1. County Hospital orders syringes from a hospital supply firm. The hospital expects to use 40,000 syringes per year. The ordering cost (cost to order and have the syringes delivered) is $800 per order. The annual holding cost per syringe is 20% of the cost of a syringe. The hospital supply firm offers the following quantity discount pricing schedule.
|
Order Quantity
|
Price per Syringe
|
|
0 - 5,999
|
$3.40
|
|
6,000 - 10,999
|
$3.30
|
|
11,000 - 19,999
|
$3.26
|
|
20,000 and over
|
$3.23
|
a) What is the optimal quantity per order based on the total annual cost (composed of the holding cost and ordering cost and the acquisition cost)? Provide the lowest total cost for each of the price options. Include the holding, ordering and acquisition cost.
b) For an exclusive agreement, the supplier has offered to reduce the cost to $3.10 per syringe with no restriction on the order quantity. The ordering cost per order remains the same. If County Hospital selects this option, it will need to increase the annual holding cost per syringe to 23% of the cost of a syringe. Based on the total annual cost, should Douglas County select this option compared to the one found in a)? Explain your answer.
2. The Austin, Texas plant of Computer Products produces disk units for personal and small business computers. Gerald Knox, the plant's production planning director, is looking over next year's sales forecasts for these products and will be developing an aggregate capacity plan for the plant. The quarterly sales forecasts for the disk units are as follows:
|
1st Quarter
|
2nd Quarter
|
3rd Quarter
|
4th Quarter
|
|
2,000
|
1,980
|
2,340
|
2,160
|
Ample machine capacity exists to produce the forecast. Each disk unit takes an average of 20 labor-hours. In addition, you have collected the following information:
a. Inventory carrying cost is $100 per disk unit per quarter. The cost is applied to all units in inventory at the end of a quarter.
b. The plant works the same number of days in each quarter, 12 five-day weeks, 6 hours per day.
c. Beginning inventory is 200 disk units. These will be used to help satisfy the 1st Quarter demand.
d. In a backlog situation, the customer will wait for his order to be filled but will expect a price reduction each quarter he waits. The backlog costs are $300 per disk for the first quarter the customer waits, $700 for the second quarter the customer waits, and $900 for the third quarter the customer waits. In filling orders, backlogged items will always be filled before current quarter items,
e. The cost of hiring a worker is $800 while the cost of laying off a worker is $950.
f. The straight time labor rate is $20 per hour for the first quarter and increases to $22 per hour in the second quarter.
g. Overtime work is paid at time and a half (150%) of the straight time work.
h. Outsourcing (contract work) is paid at the rate of $475 per disk unit for the labor and Computer Products provides the material.
i. Demand during the fourth quarter of the prior year was 1,980 units. The demand for the first quarter of the next year (year following the year you are analyzing) is projected to be at the 1,980 unit level.
Compare the following three sales and operations plans.
i) Computer Products is considering the "chasing" or "matching" demand planning model for meeting the disk production. As workers are added to the workforce, all workers being considered do not qualify for one reason or another. So, the company will need to process more potential workers than are needed to match the demand. Historically, only 50% of the workers being considered are qualified. Hence the company needs to "process" more potential workers. For those workers who are not qualified, there is still a cost the company incurs for processing them. This amounts to $650 per unqualified worker. For the workers who are hired, the cost is the $800 referenced in item e. above. Ignoring the material cost, what is the total cost to produce the disks for the year? All workers will be fully utilized each quarter, in other words, there is no under utilization.
ii) As an alternative, the company will maintain a workforce capable of producing the demand during the fourth quarter of last year. If there are more workers in a quarter than required to produce the demand for that quarter, only the units required will be produced in that quarter and there will be underutilization. If demand is greater in a quarter than can be produced by the available workforce using straight time, the excess units will be outsourced. What is the total cost of this option, excluding the material cost?
iii) As an alternative, the company will establish in quarter one and then maintain a workforce capable of producing 2,160 units in a quarter. If there are more workers in a quarter than required to produce the demand for that quarter, only the units required will be produced in that quarter and there will be underutilization. If demand is greater in a quarter than can be produced by the available workforce using straight time labor, the excess units will be backlogged until the next quarter when they will be produced using regular time labor and then overtime if there are not sufficient workers. What is the total cost of this option, excluding the material cost?
