Question

Festive Floral is gearing up for online carnation sales this Mother’s Day. They specialize in selling organic extra-large red and pink carnations. The price is $0.7 per stem, which includes free one-day shipping to the customer. Festive Floral pre-orders carnations directly from a certified organic farm at the cost of $0.15 per stem. The order is made prior to the growing season and flowers are grown accordingly, so the pre-order quantity cannot be changed. However, if Festive Floral runs out of pre-ordered carnations, they can always pick up more immediately from a local wholesaler that carries carnations of the same quality, at the price of $0.5 per stem. Historical demand for the past 10 years are given below.

Year: Red, Pink; 2008: 4008, 3288; 2009: 3948, 3648; 2010: 4092, 3636; 2011: 3984, 3684; 2012: 3996, 3792; 2013: 3888, 3720; 2014: 4128, 3564; 2015: 4104, 3744; 2016: 4380, 3828; 2017: 4392, 3744

For all questions below, please round your answers to two decimal points. Show your work by explaining the steps of your calculation.

(a) Using exponential smoothing with parameter ?? = 0.9, what is your forecast for red carnations in 2018? What is the MAD of your forecast?

(b) Based on the forecast above, what is the optimal number of red carnations to pre-order from the farm?

(c) Repeat Parts (a) and (b) for pink carnations.

Answer 1

price/stem	0.7
cost	0.15
cost from a local wholesaler	0.5
	Demand
Year	Red	Pink
2008	4008	3288
2009	3948	3648
2010	4092	3636
2011	3984	3684
2012	3996	3792
2013	3888	3720
2014	4128	3564
2015	4104	3744
2016	4380	3828
2017	4392	3744
a) ?	0.9
Exponential Smoothing:
F(t+1)=?D(t)+(1-?)F(t)
MAD = ?|Demand-Forecast|/n
Year	Red	Forecast	|Demand-Forecast|
2008	4008	4008.00	0.00
2009	3948	4008.00	60.00
2010	4092	3954.00	138.00
2011	3984	4078.20	94.20
2012	3996	3993.42	2.58
2013	3888	3995.74	107.74
2014	4128	3898.77	229.23
2015	4104	4105.08	1.08
2016	4380	4104.11	275.89
2017	4392	4352.41	39.59
2018		4388.04
(assuming F(2008)=4008)
Forecast for red carnations in 2018=			4388.04
MAD=			94.83
b) Optimal number of red carnations:
mean demand	4092.00
std dev of demand	171.49
Overage cost (cost of overstocking), Co = Cost-Salvage value
Underage cost (cost of understocking), Cu = Selling price - cost
Co	0.15
Cu	0.55
Critical ratio, C = Cu/(Cu+Co)
C	0.79
corresponding z value	0.81
optimal number of red carnations to pre-order from the farm= mean demand + z * std dev of demand
=	4230.29	carnations
c)
?	0.9
Exponential Smoothing:
F(t+1)=?D(t)+(1-?)F(t)
MAD = ?|Demand-Forecast|/n
Year	Pink	Forecast	|Demand-Forecast|
2008	3288	3288.00	0.00
2009	3648	3288.00	360.00
2010	3636	3612.00	24.00
2011	3684	3633.60	50.40
2012	3792	3678.96	113.04
2013	3720	3780.70	60.70
2014	3564	3726.07	162.07
2015	3744	3580.21	163.79
2016	3828	3727.62	100.38
2017	3744	3817.96	73.96
2018		3751.40
(assuming F(2008)=3288)
Forecast for pink carnations in 2018=			3751.40
MAD=			110.83
Optimal number of pink carnations:
mean demand	3664.80
std dev of demand	153.49
Overage cost (cost of overstocking), Co = Cost-Salvage value
Underage cost (cost of understocking), Cu = Selling price - cost
Co	0.15
Cu	0.55
Critical ratio, C = Cu/(Cu+Co)
C	0.79
corresponding z value	0.81
optimal number of pink carnations to pre-order from the farm= mean demand + z * std dev of demand
=	3788.58	carnations

formulae used: