MGT 3110: Exam 3 Study Guide

Discussion questions

  1. What is safety stock, and what is its purpose?
  2. Under what circumstances would the amount of safety stock held be (a) Large? (b) Small? (c) Zero?
  3. What is meant by the term service level? Generally speaking, how is service level related to the amount of safety stock held?
  4. What is the single-period model, and under what circumstances is it appropriate‘?
  5. Can the optimal stocking level in the single-period model ever be less than expected demand? Explain briefly.
  6. Why is scheduling fairly simple for repetitive systems but fairly complex for job shops?
  7. What are the main decision areas of job-shop scheduling?
  8. What are Gantt charts‘? How are they used in scheduling? What are the advantages of using Gantt charts?
  9. What are the basic assumptions of the assignment method of linear programming?
  10. Briefly describe each of these priority rules: a. FCFS b. SPT c. EDD d. S/O e. Rush
  11. Why are priority rules needed?
  12. Explain forward and backward scheduling and each one’s advantage.
  13. How are scheduling and productivity related?
  14. What factors would you take into account in deciding whether to split a job?
  15. Explain the term makespan.
  16. Explain the terms flowtime and lateness.
  17. What are the advantages and disadvantages of shortest processing time (SPT) rule?
  18. What is the Critical Ratio? To what jobs does Critical Ratio give priority to?
  19. What can be said about the jobs if CR < 1, or =1, or > 1?
  20. What can be said about the jobs negative values for S/O?
  21. What is input-output control?
  22. Identify the term being described for each of the following:

a. A sequence of activities in a project.

b. The longest time sequence of activities in a project.

c. when both earliest and latest times are the same.

d. The difference in time length of any path and the critical path.

e. The statistical distribution used to describe variability of an activity time.

f. The statistical distribution used to describe path variability.

g. Shortening an activity by allocating additional resources.

  1. Why might a probabilistic estimate of a project’s completion time based solely on the variance of the critical path be misleading? Under what circumstances would it be acceptable?
  2. What is AOA convention? Describe its salient aspects. What is main disadvantage of this convention?
  3. What is AON convention? Describe its salient aspects.
  4. How is slack time of an activity calculated?
  5. What are the three activity times used in a PERT project? How are they used?

Problems

  1. The Winfield Distributing Company has maintained an 80% service level policy for inventory of string trimmers. Mean demand during the reorder period is 130 trimmers, and the standard deviation is 80 trimmers. What is the value of ROP and SS?
  1. The new office supply discounter, Paper Clips, Etc. (PCE), sells a certain type of ergonomically correct office chair which costs $300. The annual holding cost rate is 40%, annual demand is 600, and the order cost is $20 per order. The store is open 300 days per year and PCE has decided to establish a customer service level of 90%.
  1. Suppose that the lead time is a constant 4 days and the demand is variable with a standard deviation of 2.4 chairs per day. What is the safety stock and reorder point?
  2. Suppose that the lead time is a variable with an average of 4 days and standard deviation of 3 days. Further suppose that the demand is constant. What is the safety stock and reorder point?
  3. Suppose that the lead time is a variable with an average of 4 days and standard deviation of 3 days. Further suppose that the demand is also variable with a standard deviation of 2.4 chairs per day. What is the safety stock and reorder point?
  1. An oyster bar buys fresh oysters for $3 per pound and sells them for $10 per pound. Unsold oyster at the end of the day is sold to a grocery store for $1.20 per pound. Determine the pounds of oysters that must be ordered each day under each of the following conditions.

a.  The daily demand follows normal distribution with mean of 150 pounds and standard deviation of 12 pounds.

b.  The daily demand follows uniform distribution with between 100 and 200 pounds.

c.  The daily demand follows a discrete distribution with the following probabilities.

Demand during lead time / Probability
100 / 0.05
120 / 0.10
140 / 0.10
160 / 0.25
180 / 0.30
200 / 0.20
  1. Consider the following planned and actual hours of input and output.

Week ending / 1 / 2 / 3 / 4 / 5 / 6
Planned input / 500 / 800 / 700 / 600 / 600 / 800
Actual input / 700 / 700 / 700 / 800 / 600 / 500
Planned output / 650 / 650 / 650 / 650 / 650 / 700
Actual output / 600 / 700 / 800 / 700 / 650 / 500

Prepare the Input/Output Control chart for this workstation. Assume an initial actual backlog of 120 hours and zero for the two cumulative deviations.

  1. The following jobs are waiting to be processed at a work center.

Job / Production days needed / Date job due / Remaining operations
A / 30 / 40 / 2
B / 20 / 165 / 4
C / 40 / 125 / 3
D / 50 / 65 / 1
E / 20 / 170 / 5
F / 35 / 130 / 2

Sequence the jobs in the order of SPT, EDD, S/O, and Critical Ratio, and compute (i) Average flow time, (ii) Average lateness, and (iii) Average no. of jobs in the system, for each of the three schedule of jobs.

6.  An antique restoration operation uses a two-step sequence that all jobs in a certain category follow. For the group of jobs listed.

a.  Find the sequence that will minimize total completion time.

b.  Determine the amount of idle time for workstation 102.

c.  What jobs are candidates for splitting‘? Why? If they were split, how much would idle time and makespan time be reduced? Assume the very first job can be split 50% and the remaining jobs can be spit 60%.