3. Assume that Product Z is made up of two units of A and four units of C. A is made of three units of D. The lead time for Z, A and D is one week while the lead time for item C is two weeks. The demand for Z is as follows:
|
Week
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Demand
|
120
|
340
|
280
|
530
|
410
|
380
|
The lot size for Z and A are Lot-for-Lot (LFL). The lot size for item C is 1500+ units. This means that when ordering, these must be ordered in at least the number of units indicated. Over the amount indicated, the lot size is LFL. The lot size for item D is 1000* units. This means that when ordering, these are ordered in multiples of 1,000 (1,000 or 2,000 or 3,000, etc.).
Additional information is the following:
|
Item
|
Z
|
A
|
C
|
D
|
|
On hand
|
750
|
430
|
460
|
1,100
|
|
Safety stock
|
0
|
120
|
140
|
200
|
|
Allocated
|
0
|
80
|
160
|
60
|
|
Scheduled Receipts
|
--
|
400 in Week 1
|
1,500 in Week 2
|
--
|
a) Prepare the product structure tree.
b) Develop an MRP schedule showing the gross and net requirements and the planned order receipts and releases for Product Z and each of its components (A, C, and D).
4. Pet Supplies Company produces 16-ounce cans of dog food by combining meat by-products, which cost $0.60 per pound, and chicken by-products, which cost $0.35 per pound. Meat by-products are 55% protein and 30% fat by weight, while chicken by-products are 40% protein and 10% fat by weight. To meet customer expectations, the final product should contain at least 50% protein and between 15% and 25% fat by weight. Pet Supplies advertises that each can of dog food has no more than 30% by weight of chicken by-products.
a) Formulate a linear programming solution to be used to determine what the composition of a can of dog food should be to meet the various requirements at the minimum cost. Hint: you can express the amount of each ingredient in a 16-ounce can of dog food as a fraction of a 16-ounce can rather than in ounces. Provide the objective function and the constraints for your linear programming formulation.
b) Using linear programming, find the optimal solution for the objective function and the optimal values of each of the variables. Provide a copy of your linear programming output, identifying the value of the objective function and the values of the variables at optimality.
c) Suppose the cost of the meat increased to 0.80 per pound. Don't resolve the problem but use the sensitivity analysis output from part b). Explain if this would change the optimal value of the objective function and the optimal value of the variables. Provide the information from part b) that you used in reaching your conclusion.
d) Suppose the maximum chicken by-product that is accepted increases by 4% to 34%. Don't resolve the problem but use the sensitivity analysis output from part b). Explain if this would change the optimal value of the objective function and the optimal value of the variables. Provide the information from those results that you used in reaching your conclusion.
e) Now suppose that each can of dog food sales for $1.50. If the required profit per can is at least $0.65, write the constraint satisfying this objective function. You do not need to resolve for the optimal answer. 5.
In preparing to teach a new course, the professor has determined that he will use six activities. He has also estimated the activity times. A listing of the various activities required, their immediate predecessors, and estimates of their times (in days) is given below.
|
Activity
|
Immediate Predecessors
|
Optimistic Time (Days)
|
Most Likely Time (Days)
|
Pessimistic Time (Days)
|
|
A
|
--
|
3
|
6
|
10
|
|
B
|
A
|
4
|
8
|
14
|
|
C
|
A,B
|
1
|
3
|
8
|
|
D
|
B,C
|
5
|
7
|
10
|
|
E
|
C
|
2
|
4
|
8
|
|
F
|
D,E
|
2
|
5
|
9
|
For any calculations you make related to time values, including any expected times and time standard deviations, calculate these values to 2 decimal places.
a) Draw the precedence diagram for this network.
b) Identify the critical path and the expected project completion time.
c) Calculate the expected slack times for each activity and for each path. For the path slack time, compute this compared to the critical path.
d) What is the probability that the critical path will be completed between 29 and 33 days?
e) How many days should the marketing manager allow for completion of the critical path if he wants to be only a 5% chance that the critical path will be completed in more than this time?
