1. E Office Supplies sells discounted office suppliers over the internet. One popular product sold is legal-size notepads. The current price is $19.45 per dozen, however, E Office Supplies offers a discount based on the quantity bought. E Office Supplies offers the following quantity discount (per dozen) structure based on how many dozen notepads are ordered:
|
Order Size
|
1-800 dozen
|
801-1499 dozen
|
1500-1999 dozen
|
2000+ dozen
|
|
Discount per Dozen
|
--
|
$0.45 per dozen
|
$0.48 per dozen
|
$0.53 per dozen
|
The STHDS law firm wants to decide how many legal notepads to order using the EOQ model for quantity discounts. Its ordering cost is $200 per order, its anticipated need (demand) in the coming year is for 180,000 notepads, and its annual holding cost is 40 percent of the acquisition cost.
Assume that shipments are received instantaneously, demand is known and the usage constant, and the lead time is known and constant.
a) Based on the lowest total annual cost (ordering plus holding plus acquisition cost), how many dozen notepads should STHDS order each time?
b) What is the total annual cost (ordering plus holding plus acquisition cost) per year for this order quantity?
c) What is the lowest total annual cost (ordering plus holding plus acquisition cost) for each of the price points?
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
|
|
2440
|
2610
|
2610
|
2520
|
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. There are 100 units on hand at the beginning of the first quarter and these will be used to help meet the first 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. Workers hired during a quarter are able to produce at full utilization for the quarter.
f. The straight time labor rate is $20 per hour for the first quarter and increases to $23 per hour starting in the third 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 you provide the material
i. Demand during the fourth quarter of the prior year was 2,430 and this was met by a workforce working full utilization with no overtime.
j. The demand for the first quarter of the next year (year following the year you are analyzing) is projected to be at the 2,610 unit level.
Compare the following three sales and operations plans.
i) Computer Products is planning on using a work force capable of producing 2520 units in any quarter. If all of the production is not required in a quarter, all of the workers will continue to be employed and there will be underutilization. During Quarters 1 and 2, it will meet any demand not filled with this workforce working straight time through a combination of overtime and outsourcing. Overtime and outsourcing will each produce 50% of the demand not met through straight time production by the company's workforce. Beginning in Quarter 3, the company will use a matching demand strategy. 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 underutilization.
ii) A form of level production where the total number of disk units needed during the year are produced during the year. Production is to be at a uniform (constant) rate throughout the entire year. All workers will be fully utilized each quarter, in other words, there is no underutilization. In any quarter, when there are backlog items from the prior quarter, these will be given priority in being filled over current quarter items. What is the total cost of this option, excluding the material cost?
iii) As an alternative, the company willmaintain a staff capable of producing 2,340 units in a quarter working at full utilization. It works overtime for any demand over 2,340 in a quarter. What is the total cost of this option, excluding the material cost? All workers will be fully utilized each quarter, in other words, there is no underutilization.
3. Whizmo Toy Company is interested in creating an MRP schedule for the manufacture of a new toy car. The Body Shop currently has a demand for 1500 Toy Cars and for an additional 1000 Hoods. It needs to set up this schedule for the toy car and all the components. The toy car is made up of one body assembly and 4 wheels. The body assembly is made up of one hood, 2 sides, and one trunk. There are other components for the body assembly but the company has plenty of those parts left over from a previous production. Hence, it is only concerned with the toy car, sub-assemblies and components identified above.
|
Item
|
Toy Car
|
Body Assembly
|
Wheels
|
Hood
|
Sides
|
Trunk
|
|
Total on hand
|
300
|
500
|
800
|
0
|
200
|
1,000
|
|
Safety stock
|
200
|
0
|
200
|
0
|
0
|
0
|
|
Allocated
|
0
|
100
|
200
|
0
|
0
|
0
|
|
Scheduled Receipts
|
--
|
--
|
--
|
500
|
800
|
--
|
How many units of the hoods, the sides, the wheels, and the trunk must be purchased to produce the demand of Toy Cars. Assume that all of the items On Hand include the Safety Stock and the Allocated. It is not necessary to provide the requirements by week.
4.
The Delicious Apple Company has orchards in Red City, Golden, and Macville Estimated amounts of apples to be available from the three orchards are the following: Red City, 15,000 bushels; Golden, 12,000 bushels; and Macville, 9,000 bushels. Apple Products Company wants to buy up to 10,000 bushels, for which it will pay $2.90 a bushel. Fruit Processors, Inc., is interested in buying up to 12,000 bushels at $3.20 a bushel. Extragood Fruit Company will buy up to 18,000 bushels at $3.10 per bushel. Delicious Apple Company would like to distribute its apples to the buyers so as to maximize its profits. The costs of shipping form the orchards to the buyers' processing plants are given in the following table. It is acceptable to have fractional bushels.
|
From Orchard
|
Apple Products
|
Fruit Processors
|
Extragood Fruit
|
|
Red City
|
$0.55
|
$0.65
|
$0.45
|
|
Golden
|
$0.40
|
$0.45
|
$0.55
|
|
Macville
|
$0.45
|
$0.45
|
$0.85
|
a) Formulate the linear programming formulation for this problem.
b) Usingany linear programming software, solve the problem for the optimal answer and provide the value of the objective function and the variables at optimality.Provide a copy of your linear programming output. In addition to providing this output, you are to specifically identifythe value of the objective function and the values of the variables at optimality.
c) Using the sensitivity analysis (ranging) output provided as part of the linear programming output, provide two sensitivity analysis interpretations. Provide one based on the objective function and one based on a constraint. Provide a copy of the sensitivity analysis output supporting your interpretations.
d) Now suppose that Delicious Apple has signed a contract with Extragood Fruitthat ensures that Extragood Fruit will receive in total at least as many apples as Fruit Processors. Provide the modification to the linear programming formulation provided in a) for this additional requirement. It is not necessary to solve the linear programming problem for the solution.
e) Write a constraint that will ensure that Apple Products obtains no more than 30% of its total number of bushels from the Golden orchard. You only need formulate this constraint. You do not need to solve the linear programming problem for the solution.
