Loading and Sequencing under Operations Management

Loading and Sequencing

1. Loading and Sequencing

2. Loading A printing company has three available typewriters (A, B and C) and three new jobs to be completed. The data is given in the table below. The value in the table represent the firm's estimate of what it will cost for each job to be completed by each typewriter. Determine how to assign the jobs to the typewriter so as to minimize the company's overall cost of assignment. The value are in ($) Typewriter JOB A B C R-34 11 14 6 S-66 8 10 11 T-50 9 12 7

3. Example 1 The Green Cab Company has a taxi waiting at each of four cabstands in Evanston, Illinois. Four customers have called and requested service. The distances, in miles, from the waiting taxis to the customers are given in the following table. Find the optimal assignment of taxis to customers so as to minimize total driving distances to the customers CAB SITE CUSTOMER A B C D Stand 1 7 3 4 8 Stand 2 5 4 6 5 Stand 3 6 7 9 6 Stand 4 8 6 7 4

4. Example 2 At the head office of a company there are five registration counters. Five persons are available for service. How should the counters be assigned to persons so as to maximize the profit? A B C D E 1 30 37 40 28 40 2 40 24 27 21 36 3 40 32 33 30 35 4 25 38 40 36 36 5 29 62 41 34 39

5. Example 3 A Medical testing company in Kansas wishes to assign a set of jobs to a set of machines. The following table provides the production data of each machine when performing the specific job. Determine the assignment of jobs to machines that will maximize total production JOB MACHINE A B C D 1 7 9 8 10 2 10 9 7 6 3 11 5 9 6 4 9 11 5 8

6. Sequencing Five architectural rendering jobs are waiting to be assigned at BR Architects. Their work (processing) times and due dates are given in the following table. The firm wants to determine the sequence of processing according to 1) FCFS 2) SPT 3)EDD 4) LPT rules. Jobs are assigned a letter in the order they arrived. JOB JOB Work (Processing) Time (DAYS) JOB Due Date (DAYS) A 6 8 B 2 6 C 8 18 D 3 15 E 9 23

7. Performance Criteria

8. Example 1 The following jobs are waiting to be processed at the same machine center . Jobs are logged as they arrive. In what sequence would the jobs be ranked according to the following decision rules: a) FCFS b) EDD c) SPT d) LPT. All dates are specified as manufacturing planning calendar days. Assume that all jobs arrive on day 275. Which decision is the best and why? JOB DUE Date Duration (Days) A 313 8 B 312 16 C 325 40 D 314 5 E 314 3

9. Sequencing of N jobs on two machines: Johnson’s Rule Five speciality jobs at a tool and die shop must be processed through two work centres (drill press and lathe). The time for processing each job is given below. The owner of the shop wants to set the sequence to minimize his total time for the five jobs JOB Work Center 1 (Drill Press) Work Center 2 (Lathe) A 5 2 B 3 6 C 8 4 D 10 7 E 7 12

10. Example 1 The following set of seven jobs is to be processed through two work centers in a printing press. The sequence is first printing, then binding. Processing time at each of the work centers is shown in the following table. What is the optimal sequence for these jobs to be scheduled? What is the total length of time of this optimal schedule? JOB PRINTING (HOURS) BINDING (HOURS) T 15 3 U 7 9 V 4 10 W 7 6 X 10 9 Y 4 5 Z 7 8

11. Example 2 Six jobs are to be processed through a two-step operation. The first step involves sanding, and the second involves painting. Processing times are as follows. Determine a sequence that will minimize the total completion time for these jobs. JOB Operation 1 (Hours) Operation 2 (Hours A 10 5 B 7 4 C 5 7 D 3 8 E 2 6 F 4 3

12. Processing of N jobs through 3/4 machines For a special n jobs and 3 machines problem, Johnson provided an extension of Johnson algorithm. For this let, tij be the processing time of job i on machine j. Here i = 1,2,3,——n and j = 1,2,3. At least one of the following conditions must be satisfied before we can use this algorithm. Minimum (ti1) ≥ Maximum (ti2) Minimum (ti3) ≥ Maximum (ti2)

13. Steps STEP 1:   Take two hypothetical machine R and S. The processing time on R and S is calculated as follows: t iR  = t i1  + t i2 t iS  = t i2  + t i3 STEP 2:   Use Johnson algorithm to schedule jobs on machine R and S with t iR  and t iS .

14. Example 2 Determine the optimal sequence of jobs that minimize the total elapsed time based on the following information. Processing time on machines is given in hours JOB A B C D E F G Machine 1 3 8 7 4 9 8 7 Machine 2 4 3 2 5 1 4 3 Machine 3 6 7 5 11 5 6 12

15. Example 3 We have four jobs each of which has to go through each of the six machines. The processing time in hours is given below. Determine a sequence of these four jobs that minimises the total elapsed time JOB Machines M1 M2 M3 M4 M5 M6 Job A 18 8 7 2 10 25 Job B 17 6 9 6 8 19 Job C 11 5 8 5 7 15 Job D 20 4 3 4 8 12

16. Example 4 Solve the following sequencing problem. The order of processing jobs is ACB. Determine the total elapsed time. Job: 1 2 3 4 5 6 Machine A 12 10 9 14 7 9 Machine B 7 6 6 5 4 4 Machine C 6 5 6 4 2 4

17. Example 5 Solve the following sequencing problem Machines JOBS A B C D E Machine M1 10 12 8 15 16 Machine M2 3 2 4 1 5 Machine M3 5 6 4 7 3 Machine M4 14 7 12 8 10

18. Example 6 Solve the following sequencing problem Item Machine (Processing time in hours) A B C D I 15 5 4 15 II 12 2 10 12 III 16 3 5 16 IV 17 3 4 17