TOBB ETÜ 2014-2015 SPRING SEMESTER
END 307- PRODUCTION SYSTEMS PLANNING
HW4
Assignment date: Feb. 12th, Due date: Feb. 19th, Submit it in the first class hour
Q1. Production setup cost to produce a component is K=180+70x(Factor X) $. Per unit cost of the
component is c=15+13x(Factor X)$ and the annual inventory holding cost ratio is estimated to be
I=20+16x(1-Factor X)%. The estimated demands for the component in the next eight weeks are given
in the following table.
a. Using the economic order quantity and the periodic order quantity heuristics, determine the
production lot sizes in each week?
b. Write down the mathematical programming model to determine optimal production lot size.
c. Write down the mathematical programming model where the objective is to minimize only the
total setup cost while restricting average inventory to be less than 350. (Explain only the differences
from the model in item b)
d. Construct the optimization model in item b above in Excel and obtain the optimal solution. Include
only the printout of the excel file in the submission.
Week
1
2
3
4
5
6
7
8
Forecasted demand
10
60
320
40
200
250
75
150
Q2. A Sports Goods store sells sports shoes. The store will sell a particular sport shoe in the summer
season. The purchase price is 65+20x(Factor X) TL per pair and selling price is 120+35x(Factor X) TL.
At the end of summer, any leftover of this particular shoe can be carried to the outlet store and sold
for 55 TL per pair. It takes 3,5*(1-Factor X) TL per pair to transport the shoes to the outlet. The store
considers that there is a 10% inventory holding cost for a summer season period. The past sale data
on similar shoes for the last 46 seasons is analyzed and the mean demand per season turns out to be
57,02 pairs and the standard deviation is 22,07 pairs (Data is given in the appendix).
a. Assuming that the demand follows a normal distribution, find the optimal number of pairs that the
store should order at the beginning of the summer season.
b. Using the empirical distribution (in the appendix), find the optimal number of pairs that the store
should order.
c. If, in case of a shortage the store can buy the shoes from a competitor firm for 125 TL per pair and
satisfy the demand, what would be the order size? (Under normal distribution assumption).
Appendix;
Q1. Data
Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Number of
pairs sold
75
63
53
79
56
86
39
82
71
36
33
39
58
72
60
73
23
58
48
11
32
20
68
21
43
114
70
72
67
27
39
67
47
68
68
36
37
38
39
40
41
42
43
44
45
46
50
58
35
76
100
42
86
61
76
33
68
Avr
Std
Empirical distribution
Bin
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
Kümülatif
Frekans
%
1
2,17%
0
2,17%
0
2,17%
0
2,17%
0
2,17%
0
2,17%
0
2,17%
0
2,17%
0
2,17%
1
4,35%
1
6,52%
0
6,52%
1
8,70%
0
8,70%
0
8,70%
0
8,70%
1
10,87%
0
10,87%
0
10,87%
0
10,87%
0
10,87%
1
13,04%
2
17,39%
0
17,39%
1
19,57%
1
21,74%
0
21,74%
57,02174
22,07713
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
0
3
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
3
0
1
1
0
1
0
0
0
2
4
0
1
1
2
1
0
1
2
0
0
1
0
0
1
0
21,74%
28,26%
28,26%
28,26%
30,43%
32,61%
32,61%
32,61%
32,61%
34,78%
36,96%
36,96%
39,13%
39,13%
39,13%
41,30%
41,30%
41,30%
43,48%
43,48%
50,00%
50,00%
52,17%
54,35%
54,35%
56,52%
56,52%
56,52%
56,52%
60,87%
69,57%
69,57%
71,74%
73,91%
78,26%
80,43%
80,43%
82,61%
86,96%
86,96%
86,96%
89,13%
89,13%
89,13%
91,30%
91,30%
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
Diğer
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
91,30%
91,30%
95,65%
95,65%
95,65%
95,65%
95,65%
95,65%
95,65%
95,65%
95,65%
95,65%
95,65%
95,65%
95,65%
95,65%
97,83%
97,83%
97,83%
97,83%
97,83%
97,83%
97,83%
97,83%
97,83%
97,83%
97,83%
97,83%
97,83%
97,83%
100,00%
100,00%