Question

Chapter 11 Process Analysis and Resource Utilization - Chapter Review

Bourbon County Court

“Why don’t they buy another copying machine for this office? I waste a lot of valuable time fooling with this machine when I could be preparing my legal cases,” noted Mr. H.C. Morris, as he waited in line. The self-service copying machine was located in a small room immediately outside the entrance of the courtroom. Mr. Morris was the county attorney. He often copied his own papers, as did other lawyers, to keep his legal cases and work confidential. This protected the privacy of his clients as well as his professional and personal ideas about the cases.

He also felt awkward at times standing in line with secretaries, clerks of the court, other attorneys, police officers and sheriffs, building permit inspectors, and the dog warden—all trying, he thought, to see what he was copying. The line for the copying machine often extended out into the hallways of the courthouse.

Mr. Morris mentioned his frustration with the copying machine problem to Judge Hamlet and his summer intern, Dot Gifford. Ms. Gifford was home for the summer and working toward a joint MBA/JD degree from a leading university.

“Mr. Morris, there are ways to find out if that one copying machine is adequate to handle the demand. If you can get the Judge to let me analyze the situation, I think I can help out. We had a similar problem at the law school with word processors and at the business school with student lab microcomputers.”

The next week Judge Hamlet gave Dot the go-ahead to work on the copying machine problem. He asked her to write a management report on the problem with recommendations so he could take it to the Bourbon County Board of Supervisors for their approval. The board faced deficit spending last fiscal year, so the tradeoffs between service and cost must be clearly presented to the board.

Dot’s experience with analyzing similar problems at school helped her know what type of information and data was needed. After several weeks of working on this project, she developed the information contained in Exhibits 11.36, 11.37, and 11.38.

Exhibit 11.36

Bourbon County Court—Customer Arrivals Per Hour (These Data Are Available in the Worksheet Bourbon County Court Case Data in MindTap.)

	Customer Arrivals in One Hour		Customer Arrivals in One Hour		Customer Arrivals in One Hour		Customer Arrivals in One Hour		Customer Arrivals in One Hour
1	5	11	10	21	3	31	11	41	14
2	9	12	17	22	9	32	8	42	7
3	7	13	18	23	11	33	9	43	4
4	13	14	14	24	10	34	8	44	7
5	7	15	11	25	12	35	6	45	7
6	7	16	16	26	4	36	8	46	2
7	7	17	5	27	8	37	14	47	4
8	11	18	6	28	9	38	12	48	7
9	8	19	8	29	9	39	11	49	2
10	6	20	13	30	9	40	15	50	8

*A sample of customer arrivals at the copying machine was taken for five consecutive nine-hour work days plus five hours on Saturday for a total of fifty observations. The mean arrival rate is 8.92 arrivals per hour.

Exhibit 11.37

Bourbon County Court—Copying Service Times (These Data Are Available in the Worksheet Bourbon County Court Case Data in MindTap.)

Obs. No.	Hours per Job	Obs. No.	Hours per Job
1	0.0700	26	0.0752
2	0.1253	27	0.0752
3	0.0752	28	0.1002
4	0.2508	29	0.0388
5	0.0226	30	0.0978
6	0.1504	31	0.0752
7	0.0501	32	0.1002
8	0.0250	33	0.0250
9	0.0150	34	0.0752
10	0.2005	35	0.0501
11	0.1253	36	0.0301
12	0.1754	37	0.0752
13	0.0301	38	0.0501
14	0.1002	39	0.0075
15	0.0752	40	0.0602
16	0.3009	41	0.2005
17	0.0752	42	0.0501
18	0.0376	43	0.0150
19	0.0501	44	0.0501
20	0.0226	45	0.0527
21	0.1754	46	0.1203
22	0.0700	47	0.1253
23	0.1253	48	0.1053
24	0.0752	49	0.1253
25	0.2508	50	0.0301

*A sample of customers served at the copying machine was taken for five consecutive nine-hour work days plus five hours on Saturday for a total of fifty observations. The average service time is 0.0917 hours per copying job or 5.499 minutes per job. The equivalent service rate is 10.91 jobs per hour (i.e., ).

Exhibit 11.38

Bourbon County Court—Cost and Customer Mix

Resource Category	Mix of Customers in Line (%)	Cost or Average Direct Wages per Hour
Lease and maintenance cost of copying machine per year @250 days/year	N/A	$18,600
Average hourly copier variable cost (electric, ink, paper, etc.)	N/A	$5/hour
Secretaries	50%	$18.75
Clerks of the court	20%	$22.50
Building inspectors and dog warden	10%	$28.40
Police officers and sheriffs	10%	$30.80
Attorneys	10%	$100.00

*The mix of customers standing in line was collected at the same time as the data in the other case exhibits. Direct wages do include employee benefits but not work opportunity costs or ill-will costs, etc.

Dot was not quite as confident in evaluating this situation as others because the customer mix and associated labor costs seemed more uncertain in the county courthouse. In the law school situation, only secretaries used the word processing terminals; in the business school situation, students were the ones complaining about long waiting times to get on a microcomputer terminal. Moreover, the professor guiding these two past school projects had suggested using queueing models for one project and simulation for the other project. Dot was never clear on how the method of analysis was chosen. Now, she wondered which methodology she should use for the Bourbon County Court situation.

To organize her thinking, Dot listed a few of the questions she needed to address as follows:

1. Assuming a Poisson arrival distribution and an exponential service time distribution, apply queueing models to the case situation and evaluate the results.

2. What are the economics of the situation using queueing model analysis?

3. What are your final recommendations using queueing model analysis.

4. Advanced Question: Do the customer arrival and service empirical (actual) distributions in the case match the theoretical distributions assumed in queueing models?

Answer 1

Calculation of loss because of waiting time

Average cost per hour = (18.75*.5+22.5*.2+28.4*.1+30.8*.1+100*.1) =29.795

Count	Job in hours	Time per job	Total time for job in hour	Loss of person time	Average cost per hour	Loss

Total cost due to loss of manpower in a week = $353.76

Lease cost per week = $18600*5/250 = $372

variable cost per week = $5*50 = $250

Total cost if new machine taken = $250+372 =$622. So, cost saving for manpower is very less in terms of extra cost for new machine. hence, it is suggested not go buy a new machine