Proceedings of the 6th International Symposium on Machinery and Mechatronics for Agriculture and Biosystems Engineering (ISMAB) 18-20 June 2012, Jeonju, Korea

Multiple-Crop Scheduling for Plant Factory Chao-Lung Yang1, Yulius Hari2, Yan-Fu Kuo3* 1

Assistant Professor, 2Master student, Department of Industrial Management, National Taiwan University of Science and Technology, Taiwan, R.O.C. 3 Assistant Professor, Department of Bio-Industrial Mechatronics Engineering, National Taiwan University, Taiwan, R.O.C. *Corresponding Author-- Voice: +886-2-3366-5329, Email: [email protected]

Abstract: A plant factory is a crop production facility in which all the environmental elements for plant growth are artificially controlled. The operating cost of plant factories is usually high due to intensive energy consumption. It is crucial to choose appropriate crops for cultivation at proper time for revenue maximization. In this research, we propose a crop scheduling approach for plant factories. The proposed approach considers the factor of crop price fluctuation and contracts between plant factories and retailers. The crop scheduling is formulated as a mixed integer programming problem and is solved using branch-and-bound algorithms. The proposed approach can be incorporated into any plant factory to increase its production and revenue. Key Words: Plant factory, mixed integer programming, crop scheduling. INTRODUCTION A plant factory is a facility that aids the steady production of crops all year round by artificially controlling the cultivation environment. It provides several advantages for crop production over traditional open field farming. In plant factories, the temperature, humidity, light illumination, and nutrients are maintained and isolated from the surrounding. Thus, the location of a plant factory is not restricted by environmental consideration. This gives plant factories the capability to cultivate crop at any season in year (Seginer & Ioslovich, 1999). Typical plant factories use multiple shelves as the planting horizon, which makes vertical farming possible and substantially increases the production rate per area (Moon, Li, & Kim, 2011). Due to the uses of nutrition solution as media rather than soil, plant factories do not need considerable time allocation for traditional fallow and green manuring. Thus crop can be cultivated year-round (Altieri, 1999; Francis et al., 2003; Kato et al., 2010). In addition, the pesticide usage in plant factories is usually minimal since the risk of pest and disease is minimized through the isolated cultivation (dos Santos, Michelon, Arenales, & Santos, 2008). Plant factories make crop cultivation sustainable and are considered as next generation farming (Yiridoe, Bonti-Ankomah, & Martin, 2005). The operation cost of plant factories is typically high due to the expenses for the The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the Korean Society for Agricultural Machinery (KSAM), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by KSAM editorial committees; therefore, they are not to be presented as refereed publications. Citation of th this work should state that it is from the 6 ISMAB paper. EXAMPLE: Author's Last Name, Initials. 2012. Title of Presentation. th The 6 ISMAB June 18-20, 2012. Jeonju, Korea. For information about securing permission to reprint or reproduce a technical presentation, please contact KSAM at [email protected] or Korean Society for Agricultural Machinery, c/o National Institute of Agricultural Engineering, 249 Seodun-dong, 441-100 Suwon Korea.

