Subject: Business    / Management    

A manufacturing firm has four production departments: A, B, C, and D. Estimates for the annual material flows between departments are as follows:
Interdepartmental Flow
(number of loads/year)

Dept.    A B C D
A – 300 200 300
B – 500 400
C – 250
D –

The firm is moving to another building consisting of six large, equal-sized areas.
1 2 3
4 5 6

All material will be transported by forklift in standard-sized crates. The transportation costs for a load are estimated to be $0.10 per metre. The distances between the locations in the new building are as follows:
Distance (metres)

Location 1 2 3 4 5 6
1 – 180 280 130 200 330
2 – 180 200 130 230
3 – 300 230 130
4 – 180 350
5 – 180
6 –

Some of the layout decisions have already been made. The corner of the building where location 1 is situated lies on a major street intersection. To enhance the firm’s image, management has decided that location 1 should house the firm’s offices. Location 5 is unavailable because the boilers and other plant utilities are located there and it would be prohibitively expensive to move them.

Other considerations further limit the number of possible layouts. Location 3 is the only area with loading docks and access for large trucks, so Department D, shipping and receiving, must be placed in location 3. The operations performed in Department C, the stamping department, are extremely noisy so it must not be placed next to the offices situated in location 1.
a.    Show all possible layouts for the factory that satisfy the preceding requirements.

b.    Evaluate the annual material handling cost for each of the possible layouts. Which layout is better in terms of material handling costs?

2. (20 marks)

The following table presents the tasks, durations, and immediate predecessors necessary to produce a particular product on an assembly line. The required daily output is 320 units, and the working day is 8.0 hours.
Activity Immediate Predecessor Duration (in minutes)
A – 0.9
B – 0.7
C – 0.8
D B 0.4
E B, C 0.5
F A, D 0.4
G E 0.6
H F, G 0.5
I H 1.1

a.    Draw the precedence diagram for this problem.

b.    Determine the required cycle time.

c.    Determine the theoretical minimum number of workstations.

d.    The positional weight of a task is the sum of the task time plus the task times of all following tasks. Calculate the positional weights of the tasks.

e.    Assign tasks to workstations, using “highest positional weight” as the primary rule and “longest operating time” as the secondary rule. Show your calculations and task assignments in a chart similar to those in used in the online lessons.

f.    Calculate the efficiency of the solution.

3. (15 marks)

Sales of an electric kettle over the last eight months are given in the following table:

Month 1 2 3 4 5 6 7 8
Sales (units) 37 38 35 39 45 42 38 44

Forecast sales of the kettle in month 9 using the following methods:
a.    a naive forecast

b.    a three-period simple moving average

c.    a three-period weighted moving average using weights of 0.6 for the most recent, 0.3 for the second most recent, and 0.1 for the third most recent observation

d.    an exponential smoothing forecast using ?= 0.2; the exponential smoothing forecast for month 8 was 39.1 units.
4. (10 marks)

Different forecasting techniques were used to forecast demand for an item. The actual demand and the two sets of forecasts are as follows:
Actual Demand Forecast Using Method 1 Forecast Using Method 2
160 148 165
150 155 170
180 174 182
190 180 190
200 205 195
275 255 215

Compute the MAD for each set of forecasts. Which forecast appears to be most accurate?

5. (15 marks)

Quarterly sales in units for the last two years are as follows:
Quarter Year 1 Year 2
I 280 380
II 345 415
III 130 148
IV 215 270

Using linear regression, a straight line was fitted to the sales data. The equation of the fitted line is Y = 210 + 15 × t. The first quarter in the data is labeled t = 1.
a.    Calculate seasonal indexes for this product using the fitted line approach.

b.    Using the fitted line and seasonal indexes you have just calculated, forecast sales in each quarter of year 3.
6. (20 marks)

Acme Fine Furniture is a major producer of bookcases. The following are the estimates of demand, cost, and production data for the next six months.
Cost data
Hiring cost/worker
Layoff cost/worker
Straight time cost/hour
Holding cost/unit/month
Backorder cost/unit/month
Subcontracting cost/unit
Overtime cost/hour N/A

Production data
Working hours/day
Labour requirement
Safety stock
Beginning inventory
Planning horizon (months) 8


Monthly demand and working days

Month Demand
Forecast Working
October 900
900 20

Develop two aggregate production schedules. (The table formats used in the aggregate planning example in your textbook may be convenient for preparing your answers.)

a) Constant Workforce Plan; Varying Inventory and Stockouts. Use a constant workforce large enough to produce enough units over the six months to meet total forecast demand. All workers must be full-time workers. Assume stockouts result in backorders which must be satisfied from production in following periods.

b) Constant Workforce Plan; Overtime. Use a constant workforce of 20 workers and use overtime to meet any additional output requirements.