7.2 Four cases
7.2.2 Case 2: Application of industrial engineering to price strategy
In a marketing mix, price has a close relationship with product design, marketing chan- nels, and promotion because while setting the price, market demand, competition, con- sumer behavior, and government regulations must be taken into account. This case takes the price prediction of the wholesale market as the research subject to demonstrate the application of industrial engineering to price strategy.
7.2.2.1 Case preface
In Taiwan, computer auction skills are implemented in four wholesale flower markets, viz., Taipei, Taichung, Changhua, and Tainan. The computer auction quantity of cut flowers in those four markets is about 90% of the total auction quantity in Taiwan. The income of a wholesale flower market comes from the auction charge, which is positively correlated to
Table 7.1 Results of the Product Combination Association of the Agricultural Enterprises Group number Association group Support (%) Confidence (%)
1 Oranges→ K153 or persimmons 13 72.22
K153→ oranges 13 100.00
Persimmons→ oranges 13 100.00
2 Grapes→ K153 6 100.00
K153→ grapes 6 100.00
3 Bamboo shoot → K100 or plums 6 100.00
K100→ bamboo shoot plums 6 66.67
→ bamboo shoot 6 66.67
4 Roses→ K170 5 71.43
the total auction value. If wholesale flower markets want to raise their total auction value, they must make an effort to increase the auction price or the auction quantity.
The objective of this case is to analyze the relationship between the auction time per box and the auction price of cut flowers in the four wholesale flower markets in Taiwan.
From the results, we formulate a mathematical model to determine the optimal auction time per box of cut flowers at the highest auction price.
7.2.2.2 The auction process in the wholesale flower market
The auction unit for cut flowers is the “box,” because the flowers are auctioned one box at a time. Before the auction, the cut flowers are packed in boxes and moved by conveyers or carts in sequence. The auction staff will auction the cut flowers box by box. They must orally describe the quality of the cut flowers, predict a deal auction price, and set an initial price by observing the “buying atmosphere” (i.e., competition among the buyers). They usually set the initial price 20% higher than the deal auction price. When the computer auction begins, the initial price set by the auction staff keeps falling at certain intervals until the first buyer presses a control button (the equipment used in computer auctions) to show that he or she wants to buy. The buyer’s information will then be shown on the information board. At this moment, the computer will stop the price from falling, and the number of cut flowers bought by the first buyer will be deducted from the total quantity.
The auction process for this box of flowers is completed (Chen, 1997). The data from the Taipei Wholesale Flower Market show that the average auction time for a box of cut flow- ers is 5 sec.
7.2.2.3 Research approach
We use cut flower auction data from the four wholesale flower markets in Taiwan collected on January 9, 2000, which, according to the auction staff, is representative of the typical auction quantity, the types of cut flowers, and the variation in auction time. The informa- tion used in this research contains auction time, price, and quantity per box for each type of cut flower. The probability density function (p.d.f.) for the auction time per box for dif- ferent types of cut flowers is then determined.
In terms of auction quantity and auction price, there are 30 types of cut flowers auc- tioned. Owing to insufficient quantity of flowers, 11 types are excluded and the remaining 19 types are our research subjects. They are: Anthurium (An), Chrysanthemum (Ch), Spray Chrysanthemum (SC), Gerbera (Ge), Gludiolus (Gl), Bird of Paradise (Bp), Butterfly Lily (Bl), Dancing Lady (DL), Rose (R), Casablanca (Cb), Longiflorum (Lf), Eustoma (Eu), Baby’s Breath (Bb), Lucky Bamboo (LB), Oncidium (On), Celosia plumosa (Cp), Solidago altissima (Sa), Gypsophila paniculata (Gp), and Dendrobium (Do).
Stat:fit software is used to determine whether the p.d.f. for the auction time per box is the same. We estimate the auction time per box for each type of cut flower using the p.d.f.
format and their parameters, and find that the auction times per box for all the 19 types do not follow the same p.d.f. at the Taipei Wholesale Flower Market. We also notice that the p.d.f. for auction time for each type of cut flower is not the same in the other three markets.
There are many factors affecting the auction time p.d.f. for each type of cut flower, such as quality and type of flower and buyer demand. The results show that the type of cut flower affects the auction time. Thus, we discuss the relationship between auction time and auction price per box with the factor “types.” We perform a regression analysis con- sidering the different types of cut flowers. We set up 19 regression models for auction time and auction price per box based on their types and compute them using SPSS software.
