carry over unchanged to the next table Repeat steps and until an optimal table is obtained Make the assignments a b c Begin with rows or columns with only one zero Match items that have zeros, using only one match for each row and each column Eliminate both the row and the column after the match 16-6 Example: Hungarian Method • Determine the optimum assignment of jobs to workers for the following data: Worker Job A B C D 6 11 10 3 10 12 16-7 Example: Hungarian Method (contd.) Worker Job A B C D Row minimum 2 11 10 3 10 12 Subtract the smallest number in each row from every number in the row Worker Job A B C D 2 4 16-8 Example: Hungarian Method (contd.) Worker Job A B C D 2 4 Column Subtract the smallest number in each column from every number in the column Worker Job A B C D 0 0 4 16-9 Example: Hungarian Method (contd.) Worker Job A B C D 0 0 4 Determine the minimum number of lines needed to cross out all zeros (Try to cross out as many zeros as possible when drawing lines Since only three lines are needed to cross out all zeros and the table has four rows, this is not the optimum Note: the smallest uncovered value is 16-10 Example: Hungarian Method (contd.) Worker Job A B C D 0 0 4 Subtract the smallest uncovered value from every uncovered number, and add it to the values at the intersection of covering lines Worker Job A B C D 0 0 16-11 Example: Hungarian Method (contd.) Worker Job A B C D 0 0 Determine the minimum number of lines needed to cross out all zeros (Try to cross out as many zeros as possible when drawing lines Since four lines are needed to cross out all zeros and the table has four rows, this an optimal assignment can be made 16-12 Example: Hungarian Method (contd.) Worker Job A B C D 0 0 Assignment Cost 2-B $7 4-A $5 1-C $2 3-D $6 Total $20 Make assignments: Start with rows and columns with only one zero Match jobs with machines that have a zero cost 16-13 Sequencing • Sequencing – Determine the order in which jobs at a work center will be processed • Priority rules – Simple heuristics used to select the order in which jobs will be processed • FCFS - first come, first served • SPT - shortest processing time • EDD - earliest due date • CR - critical ratio • S/O - slack per operation • Rush - emergency 16-14 Operations Strategy • If scheduling is done well: – Goods and services can be made or delivered in a timely manner – Resources can be used to best advantage – Customers will be satisfied • It is important to not overlook the importance of scheduling to strategy and competitive advantage 16-15 .. .Chapter 16: Learning Objectives • You should be able to: – Explain what scheduling involves and the... column after the match 16- 6 Example: Hungarian Method • Determine the optimum assignment of jobs to workers for the following data: Worker Job A B C D 6 11 10 3 10 12 16- 7 Example: Hungarian... B C D 2 4 16- 8 Example: Hungarian Method (contd.) Worker Job A B C D 2 4 Column Subtract the smallest number in each column from every number in the column Worker Job A B C D 0 0 4 16- 9 Example: