1. CBF, Inc. CBF is a small manufacturer who makes circuit boards. They are having a throughput problem. They need to complete 1000 boards/shift. They produce boards in batches. The desired batch throughput is 60 boards, but they currently start with a batch of 75 boards and lose 15% in the Inspection step and 5% in Final Test.
The basic data is 1000 boards required per 7.5 hour shift (.5hr is lost to breaks) working 5 days a week. The process step data is shown in the table below:
|
Process Step
|
# Machines
|
# Employees
|
Setup (minutes)
|
Run (mins/batch)
|
|
Load
|
1
|
1
|
5
|
3.33
|
|
Clean
|
1
|
|
|
1.5
|
|
Coat
|
1
|
|
|
2.5
|
|
Unload
|
1
|
1
|
|
3.50
|
|
Expose
|
5
|
5
|
15(each machine)
|
3.72
|
|
Load
|
1
|
1
|
5
|
5.33
|
|
Develop
|
1
|
|
|
2.33
|
|
Inspect
|
2
|
2
|
|
7.5
|
|
Bake
|
1
|
|
|
1.5
|
|
Unload
|
1
|
1
|
|
3.3
|
|
Drilling
|
6
|
3
|
15(each machine)
|
7.5
|
|
Plating
|
1
|
2
|
5
|
3.25
|
|
Final Test
|
6
|
6
|
15(each machine)
|
6.00
|
Currently the process is completing 700 boards per day. The first 4 steps use one machine. The next batch can start when the current batch completes. Steps 6-10 also use a single machine. Inspection is done with the boards loaded in that machine. Each of the other steps uses its own machine(s). Each machine can start the next batch when the current batch completes.
a. What is the maximum capacity of the process?
b. What is the impact of losses in Inspection and Final test?
c. Where is the bottleneck?
d. What do you recommend as a short term solution to the capacity problem?
e. What long term recommendations would you make?
2. Applichem wants to allocate the capacity of its worldwide manufacturing plants to fulfill its customer demand. Applichem makes a product, R, which is used by plastic molding companies around the world. R sells for $1/lb. Its plants are located in Gary, Indiana, Windsor, Ontario, Frankfurt, Germany, Mexico City, Caracus, Venezula, and Osaka, Japan. Its current strategy is to make and ship R as shown in the table below (x 100,000 lbs)
|
From/To
|
Mexico
|
Canada
|
Venezula
|
Europe
|
United States
|
Japan
|
|
Mexico City
|
3.0
|
|
6.3
|
|
|
|
|
Windsor
|
|
2.6
|
|
|
|
|
|
Caracus
|
|
|
4.1
|
|
|
|
|
Frankfurt
|
|
|
5.6
|
20.0
|
12.4
|
|
|
Gary
|
|
|
|
|
14.0
|
|
|
Japan
|
|
|
|
|
|
4.0
|
Plant Production Costs and Capacity are shown in the table below:
|
Plant
|
Cost/1000lbs
|
Capacity (100,000 lbs)
|
|
Mexico City
|
95.01
|
22.0
|
|
Windsor
|
97.35
|
3.7
|
|
Caracas
|
116.34
|
4.5
|
|
Frankfurt
|
76.69
|
47.0
|
|
Gary
|
102.93
|
18.5
|
|
Osaka
|
153.80
|
5.0
|
The current Transportation Cost ($/1000 lb), Import Duties, and current customer Demand are shown in the table below:
|
Plant/Country
|
Mexico
|
Canada
|
Venezuela
|
Europe
|
United States
|
Japan
|
|
Mexico City
|
0
|
11.40
|
7.00
|
11.00
|
11.00
|
14.00
|
|
Windsor
|
11.00
|
0
|
9.00
|
11.50
|
6.00
|
13.00
|
|
Caracas
|
7.00
|
10.00
|
0
|
13.00
|
10.40
|
14.30
|
|
Frankfurt
|
10.00
|
11.50
|
12.50
|
0
|
11.20
|
13.30
|
|
Gary
|
10.00
|
6.00
|
11.00
|
10.00
|
0
|
12.50
|
|
Osaka
|
14.00
|
13.00
|
12.50
|
14.20
|
13.00
|
0
|
|
Demand
(100,000 lbs)
|
3.0
|
2.6
|
16.0
|
20.0
|
26.4
|
11.9
|
|
Import Duty
|
|
|
50%
|
9.5%
|
4.5%
|
6%
|
Your boss has asked you to look at this and suggest improvements to increase profit.
a. What is the current cost being incurred and profit earned?
b. Build a LP model to represent the situation. Hint you need a variable for product shipped from each plant to each destination, for the total produced at each plant and the total received in each country.
c. Solve the LP model using POM/QM and develop your recommendation.
3. DAT, Inc. needs to develop an aggregate plan for its product line. Its relevant data is given below:
Production Time 1 hr/unit Beginning Inventory 500 units
Std Labor Cost $10/hr Safety Stock 1000 units
Overtime 150%
Workweek 5 days, 8 hrs/day Shortage Cost $20/unit/month
Days/Month 20 Carrying Cost $5/unit/month
Demand forecast is given in the table below:
|
Month
|
Demand (units)
|
|
January
|
2500
|
|
February
|
3000
|
|
March
|
4000
|
|
April
|
3500
|
|
May
|
3500
|
|
June
|
3000
|
|
July
|
3000
|
|
August
|
4000
|
|
September
|
4000
|
|
October
|
4000
|
|
November
|
3000
|
|
December
|
3000
|
If management wants a constant workforce and to limit overtime to 10 hrs/employee/week, determine the level of employment which minimizes cost
Make any necessary assumptions.
4. Given the following information, determine an inventory management system for an item in demand 50 weeks/year.
Item Cost $10
Order Cost $250
Annual Holding Cost $3.33/unit
Annual Demand 25,750
Weekly demand 515
Std Dev of Demand 25/week
Lead Time 1 week
Std Dev of Lead Time 0.1 week
Service Level 95%
a. State the order quantity and re-order point
b. Determine the annual holding and order costs
c. If a price break of $50/order was offered for orders over 2000 units, should you plan on 2000 unit orders?
5. Assume that you have been selected by your executives to teach your fellow managers about Bottlenecks and the Theory of Constraints. Prepare a Powerpoint presentation on this subject for a 45 minute slot at the Manager's Kickoff meeting in January. Include speaker notes for each slide, as the HR manager wants to use this presentation at the quarterly new manager training, and you will not be the presenter.