As required, you must submit your linear programming formulation and show the linear programming software solution to this problem to receive credit.
5.
You are given the following network.
|
Activity
|
Immediate Predecessors
|
Normal Completion Time (Weeks)
|
Crash Completion Time (Weeks)
|
Normal Cost (Total)
|
Crash Cost (Total)
|
|
A
|
--
|
6
|
6
|
$100
|
$100
|
|
B
|
A
|
10
|
4
|
$2,000
|
$2,600
|
|
C
|
A
|
10
|
8
|
$800
|
$920
|
|
D
|
B
|
6
|
5
|
$700
|
$750
|
|
E
|
B
|
8
|
6
|
$1,000
|
$1,140
|
|
F
|
C,D
|
9
|
7
|
$1,400
|
$1,550
|
|
G
|
E
|
14
|
10
|
$3,000
|
$3,320
|
|
H
|
E,F
|
10
|
8
|
$900
|
$1,020
|
The Normal Cost for an activity is the total cost to complete that activity in the Normal Time and the Crash Cost is the total cost to complete that activity in the Crash Time. Use the Normal Times to answer parts a) through c).
a) Draw the project network
b) Calculate the slack time for each activity and for each path (relative to the critical path).
c) Identify the critical path and the project completion time.
d) Suppose you want to reduce the project time by two weeks. Based on the information provided, what would be the additional project cost to achieve this and what activity(ies) are crashed?
e) What is the minimum project completion time? Identify which activities to crash and by how many weeks to achieve that time.
f) What is the resulting project cost for the project completion time in e)?
6. A copy business operates with a single copier. It is now the beginning of the fourth (4th) hour. The jobs listed in the following table are waiting to be processed. The due date is the end of that hour. For example, Job 1 is due at the end of hour 42.
|
Job
|
Job Processing Time (Hours)
|
Due Date (in Hours) from Time 0
|
|
1
|
20
|
42
|
|
|
|
|
|
2
|
18
|
24
|
|
|
|
|
|
3
|
25
|
70
|
|
|
|
|
|
4
|
32
|
90
|
|
|
|
|
|
5
|
30
|
65
|
|
|
|
|
a) Determine the sequence of jobs using the following rules as these were defined during our weekly assignments:
• Critical ratio rule (CR)
• Slack time
b) Prioritize (rank) the rules used in a) based on average flow time measured from now.
c) Prioritize (rank) the rules used in a) based on average lateness with no credit for completing any job early.
d) Prioritize (rank) the rules used in a) based on average early time with no penalty for completing any job late (in other words, the early time would be set at zero if a job is late).
7.
First City Bank orders cash from the Federal Reserve Board to meet daily transaction needs. Linda Davis, the operations manager, estimates that $5,000,000 in cash will be needed next month. She has estimated that the cost to order, receive, and store each shipment of cash from the Federal Reserve Board will be $675 per shipment. First City Bank is open for business 250 days each year. These are considered its working days for the year.
The bank's related carrying cost for cash is 0.65 percent per month. That is, each dollar held in the bank's vault costs $0.0065 per month in foregone profits.
a) How much should Linda order from the Federal Reserve Board each time a cash order is placed if she wants to minimize her cost?
b) What is the expected total annual holding cost plus ordering cost?
c) If the lead time is 3 days what is the reorder point? Also, what is the inventory position immediately after reordering?
d) If it is against First City Bank's policy to order more than $750,000 when placing a cash order. How much should it order each time? Explain or support your answer.
8.
It costs a total of $2,000 to perform preventive maintenance (PM) on five identical production machines. If one of the machines malfunctions between PM inspections, this breakdown cost averages $5,000. Following is the historical breakdown for the machines.
|
PM every n months
|
Average Number of Breakdowns between PM Inspections
|
|
2
|
0.1
|
|
3
|
0.5
|
|
4
|
1.6
|
|
5
|
3.2
|
a) Which PM policy provides the minimum cost strategy based on the information provided?
b) With everything else the same, what is the average breakdown cost that results in the same total cost for a 3-month PM strategy and a 4-month PM strategy?
9.
USA Company's current switch design is composed of two components, A and B, in series. The company wants to upgrade the reliability of the switch. As one option, the company is considering the switch option shown below. The reliability of A is 0.9, and the reliability of B is also 0.9.
What will be the improved reliability should USA upgrade to the Switch Option shown above? Provide the reliability of this option.
10.
The estimated times and immediate predecessors for the activities in a project at John Black's company are given in the following table. Assume that the activity times are independent. All times are in weeks.
|
Activity
|
Predecessors
|
Optimistic Time (a)
|
Most Likely Time (m)
|
Pessimistic Time (b)
|
|
A
|
--
|
2
|
4
|
6
|
|
B
|
--
|
1
|
2
|
9
|
|
C
|
A
|
2
|
4
|
6
|
|
D
|
B
|
5
|
8
|
17
|
|
E
|
C
|
3
|
4
|
11
|
a) What is the critical path? You may use any method to determine this.
b) What is the expected completion time of the project?
c) What is the probability of completing the project in 16 weeks or more?