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environmental control. For example, lighting for plant growth usually runs for a significant amount of time (Mills & Jacobson, 2011). The air conditioning for temperature and humidity control also consumes considerable electricity. The energy consumption is a major cost of plant factory operation, and is considered fixed (Fang, Ting, & Giacomelli, 1990). It is crucial to choose appropriate crop at right time for cultivation, so that the profit margin of each crop can be increased. Many factors determine the crop selection for plant factory. The cultivation time of each crop governs the duration of the space occupation. The demand of crops determines the occupation of cultivation shelves. Variety of nutrition solutions needed for different crops also influence the decision of space utilization. The flexibility of allowing reusing the same nutrition solution can reduce the setup cost of crop planting. In addition, the selling price while harvesting can also affect the decision of planting timing for a particular crop. Scheduling is the process of deciding how to commit resource between variations of possible combinations. It has been introduced in the field of agriculture research. Alfandari et al. (2011) applied scheduling to maximize the utilization of the available farming land in Madagascar. Dos Santos et al. (2008) and Costa et al. (2011) performed the crop rotation with scheduling while considering the soil fertility and other natural factor. Ferrer et al.(2008) described the best schedule to harvest the grape with quality loss function constrains. In plant factory, the scheduling approach can be used for cultivation timing and crop selection. The maximization of revenue can be achieved through the better crop scheduling. In this research, we propose a crop scheduling approach for multiple-crop plant factories where any crop can be planted at any time year-round. The proposed approach considers the seasonal effect of crop price fluctuation to achieve better profitability of a plant factory. In addition, the contracting planting which is common in agriculture is integrated with the scheduling model. With the supply agreements contracted between plant factories and food retailers or restaurants, plant factories are required to supply a certain type of crop in a specific duration. These two factors are essential for practical operation of plant factory. The objective of this research is to optimize the revenue of a plant factory by crop scheduling. The scheduling is formulated as a mixed integer programming problem, and is solved using branch-and-bound algorithms provided. The solution provides the guideline of the choices of crops and the planting timing for plant factory operation and management. RESEARCH METHODOLOGY TERMINOLOGY IN PLANT FACTORY MODEL This section explains the proposed scheduling model formulation. First, we assume the plant factory is facilitated with a rack system. A rack can be divided into multiple plots. For simplicity, in this research, we assume all the racks contain the same number of plots. Each plot can be used to cultivate a crop at a time. This model does not concerns about reusable nutrition, but it is assumed that each rack shares the same nutrition solution. Therefore, the crop selection in each rack is homogenous (only one type of crop on each rack), i.e., the plants in all the plots of a rack are the same at any time. Also, we assume contract agreements between the plant factory and retailers are arranged. The contracts indicate the

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amount and category of the crops that the plant factory has to supply during a certain period of time. In addition, we assume historic data of crop sale price is available. The sale price data is incorporated in the scheduling problem formulation to maximize the plant factory revenue. It is further assumed that the seasonal effect of crop price is repeated annually. PROBLEM FORMULATION The crop scheduling is modeled as a mixed integer programming problem. Assume the plant factory is facilitated with K racks, and a total of n different crops are available for cultivation. Let i denote a crop. Each crop belongs to a category Gp, i.e., i ∈ Gp, where p is the index of crop category. Let t denote a period in time, and T denote the total number of periods. Each crop i has a cultivation period Qi and price information Pit during period t. The list of the parameters is shown below: Total number of crops Total number of racks Total number of periods of time Index of crop; i = 1,..,n Index of rack; j =1,.., K Index of period; t =1,..,T Production period of crop i Price for crop i at time t Number of crop categories Category of crop p, where p =1,..,NG Number of plots in a rack

n K T i j t Qi Pit NG Gp c

OBJECTIVE FUNCTION Let binary variable Sijt ∈ {0, 1} denote the decision variable. The decision variable Sijt is 1 if crop i is planted on rack j at time t; otherwise, it is 0. The objective function to maximize the total revenue for a plant factory can be written as n

K

T

z = Max∑∑∑ Sijt Pi (t +Qi ) c ,

(1)

i =1 j =1 t =1

where Pi (t +Qi ) represents the crop selling price at harvest, and Sijt Pi ( t +Qi ) c represents the revenue for crop i on rack j during period t. The number of plots c can be omitted in Equation (1) since it is a constant. Note that if t + Qi > T , the Pi (t +Qi ) is replaced with Pi ( t +Qi −T ) . Three constraints are applied in the scheduling model formulation. First, the occupancy constraint is defined as n Qi −1

∑∑ S i =1 r =0

ij ( t − r )

≤ 1 for every j = 1,..,K; and t = 1,..,T,

(2)

where r represents a period during cultivation. This constraint ensures that no more than one

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crop can be cultivated at any time. Note that in this constraint, if t − r ≤ 0 , substitute t − r for t − r + T to accomadate the time slot for the next cycle of time horizon. Secondly, the maximum capacity constraint is defined as K

∑S j =1

ijt

≤ K for every i = 1,..,n ; and t = 1,..,T.