6. The following jobs are waiting to be processed at Rick Carlson's machine center. Carlson's machine center has a relatively long backlog and sets fresh schedules every 2 weeks, which do not disturb earlier schedules. Below are the jobs received during the previous 2 weeks. They are ready to be scheduled today, which is the beginning of day 241. At this time, no other jobs are in process or waiting to be worked. The jobs are due at the end of the day shown.
|
Job
|
Date Job Received
|
Production Days Needed
|
Date Job Due
|
|
A
|
225
|
25
|
270
|
|
B
|
228
|
15
|
300
|
|
C
|
230
|
35
|
325
|
|
D
|
231
|
30
|
310
|
|
E
|
235
|
40
|
360
|
For the following 2 sequencing rules, compute the average flow time from today (consider that today, which is the beginning of day 241, is day 1 for determining flow time), average days late (with no credit for being early) and average days early (with zero days early for a job that is late). The Remaining Shop Time is equal to the Production Days Needed. The rules are the following:
- Slack
- CR (Critical Ratio)
7. ABC has a demand (which is deterministic) for 27,000 DVD's per month. The cost of a DVD is $2.30 and the holding cost is 30 percent of the product cost per year. The ordering cost is $700 per order. There are 350 days per year. The lead time is 7 days.
a) What is the economic order quantity?
b) What is the time between orders?
c) What is the reorder point and what is the inventory position after the order is placed?
d) What are the annual cost of ordering and the annual holding cost?
e) Suppose that the demand has now changed. It is probabilistic and follows a normal distribution with a mean demand during lead time of 21,000 DVD's and the standard deviation of the demand during lead time equal to 1,000 DVD's. What are the safety stock and the reorder point if the company wants only a 5 percent chance of a stockout?
8. The fire department has a number of failures with its oxygen masks and is evaluating the possibility of outsourcing the preventive maintenance to the manufacturer. Because of the risk associated with a failure, the cost of each failure is estimated at $2,000. The current maintenance policy (with station employees performing maintenance) has yielded the following history:
|
Number of Failures
|
Number of years in which Failures Occurred
|
|
0
|
4
|
|
1
|
3
|
|
2
|
1
|
|
3
|
5
|
|
4
|
5
|
|
5
|
0
|
In reading this chart, there are 4 years in which there were no failures, 3 years in which there was one failure, etc.
The manufacturer who is offering the preventive maintenance contract will guarantee repairs on any and all failures as part of a service contract. The cost of this service contract is $5,000 per year which includes all costs related to the failure. The manufacturer will also provide spare units. Hence, the fire department incurs no cost by selecting to outsource to the manufacturer other than the cost of the service contract.
a) What is the expected annual cost of the current maintenance policy with station employees performing maintenance?
b) Which is the more economical policy? Assume that if the maintenance is outsourced, the workers currently performing this work will keep their jobs.
a) A medical control system has three components in series with individual reliabilities (R1, R2, and R3) as shown:
What is the reliability of this system?
b) The company is now considering a redesign of the medical control system to include a redundant parallel system:
Expressed as a percentage of the original design, how much has the reliability improved with this new medical control system?
10. ABC Construction is designing a new highway project. Shown below are the activities that need to be completed in this project. The Crash Time for an activity represents the resulting time after the activity has been crashed. The Normal Cost represents the cost to complete the activity in the Normal Time. The Crash Cost represents the cost to complete the activity in the Crash Time. In addition to the costs identified below, there are indirect costs of $300 per week. In addition, there a penalty cost of $500 per week for each week the project lasts beyond week five.
|
Activity
|
Predecessor
|
Normal Time (Weeks)
|
Crash Time (Weeks)
|
Normal Cost
|
Crash Cost
|
|
A
|
--
|
4
|
3
|
800
|
1200
|
|
B
|
A
|
3
|
2
|
900
|
1000
|
|
C
|
A
|
5
|
3
|
1250
|
2250
|
|
D
|
A
|
2
|
2
|
800
|
800
|
|
E
|
B,C
|
5
|
4
|
1500
|
2000
|
|
F
|
C,D
|
6
|
5
|
2000
|
3000
|
|
G
|
E,F
|
4
|
3
|
600
|
900
|
|
H
|
G
|
3
|
3
|
900
|
900
|
As with the other test problems, you must show your work to receive full credit.
a) What are the normal project completion time and the critical path?
b) What activity should be crashed to reduce the completion time found in a) by one week? Why?
c) What is the minimum cost schedule for this project and what is the cost of this schedule?
d) What is the project completion time if all activities are crashed to their minimum Crash Time?