150 Handbook of industrial and systems engineering 7.2.2.4 Research results
After concluding the regression relationship for the auction time and the price per box, we set up an integer linear programming model M1 and solve it using CPLEX software. In model M1, we attempt to determine “the optimal auction time for each main type of cut flower at its highest auction price.”
The objective function in model M1 is to maximize the auction price for all varieties of cut flowers at the four wholesale flower markets net. Amfn,Bmfn, Cmfn, and Dmfn be the coefficients in the regression models. The optimal auction time per box multiplied by the number of boxes should not exceed the total auction time for each auction line at each wholesale flower market.
We use the average and standard deviation of the auction time for each main type of cut flower to determine the upper and lower limits of auction time and to exclude extreme values. We test the auction time per box on the basis of one, double, or triple standard deviation. Within one standard variation, the estimated auction time per box is closest to the real auction time. Therefore, we set the auction time per box to be within one standard deviation of the auction time, as shown in Equation 7.3.
(M1) Maximize
(Amfn B S C Smfn mfn D S Xmfn ) mfnS S U
V
n mfn
mfn
+ + +
=
=
∑
∑
31 2 3ff m=
∑
=∑
41 191 (7.1)subject to
(Qmfn S XmfnS) Tmn,m , , , ;n , ,
S U V
mfn mfn
× × ≤ = =
∑
= 1 2 3 4 1 2 3ff=
∑
191 (7.2)Umfn≤ (S X× mfnS)≤Vmfn,m=1 2 3 4, , , ;n=1 2 3, , ;f =1 2 3 ..., 19, , ,.
S U V
mfn mfn
∑
= (7.3)XmfnS m n f
S U V
mfn
≤ = = =
=
1, 1 2 3 4, , , ; 1 2 3, , ; 1 2 3, , ,...,19
∑
mfn (7.4)XmfnS is binary where
m: indicator of the wholesale flower markets, m= 1,2,3,4 f: indicator of the types of cut flowers, f= 1,2,…,19 n: indicator of the auction lines, n= 1,2,3
S: auction time for a box of cut flowers, S= Umfn,Umfn + 1,…,Vmfn
Decision variables:
XmfnS:
represents the auction time for a box
=
1, of type cut flowers at auction line
in w
f n
m holesale flow otherwise
0,
⎧
⎨⎪⎪
⎩⎪
⎪
S: auction time for a box of cut flowers (unit: sec) Parameters:
Amfn:the intercept for the regression model between auction time and price for a box of f-type cut flowers at n auction line in m wholesale flower market
Bmfn: the first-degree coefficient of the regression model between auction time and price for a box of f-type cut flowers at nauction line in m wholesale flower market
Cmfn: the second-degree coefficient of the regression model between auction time and price for a box of f-type cut flowers at n auction line in mwholesale flower market
Dmfn: the third-degree coefficient of the regression model between auction time and price for a box of f-type cut flowers at n auction line in mwholesale flower market
Qmfn: total number of boxes of f-type cut flowers auctioned at nauction line in mwhole- sale flower market
Tmn: total auction time for nauction line in mwholesale flower market (unit: sec)
Umfn: lower limit of auction time for f-type cut flowers at n auction line in mwholesale flower market
Vmfn: upper limit of auction time for f-type cut flowers at n auction line in mwholesale flower market
CPLEX software is used to calculate the optimal auction time per box of each type of cut flower when its auction price is the highest. The results are shown in Table 7.2. The same type of cut flower has different optimal auction times and a maximal auction price if it is auctioned at different wholesale flower markets. The farmers will choose the wholesale flower market with the maximal auction price for each type of cut flowers and sell cut flowers in that market.
On the basis of the information in Table 7.2, the auction staff at the four wholesale flow- ers markets are provided with a benchmark number to adjust the auction time per box, to increase the auction price, and to benefit the farmers.
7.2.2.5 Conclusion
For auction operations in the wholesale flower market, both buyers and auction staff must consider many factors, such as supply, demand, and quality of commodity, and they must make a decision within a very short time. In this research, “auction time” is an index to represent the relationship between all factors to predict the auction price.
As a result, the cost and time to gather data can be saved and easily applied to other kinds of wholesale markets, e.g., wholesale fruit and vegetable markets. We believe that the results from this research will also benefit agricultural industries in other countries.
152 Handbook of industrial and systems engineering