(3)

The constraint ensures that the total number of crops is not larger than the total capacity. Third, the supply contract is defined as b

∑ ∑S

i∈G( p ) t = a

ijt

≥ 1 for each j = 1, .., K,

(4)

where a to time b are two points in time and b > a . The constraint ensures that at least one type of crop from the selected category G(p) is supplied to the retailers during the period from time a to time b, under the contract agreement. In a supply contract, different crop categories might have distinct supply durations.

EXPERIMENTAL RESULT AND DISCUSSION An experiment was performed to evaluate the performance of the proposed approach. A 5rack plant factory that can cultivate 13 different crops was considered. The name, category, and cultivation time of the crops are shown in Table 1. The supply contracts used in the experiement are shown in Table 2. The contracts specify the crop category that has to be supplied in a specific period. For example, the agreement 1 specifies that the plant factory needs to cultivate at least one crop in the Herb and one in the Brassicas category from month 1 to month 6. Figure 1 shows the unit sale price of each crop over a period of one year. The price variation is considered in the experiment. Table 1. Crop data No

Name

Category

a. b. c. d. e. f. g. h. i. j. k. l. m.

Parsley Celery Spinach Lettuce Broccoli Cauliflower Onion Tomato Pepper Pea Jack bean Cucumber Pumpkin

Herb Herb Leafy Leafy Brassicas Brassicas Aliacea Solanaceae Solanaceae Leguminosae Leguminosae Cucurbitaceae Cucurbitaceae

Table 2. Supply contract agreement Cultivation time 2 month 3 month 3 month 4 month 4 month 3 month 3 month 5 month 4 month 3 month 3 month 4 month 5 month

No 1. 2. 3. 4.

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Crop categories herb and brassicas leafy and solanaceae legamiosae and aliacea, cucurbitacene

Supply period 1-6 month 7-12 month 13-18 month 19-24 month

Figure 1. Crop sale price over a period of one year. The experiment was run for 24 months, i.e., T = 24, and the period t was one month. The scheduling problem was solved using branch-and-bound algorithms provided by CPLEX®. Figure 2 shows the crop scheduling result. It shows that in month 2, jack bean (k) is planted on rack 1 to 4. Also, from month 1 to 6, at least one herb (a) and brassicas (f) are planted to satisfy the agreement 1 shown in Table 2. As can be seen, crop f and k are selected most of time because of their high sale prices. Therefore, this scheduling is shown to maximize the revenue by choosing the most profitable crop and also satisfy the supply contracts. Year

Rack

Month

1 1

2

3

4

5

6

7

2 8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

1

k

f

f

l

2

k

f

f

f

k

f

f

f

3

k

f

f

f

k

f

f

f

4

k

f

f

f

f

f

l

5

f f

l a

c

g

h f

k

a

24

f

Figure 2.The crop scheduling result of a 5-rack plant factory for a period of 24 months. Each letter specifies one kind of crop planted at a particular time.

CONCLUSIONS & FURTHER RESEARCH In this study, a scheduling approach is proposed to maximize the space utilization and revenue for plant factories. The proposed approach considers the factor of crop price fluctuation and contract between plant factories and retailers. The scheduling is formulated as a mixed integer programming problem and is solved using branch-and-bound algorithm. The computation is performed using CPLEX®. A case study is conducted to evaluate the performance of the proposed approach. The results show that the proposed approach provides the optimal crop selection and schedule. Further research as an extension of this model would be to include costs and labor usages which are critical parameters in plant factory development. The constraint which limits the crop selection by considering reusability of nutrition solution in a rack can be included in the

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model. The production loss due to the crop transplant from one rack to another can also be formulated in the objective function.

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