Operation Homework

August 14

 

Jan Kottas is the owner of a small company that buys and resells electric knives used to cut fabric. The annual demand is for 8,000 knives, and Jan is currently buying from Knives-R-Us. The ordering cost is $100 per order. The carrying cost per year is 4% of the acquisition cost of the knife, which is $20.00.

 

Jan has been approached by Knives-R-Us about buying knives under a new pricing schedule. One option is to order the knives in quantities between 1400 and 1599. If she does this, Knives-R-Us will lower the acquisition price to $19.75 each. If she buys 1600 or more at a time, the company will lower the price to $19.50. Of course, for all other quantities she can still buy the knives at $20.00 per knife.

 

If your order quantities are in fraction of units, please leave them as such.

 

a) Considering the total cost, composed of the holding cost and ordering cost and including the acquisition cost of the knives, how many should she buy per order to realize the lowest total cost?

 

 

 

 

 

 

 

b) Provide the lowest total cost for each of the three price options: $19.50, $19.75, and $20.00. Include the holding, ordering and acquisition cost.

2. (30 points)

 

The Austin, Texas plant of Computer Products produces external hard drives 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 external hard drives are as follows:

 

1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
2,040 2,520 2,340 2,790

 

 

Ample machine capacity exists to produce the forecast. Each external hard drive takes an average of 20 labor-hours. In addition, you have collected the following information:

 

a. Inventory carrying cost is $100 per external hard drive 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. For several reasons, there is a shortage of 300 units carried over from last year and these units must be provided during the first quarter. There is no holding or backlog costs associated with these 300 units.

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 external hard drive 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 any quarter, if there is a backlog, this backlog will be filled before the demand for that period is filled.

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 fourth 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 external hard drive for the labor and you provide the material.

i. Demand is projected to increase this year. Demand during the fourth quarter of the prior year was 2,340 units. The demand for the first quarter of the next year (year following the year you are analyzing) is projected to be at the 2,700 unit level.

j. Assume that individuals hired in a quarter are capable of working at the100% production level if the demand is requires it..

 

a) You want to maintain a work force capable of producing 2,520 in a quarter and work overtime for any hard drives over this quantity. If the total demand for a quarter does not require full production, there will be underutilization and no production will be carried over to the next quarter. If there is underutilization, the works will still be paid at the straight time rate. Any additional demand that cannot be met during the workforce at 100% production will be met through overtime. What is the total cost of this option, excluding the material cost?

 

 

b) Use a matching demand strategy not to exceed production capacity of 2,520 external hard drives per quarter with outsourcing for any production above this to ensure that all production requirements are met during each quarter. What is the total cost of this option, excluding the material cost?

3. (14 points)

 

Electrofans has the following orders for two of its fans.

· For its B style fan, 220 fans

· For its M style fan, 300 fans

 

The B style fan consists of two D and one E. The M style fan is made up of two E and one F. Each E consists of one G and each F is made up of two H.

 

You are also given the following information:

 

Item B M D E F G H
On Hand 80 25 50 55 50 15 10

 

 

How many units of D, G, and H must be purchased to produce the required number of fans to meet the given demand? Assume that all of the items On Hand can be used in meeting the demand.

4. (29 points)

 

MSA Computer Corporation manufactures three models of computers: the Alpha4, Beta5, and the Delta6. The firm employs thirteen technicians working 160 hours each per month on its assembly line. Management insists that no more than full employment on the assembly line (i.e., all 160 hours of time) can be maintained for each worker during next month’s operations, so there will be no overtime. It requires 20 labor hours to assemble each Alpha4 computer, 25 labor hours for each Beta5 model, and 15 hours for each Delta6. Final testing and inspection requires 3 hours for each Alpha4, 1.5 hours for each Beta5, and 1.2 hours for each Delta6. The company has up to 80 hours available for inspection and testing each month. Demand is such that the company can and will sell all of the computers that it produces. MSA must produce at least 10 Delta6 computers. In addition, the number of Alpha4 computers produced each month must equal or exceed the combined total of Beta5 and Delta6 computers produced. Alpha4 computers generate $1,200 profit per unit, Beta5 computers yield $1,800 each, and Delta6 computers yield $1,000 per unit. If the optimal answer is in fractions of computers that is acceptable.

