ENM 509 - Homework 2
Due 31.03.2016
1. Consider the data below. Assume that you are at the beginning of year 2015 and using the
data for year 2012, 2013 and 2014, forecast the demand in each quarter of years 2015 and
2016:
Year
Quarter
2012
I
II
III
IV
I
II
III
IV
I
II
III
IV
I
II
III
IV
I
II
III
IV
2013
2014
2015
2016
Black
Plastic
Demand
2250
1737
2412
7269
3514
2143
3459
7056
4120
2766
2556
8253
5491
4382
4315
12035
5648
3696
4843
13097
Clear
Plastic
Demand
3200
7658
4420
2384
3654
8680
5695
1953
4742
13673
6640
2737
3486
13186
5448
3485
7728
16591
8236
3316
a) Using the static forecasting method
b) Using Winter’s method considering =0.3, =0.2, =0.1
c) Find the bias, TS, MAD, MAPE and MSE for both parts (a) and (b) using your forecasts
and the actual data for years 2005 and 2006.
d) Find the optimal values of ,  and  that minimizes the total MSE of your forecasts for
years 2005 and 2006. (You can use Excel Solver to find these optimal values.)
2. Consider the following data which shows the demand(D), unit holding cost(h) and
ordering cost(A) in each of the following 8 months. Find the optimal ordering strategy using
Wagner-Whitin Algorithm and compare it with the strategy obtained by the Silver-Meal
Heuristic.
t
1
2
3
4
5
6
7
8
D
30
10
60
25
45
50
20
40
h
1
1
1
2
2
1
2
1
A
100
50
150
100
100
100
50
100
3. A company manufactures 2 types of products, product A and product B with DAt and DBt
denoting the demand for products A and B respectively in month t. The company needs to
make a production plan for the following N months. The plant operates 8 hours a day for Mt
days in month t. Production of product A takes pA hours and production of product B takes pB
hours of worker time. Each worker is paid $S per hour with a 50% premium for any overtime.
The plant currently has W0 workers. Overtime is limited to Ot hours per worker in period t.
The cost of holding product A in inventory is $hA per month and the cost of holding product
B in inventory is $hB per month. The cost of backlog of product A is $bA per month and the
cost of backlog for product B is $hB per month. The company requires to have KA units of
inventory of product A and KB units of inventory of product B at hand at the end of month N.
The cost of hiring a new worker is $H and the cost of firing a worker is $F. It takes a worker 2
months to reach full potential. During these two months, a new worker provides only 50
percent productivity. The company can also buy products A and B from a third party instead
of producing it himself. The third party charges $cA and $cB for products A and B,
respectively. Write the LP model to minimize the total cost of production for this problem.