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3Num lExp imen s
In this section, we conduct the numerical experiments to illustrate our results.
The parameters are set as follows:
s
= 20,
c
= 10,
v
= 5. Consider two different
demand distributions: one is the exponential distribution with mean
μ
= 100,
the other is the truncated normal distribution with mean
μ
= 100 and standard
deviation
σ
∈{
25
,
50
,
100
}
. Note that the truncated normal distribution is de-
√
2
πσ
x
fined as
F
(
x
)=
I
(
x
)
−I
(0)
1
e
−
(
t−μ
)
2
/
2
σ
2
dt
. Suppose that
Y
is uniformly distributed and given by
g
(
y
)=1
,
0
1
,where
I
(
x
)=
−
I
(0)
−∞
1. We first analyze
the optimal ordering policy by fixing
h
= 5 and varying
λ
from1to5insteps
of 0.1. Then we test Corollary 1 by varying
h
from 0 to 50 in steps of 1.
Figures 2 and 3 illustrate the retailer's optimal order quantity with respect to
the loss aversion coecient when demand follows the exponential distribution
and truncated normal distribution, respectively. As shown in Fig. 3, the optimal
order quantity may be increasing or decreasing in
λ
under different levels of
≤
y
≤
300
σ
=25
σ
=50
σ
=100
240
280
230
220
260
210
240
200
190
220
180
200
170
1
1.5
2
2.5
3
3.5
4
4.5
5
1
1.5
2
2.5
3
3.5
4
4.5
5
Loss Aversion Coefficient
λ
Loss Aversion Coefficient
λ
Fig. 2.
Optimal policies with respect to
different loss aversion coecients. Demand
follows an exponential distribution.
Fig. 3.
Optimal policies with respect to
different loss aversion coecients and lev-
els of demand variation. Demand follows a
truncated normal distribution.
0.06
σ
=25
0.09
0.05
σ
=50
σ
=100
0.08
0.04
0.07
0.03
0.06
0.02
0.05
0.04
0.01
0.03
0
0.02
−0.01
0.01
−0.02
0
−0.03
−0.01
0
10
20
30
40
50
0
10
20
30
40
50
Shortage Cost h
Shortage Cost h
Fig. 4.
The values of
M
(
h, Q
0
)withre-
spect to different shortage costs. Demand
follows an exponential distribution.
Fig. 5.
The values of
M
(
h, Q
0
)withre-
spect to different shortage costs and lev-
els of demand variation. Demand follows a
truncated normal distribution.
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