 

a) Formulate the linear programming problem to maximize the profit during the coming month. Provide the variable being used, the objective function and all of the constraints that are indicated by the above description of the problem.

 

 

 

 

b) Using any available software package (POM/QM, Solver, etc.), what is the maximum profit and the quantity of each type of computer to produce. Provide your computer software input and output supporting your answers to parts a) and b). Not doing this will result in loss of 75% of the credit on this problem. If the optimal answer is in fractions of computers that is acceptable.

 

 

c) Based on the computer output provided as part of part b) and not resolving the problem, provide two sensitivity analysis interpretations. One interpretation must use the objective function variables and one must use a constraint(s). Provide your supporting sensitivity analysis (ranging) output.

 

 

d) Instead of the constraint that requires that MSA must produce at least 10 Delta6 computers, suppose it is now required that at least 25% of the computers produced must be Delta6 computers. Write the constraint to express this relationship. You do not need to resolve the revised linear programming formulation for the optimal answer.

 

 

e) The company now wants to ensure that for every Alpha4, MSA must produce at least two Beta5. Write the constraint to express this requirement however you do not need to resolve the revised linear programming formulation for the optimal answer. 5. (23 points)

 

The marketing department at Bodnar Industries is developing a promotional campaign to introduce a new product. A listing of the various activities required, their immediate predecessors, and estimates of their times (in days) is given below.

 

a) Draw the precedence diagram for this network.

b) Identify the critical path and the expected project completion time.

c) Provide the slack time for each path relative to the critical path completion time.

d) What is the probability that the critical path will be completed in more than 65 days?

e) How many days should the marketing manager allow for completion of the critical path if he wants to be 99% sure that the critical path will be completed within this allowed time? Provide this answer to two decimal points (xx.xx)

 

For any calculations that you make that involve time, use the time (days) to two decimal places (xx.xx).

 

Activity Description Immediate Predecessors Optimistic Time Most Likely Time Pessimistic Time
A Rough brochure layout 2 3 5
B Review brochure A 6 8 10
C Final brochure layout B 4 6 8
D Final brochure artwork C 5 7 11
E Design display 12 15 20
F Rough display artwork E 2 3 4
G Review display E 6 8 10
H Revise display G 2 3 4
I Final display artwork F,H 1 2 4
J Make display plates I 18 23 26
K Make brochure plates D,I 10 13 16
L Make and ship displays J 7 10 14
M Print and ship brochures K 6 8 10

 

 

 

6. (18 points)

 

Alice’s Alterations has eight jobs to be completed and only one sewing machine (and one sewing machine operator). The following jobs are waiting to be scheduled for the sewing machine. The letter of the alphabet indicates the sequence in which the jobs arrived. It is now the beginning of Day 5 and jobs are due at the end of the promised day.

 

Job Processing Time (in days) Promised Time (days from Day 0)
A 5 10
B 8 15
C 6 15
D 3 20
E 10 25
F 14 40
G 7 45
H 4 50

 

 

a) Prioritize these jobs by CR the (Critical Ratio) and Slack priority sequencing schemes using the definitions of these two schemes that were provided by your instructor.

 

 

 

 

 

 

 

 

b) Evaluate your priority sequences in a) on average flow time from now, average lateness (with no credit for being early) and average days early (with zero days early for a job that is late).

 

 

 

 

 

 

 

 

c) Based on your analysis in b), what sequencing scheme would you select? Why?

7. (22 points)

 

Weedandfeed Corporation retails chemicals for homes. One of Weedandfeed’s best selling pesticides is Pest-be-gone. The product is ordered from a wholesaler at a price of $600 per 100 pounds. 100,000 pounds of Pest-be-gone are estimated to be needed next year. Weedandfeed will use one of the following purchasing options for acquiring its product.

