UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING
FINAL EXAMINATION, APRIL 2002
MIE363H1S - RESOURCE AND PRODUCTION MODELING
Exam Type: B
Examiner: D.M. Frances
A sheet of Formulas is provided.
20
1. A regional automotive parts wholesaler purchases catalytic converters from the
manufacturer for distribution to regional dealers and automotive repair shops. Annual
demand is constant at 100,000 units, carrying cost is $30 per unit per year, ordering cost
is $250 per order, orders are delivered without delay and backorders are not allowed.
The purchase cost is $200 per converter. For orders of at least 1,000 units the price is
reduced by 2%, for orders of at least 5,000 units the price is reduced by 3% and for orders
of at least 10,000 units the price is reduced by 3.5%. All reductions apply to the per-unit
cost of $200. Determine the ordering policy which minimizes the total cost per year.
20
2. The Gotham City Hospital (GCH) is in the process of studying the inventory policies of
its blood bank. Most of the time the daily blood demand is fairly steady at 440 units, but
for 21% of the days it jumps to 460 units, and for 15% of the days it dips to 420 units.
The carrying cost of blood is estimated at $2.25 per unit per year. Ordering is estimated at
$63 per order, and it takes 2 days before the order arrives. If GCH incurs a temporary
blood shortage it can receive “express” delivery at a cost of $1.50 per unit; these units are
then subtracted from the next order. How low should GCH allow its inventories to drop
before it reorders, and how much should it reorder?
20
3. Six chapters must be typed and proofed as soon as possible. Jack does the typing; Jill
does the proofing and correcting. Generally the typing takes longer than the proofing, but
some chapters are easier to type than to proof. The estimated time, in minutes, for each
activity is as follows:
Chapter
Typing
Proofing/Correcting
1
30
20
2
90
25
3
60
15
4
45
30
5
75
60
6
20
30
In what order should the chapters be processed? When can they expect to finish?
4. The Bill Deplant Company is planning an expansion program over the next 4 years. At
the beginning of period 1, the firm has a capacity of 100 units. The company estimates
that it should have at least a capacity of 120 units in year 2, 150 units in year 3, and 190
units in year 4. It takes a full year to construct the capacity expansion. During the
construction period only the existing production is accessible. The expansion costs in
2002 dollars are given in the table below:
From
100
120
150
120
1000
-
To
150
1800
1500
-
190
3000
3000
2000
The operating costs in 2002 dollars associated with running a plant of a given capacity at
a given level of demand are as follows:
Capacity
100
120
150
190
100
500
1200
1700
2500
Demand
120
150
1000
1600
1500
2400
2200
190
2000
Use Dynamic Programming to determine the optimal expansion plan.
5. The Yeasty Brewing Company produces a popular local beer known as Iron Stomach.
Beer sales are somewhat seasonal, and Yeasty is planning its production and manpower
levels on March 31st for the next six months. The demand forecasts are
Month
April
May
June
July
August
September
Production
Days
11
22
20
23
16
20
Forecast Demand
(in hundreds of cases)
85
93
122
176
140
63
As of March 31, Yeasty had 86 workers on the payroll. Over a period of 26 working days
when there were 100 workers on the payroll, Yeasty produced 12,000 cases of beer. The
cost to hire each worker is $125, and the cost of laying-off each worker is $300. Holding
costs amount to 75 cents per case per month. As of March 31st, Yeasty expects to have
4,500 cases of beer in stock, and it wants to maintain a minimum buffer inventory of
1,000 cases each month. It plans to start October with 3,000 cases in hand. Formulate the
linear program that minimizes Yeasty’s costs.
Formulas*
[D
Demand Variability 
 E(D)] 2
n
E(D)
i
For the backlog case, where x is the demand during the lead time (L) period:
r*  Min{r | Pr(x  r) 
hq *
}
c B E(D)
For the lost sale case, where x is the demand during the lead time (L) period:
r*  Min{r | Pr(x  r) 
hq *
}
hq * c LS E(D)
For the backlog case, where x is the demand during the period L+R, where L is the lead time and
R is the time between inventory reviews:
S*  Min{S | Pr(x  S) 
Rh
}
cB
For the lost sale case, where x is the demand during the period L+R:
S*  Min{S | Pr(x  S ) 
Rh
}
Rh  c LS
If D is a normally distributed demand in a period of length T, with mean D and variance D2,
then the demand over a period kT will be normally distributed with mean kD and variance kD2.
*Note: Not all formulas are relevant to the questions on the exam.