A company needs to replace its high-use photocopying machine. Should the company purchase a model similar to the one it currently has or purchase a slightly more expensive one that promises to be 20% faster on jobs that involve collating but 10% slower on jobs that do not involve collating? Time-study data for 10 jobs are given below (times are in hours). Perform sample-path decomposition; then generate the sample path that would result from installing the more expensive copier. Compare the two sample paths in terms of makespan, which is the time required to finish a fixed number of jobs, 10 in this case.
A spreadsheet program can be used to perform the sample-path decomposition and the simulation for this problem. Set up columns A-G as shown below:
Number the customers from 0 to 10 in column A, where customer 0 is a phantom customer included to make the calculations work. Enter the customer arrival times in column B; the finish times in column C; and a 0.8 or 1.1 in column D for collate and no-collate jobs, respectively. Column D is the factor by which the customer’s copying time would increase or decrease if the new machine was installed.
Column E, the time the customer spends copying, is determined by the formula
E[i] = C[i] − MAX (B[i],C[i − 1])
as described in Section 2.3, where [i] indicates the row number in the spreadsheet. The new copying times are F[i] = D[i]*E[i]. Finally, the new finish time for customer i is the maximum of the time customer i – 1 finished and the time customer i arrived, plus the new copy time of customer i; that is,
G[i] = MAX (G [i − 1], B[i]) + F[i]
Notice that this approach hides the two system events, the arrival of a customer and finishing a job, which is not possible in more complex simulations.