 

· It can order in the 1-15,000 pound range. If it selects this option, the holding cost is 35% of the acquisition cost per pound per year, and the ordering cost is $1,500 per order. If it selects this option, it can order any quantity as long as it is between 1 and 15,000 pounds

· As the second option, Weedandfeed can buy Pest-be-gone in quantities greater than 15,000 pounds. If it selects this option, it can order any quantity as long as it at least 15,001 pounds. If it selects this option, then the holding cost drops to 25% of the acquisition cost per pound per year because the supplier gives special late-payment privileges that reduce the interest charges that must ordinarily be paid to finance the inventory. However, ordering costs increase to $2,500 per order because of the extra handling costs.

 

a) Based on this information and wanting to use the low cost strategy, what is the optimal order quantity that Weedandfeed should select for acquiring its Pest-be-gone next year? Also, what is the lowest total cost for each of the two purchase options?

 

 

 

 

 

 

 

 

 

 

b) For the optimal order quantity selected in a) that provides the lowest total cost, determine the number of orders per year, time between orders, and the reorder point. There are 350 working days per year and the lead time is 5 days.

 

8. (10 points)

 

IPC manufactures resins and molded plastic products. One production department has ten injection-molding machines. The maintenance manager at the plant is studying this group of machines to determine how often the department should shut down all of the machines and perform preventive maintenance (PM). The nature of the department and its processes causes preventive maintenance (PM) to be performed on all of the machines at one time at a cost of $10,000 for the entire group of machines. When a machine breaks down, it costs $2,000 to repair it. The data from production records about machine breakdowns between PM has been analyzed and is provided below:

 

PM every n months Average Number of Breakdowns between PM
1 1.0000
2 2.6000
3 4.9100
4 8.0810
5 12.3146

 

 

 

a) Which PM policy provides the minimum cost strategy based on the information provided?

 

 

 

 

 

 

b) For each of the PM policies not selected in a), how much of a reduction in the PM cost (the total cost of performing a PM for all of the machines and not expressed in PM cost per machine per month) is required to have this PM policy equal to the PM policy selected in a)?

 

 

9. (10 points)

 

a) A product has four components A, B, C, and D. The finished product must have a reliability of .95. The first three components come from a supplier, and have reliabilities of working correctly of 0.99, 0.98, and 0.995 respectively. The fourth component is being designed now. What must the reliability of component D be in order to meet the product reliability condition? Calculate your result to 4 decimal places (0.xxxx).

 

 

 

 

 

 

 

 

 

b) General Grant must send orders to General Butler. Carrier pigeons are the medium of choice. A single pigeon has a 0.7 probability of arriving at the proper destination in a timely fashion. How many pigeons, each carrying an identical set of orders, must Grant send in order for him to have 98% confidence (reliability) that the orders reach General Butler?

10. (27 points)

 

Bragg’s Bakery is building a new automated bakery in downtown Omaha. Here are the activities that need to be completed to get the new bakery build and the equipment installed.

 

Activity Predecessor Normal Completion Time (Weeks) Crash Completion Time (Weeks) Crash (Expediting) Cost/Week
A 9 6 $3,000
B A 8 5 $3,500
C A 15 10 $4,000
D B,C 5 3 $2,000
E C 10 6 $2,500
F D,E 2 1 $5,000

 

 

You must show your work to receive full credit.

 

a) What are the values of the normal project completion time, the total work time using the normal times, and the critical path?

 

 

 

 

 

b) What activity(ies) should be crashed to reduce the completion time found in a) by one week? What activity(ies) should be crashed if you want to reduce the completion time found in a) by six weeks?

 

 

 

 

 

c) Bragg’s loses $3,500 in profit per week for every week the bakery is not completed. How many weeks will the project take if the bakery is willing to pay the crashing cost as long as it is economically the right decision?

 

 

 

 

 

 

d) What is the project completion time if all activities are crashed to their minimum Crash Time? Also, ignoring the $3,500 lost profit in c), what is the total additional cost incurred for crashing all of the activities to their minimum Crash Time compared to the Normal Times?

 
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