Business Process Improvement - Exercises

Session 4 – Break-Even Analysis

  1. Assume a fixed cost of $900, a variable cost of $4.50 and a selling price of $5.50.
  1. What is the break-even point?
  2. How many units must be sold to make a profit of $500?
  3. How many units must be sold to average $0.25 profit per unit? $0.50 per unit? $1.50 per unit?
  1. A firm is selling two products, chairs and bar stools, each at $50 per unit. Chairs have a variable cost of $25 and bar stools have a variable cost of $20. Fixed costs for the firm are $20,000.
  1. If the sales mix is 1:1 (one chair sold for every bar stool sold), what is the break even point in dollars of sales? In units of chairs and bar stools?
  2. If the sales mix changes to 1:4 (one chair sold for every four bar stools), what is the break-even point in dollars of sales? In units of chairs and bar stools?

Session 4 – Process Design

  1. The desired daily output for an assembly line is 360 units. This assembly line will operate 450 minutes per day. The following table contains information on this product’s task times and precedence relationships.

Task / Task Time (seconds) / Immediate Predecessor
A / 30 / -
B / 35 / A
C / 30 / A
D / 35 / B
E / 15 / C
F / 65 / C
G / 40 / E,F
H / 25 / D,G
  1. Draw the precedence diagram.
  2. What is the workstation cycle time?
  3. Balance this line using the largest number of following tasks. Use the longest task time as a secondary criterion.
  4. What is the efficiency of your line balance?
  1. An assembly line is to be designed to operate 7½ hours per day and supply a steady demand of 300 units per day. Here are the tasks and their performance times:

Task / Preceding Tasks / Performance Time (seconds)
A / - / 70
B / - / 40
C / - / 45
D / A / 10
E / B / 30
F / C / 20
G / D / 60
H / E / 50
I / F / 15
J / G / 25
K / H, I / 20
L / J, K / 25
  1. Draw the precedence diagram.
  2. What is the workstation cycle time?
  3. What the theoretical minimum number of workstations?
  4. Assign tasks to workstations using the longest operating time.
  5. What is the efficiency of your line balance?
  6. Suppose demand increases by 10 percent. How would you react to this? Assume that you can only operate 7½ hours per day.

Session 5 – Capacity Management

  1. DroughtBreaker Irrigation P/L would like to determine capacity requirements for the next four years. Currently two production lines are in place for bronze and plastic sprinklers. Three type of sprinklers are available in both bronze and plastic: 90 degree nozzle sprinklers, 180 degree nozzle sprinklers, and 360 degree nozzle sprinklers. Management has forecast demand for the next four years as follows:

Yearly Demand
1 (in 000s) / 2 (in 000s) / 3 (in 000s) / 4 (in 000s)
Plastic 90 / 32 / 44 / 55 / 56
Plastic 180 / 15 / 16 / 17 / 18
Plastic 360 / 50 / 55 / 64 / 67
Bronze 90 / 7 / 8 / 9 / 10
Bronze 180 / 3 / 4 / 5 / 6
Bronze 360 / 11 / 12 / 15 / 18

Both production lines can produce all the different types of nozzles. Each bronze machine requires two operators and can produce up to 12,000 sprinklers. The plastic injection moulding machine requires four operators and can produce up to 200,000 sprinklers. Three bronze machines and one injection machine are available. What are the capacity requirements for the next four years.

Session 6 – Critical Path Method (CPM)

  1. The following activities are part of a project to be scheduled using CPM:

Task / Immediate Predecessor / Time (weeks)
A / - / 6
B / A / 3
C / A / 7
D / C / 2
E / B, D / 4
F / D / 3
G / E,F / 7
  1. Draw the network.
  2. What is the critical path?
  3. How many weeks will it take to complete the project?
  4. How much slack does activity B have?
  1. Schedule the following activities using CPM:

Task / Immediate Predecessor / Time (weeks)
A / - / 1
B / A / 4
C / A / 3
D / B / 2
E / C,D / 5
F / D / 2
G / F / 2
H / E, G / 3
  1. Draw the network.
  2. What is the critical path?
  3. How many weeks will it take to complete the project?
  4. Which activities have slack, and how much?
  1. A construction project is broken down into the following 10 activities:

Task / Immediate Predecessor / Time (weeks)
1 / - / 4
2 / 1 / 2
3 / 1 / 4
4 / 1 / 3
5 / 2, 3 / 5
6 / 3 / 6
7 / 4 / 2
8 / 5 / 3
9 / 6, 7 / 5
10 / 8, 9 / 7
  1. Draw the network.
  2. What is the critical path?
  3. If activities 1 and 10 cannot be shortened, but activities 2 through 9 can be shortened to a minimum of one week each at a minimum of $10,000 per week, which activities would you shorten to cut the project by four weeks?

Session 8 – Cost of Quality

  1. A company currently using an inspection process in its material receiving department is trying to install an overall cost reduction program. One possible reduction is the elimination of one inspection position. This position tests material that has a defective content on the average of 0.04. By inspecting all items, the inspector is able to remove all defects. The inspector can inspect 50 units per hour. The hourly rate including fringe benefits for this position is $9. If the inspection process is eliminated, defects will go into product assembly and will have to be replaced later at a cost of $10 each when they are detected in final product testing.
  1. Should this inspection position be eliminated?
  2. What is the cost to inspect each unit?
  3. Is there a benefit (or loss) from the current inspection process? How much?
  1. Output from a process contains 0.02 defective units. Defective units that go undetected into final assemblies cost $25 each to replace. An inspection process, which would detect and remove all defectives, can be established to test these units. However the inspector, who can test 20 units per hour, is paid $8 per hour, including fringe benefits.
  2. Should an inspection station be established to test all units?
  3. What is the cost to test each unit?
  4. What is the benefit (or loss) from the inspection process?

Session 9 – Operations Scheduling

  1. A hotel has to reschedule its receptionists according to hourly loads. Management has identified the number of receptionists needed to meet the hourly requirement, which changes from day to day. Assume each receptionist works a four hour shift. Given the following staffing requirements in a certain day, use the first hour principle to find the personnel schedule:

Period
8am / 9am / 10am / 11am / Noon / 1pm / 2pm / 3pm / 4pm / 5pm / 6pm / 7pm
Requirement / 2 / 3 / 5 / 8 / 8 / 6 / 5 / 8 / 8 / 6 / 4 / 3
Assigned
On Duty

Session 9 – Kanban

  1. A supplier of instrument gauge clusters uses a Kanban system to control material flow. The gauge cluster housings are transported five at a time. A fabrication centre produces approximately 10 gauges per hour. It takes approximately two hours for the housing to be replenished. Due to variations in processing times, management has decided to keep 20 percent of the needed inventory as safety stock. How many Kanban card sets are needed?
  1. Transmissions are delivered to the fabrication floor four at a time. It takes one hour for transmissions to be delivered. Approximately four vehicles are produced each hour, and management has decided that 50 percent of expected demand should be maintained as safety stock. How many Kanban card sets are needed?

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