JOB TIMES (minutes)

A / B / C / D / E
Workstation 101 / 27 / 18 / 70 / 26 / 15
Workstation 102 / 45 / 33 / 30 / 24 / 10

7.  Consider the tasks, durations in weeks, and predecessor relationships in the following network.

Activity Description / Immediate
Predecessor(s) / to / tm / tp
A / --- / 4 / 7 / 10
B / A / 2 / 8 / 20
C / A / 8 / 12 / 16
D / B / 1 / 2 / 3
E / D, C / 6 / 8 / 22
F / C / 2 / 3 / 4
G / F / 2 / 2 / 2
H / F / 6 / 8 / 10
I / E, G / 4 / 8 / 12
J / I / 1 / 2 / 3

a.  Find the expected time te for all the activities.

b.  Draw the AON network

c.  Determine all the paths unique paths and find the expected project completion time using the te values found in (a).

d.  Determine the earliest and latest start and finish times, slacks, and all the critical paths.

e.  Determine the path variance for the critical path and the next longest path.

f.  What is the probability of completion of the project before week 42?

g.  What is the probability of completion of the project before week 35?

h.  With 99% confidence what is your estimate for the project completion time.

Answers to discussion questions

1.  What is safety stock, and what is its purpose?

Safety stock is inventory held in excess of expected demand to reduce the risk of stockout presented by variability in either lead time or demand rates.

2.  Under what circumstances would the amount of safety stock held be (a) Large? (b) Small? (c) Zero?

Safety stock is large when large variations in lead time and/or usage are present. Conversely, small variations in usage or lead time require small safety stock. Safety stock is zero when usage and lead time are constant, or when the service level is 50 percent (and hence, z = 0).

3.  What is meant by the term service level? Generally speaking, how is service level related to the amount of safety stock held?

Service level can be defined in at least two different ways – (a) as the probability that demand will be met with available stock on hand, and (b) the percentage of annual demand satisfied from inventory.

Increasing the service level requires increasing the amount of safety stock.

4.  What is the single-period model, and under what circumstances is it appropriate‘?

The Single-Period Model is used when inventory items have a limited useful life (i.e., items are not carried over from one period to the next).

5.  Can the optimal stocking level in the single-period model ever be less than expected demand? Explain briefly.

Yes. When excess costs are high and shortage costs are low, the optimum stocking level is less than expected demand.

6.  Why is scheduling fairly simple for repetitive systems but fairly complex for job shops?

Job shops are intended to handle a wide range of processing requirements; jobs tend to follow many different paths through the shop, and often differ significantly with respect to processing times. In addition, rush orders, changes in specs, and short planning horizons must be contended with. Consequently, scheduling can be exceedingly complex. Conversely, in continuous systems there is a high degree of uniformity which presents much less difficulty in terms of scheduling.

7.  What are the main decision areas of job-shop scheduling?

The main decision areas of job shop scheduling concern loading and sequencing.

8.  What are Gantt charts‘? How are they used in scheduling? What are the advantages of using Gantt charts?

Gantt charts are visual aids used by managers to plan and adjust facility and equipment loading. Advantages of Gantt charts include ease of manipulation, the fact that they provide a visual model of loading, and the ability to assist in trial and error changes. Disadvantages include the need to repeatedly update the chart, the inability to reveal costs associated with different alternatives and the inability to include other details (e.g., processing items which are dependent on the equipment being used rather than the same regardless of the equipment being used).

9.  What are the basic assumptions of the assignment method of linear programming?

The assignment model assumes a one-for-one matching is possible, that costs for each combination are known and fixed, and that in general, each machine is capable of handling each job. (The last assumption is not strict, however. For example, certain combinations may be “undesirable” because certain jobs cannot be processed on certain pieces of equipment.)

10.  Briefly describe each of these priority rules: a. FCFS b. SPT c. EDD d. S/O e. Rush

a.  FCFS: process jobs in order of arrival.

b.  SPT: process jobs according to processing times, shortest ones first.

c.  DD: process jobs by due date, earliest due dates first.

d.  S/O: takes into account remaining processing time on all remaining operations for each job. Jobs with lowest slack per remaining operations are scheduled first.

e.  Rush: Emergency or preferred customers first.

11.  Why are priority rules needed?

Priority rules allow for the fact that jobs are not equally important: different processing sequences will have different consequences for the organization. Priority rules enable an organization to emphasize those measures of effectiveness deemed most important.

12.  Explain forward and backward scheduling and each one’s advantage.

Forward scheduling is when scheduling starts with a specific date and moves forward; backward scheduling starts at a specific end date and moves backward. Forward scheduling shows the earliest finish date; backward scheduling shows the latest start date.

13.  How are scheduling and productivity related?

To the extent that scheduling efforts can achieve a balance in facility or equipment loading, the amount of output for a given amount of input will be higher than it otherwise would, and hence, productivity will be higher than otherwise. Conversely, poor scheduling will adversely affect productivity because it will not enable maximum use of resources.

14.  What factors would you take into account in deciding whether to split a job?

Will throughput time decrease? Is it technically feasible to split a job? How disruptive will it be? What additional costs will be involved (e.g., setup, increased paperwork)?

15.  Explain the term makespan.

Makespan is the total time needed to complete a group of jobs from the beginning of the first job to the completion of the last job.

16.  Explain the terms flowtime and lateness.

Flow time is the length of time a job is in the system; lateness is completion time minus due date.

17.  What are the advantages and disadvantages of shortest processing time (SPT) rule?

SPT minimizes the average flow time, average lateness, and average number of jobs in the system. It maximizes the number of jobs completed at any point. The disadvantage is that long jobs are pushed back in the schedule.

18.  What is the Critical Ratio? To what jobs does Critical Ratio give priority to?

The Critical Ratio (CR) is an index number computed by diving the time until due date by the working time remaining. The CR gives priority to jobs that must be done to keep shipping on schedule.

19.  What can be said about the jobs if CR < 1, or =1, or > 1?

If CR < 1, then the job has fallen behind, the work remaining exceeds the time until due date. If CR = 1, then the job is on schedule, the work remaining exactly equals the time until due date. If CR > 1, then there is slack, the time until due date exceeds the work remaining.