Designing price-contingent vegetable rotation schedules using agent-based simulation

LI Jing, Daniel Rodriguez, WANG Hao-xiang, WU Liu-san

1 Faculty of Engineering, Nanjing Agricultural University, Nanjing 210031, P.R.China

2 Queensland Alliance for Agriculture and Food Innovation (QAAFI), University of Queensland, Toowoomba 4350, Australia

1. Introduction

Vegetable production cooperatives are developing across China; in 2015 approximately 20% of all farmers are members of cooperatives (Lianget al. 2015). Cooperatives are usually formed by groups of smallholder farmers that own their land (Palsule-Desai 2015). Every year a cooperative proposes a rotation schedule of vegetables for each of its members. Based on the rotation schedule, the cooperative then supplies seeds, seedlings, fertilizers, fuel, machinery services and a unifying selling brand (Xiong and Zheng 2008; Lianget al. 2015). However, to diversify products during the year, the cooperative requires that members do not plant with the same rotation schedule. Different rotation schedules for different members also reduce the risk of pests and diseases by not having successive crops from the same family within the same year on the same farm. Since the prices of vegetables can vary during the year, an optimal crop rotation schedule can also change during the year. In addition, cooperative members are likely to be unsatisfied if their profits are substantially lower than their neighbors or lower than the average profit of the cooperative. Thus,it is also important to consider the average-per-member profit (Xu 2005). Maximum profits and similar average-permember profits are important objectives for the cooperative when designing a rotation schedule. Mackrellet al. (2009)found that farmers using an agricultural decision support system (DSS) could achieve higher profits.

In Southeast China, the use of greenhouses allows many types of vegetables to be planted year-round (Yinet al. 2015).These vegetables present multiple and varied harvesting periods and productivities (Heet al. 2007; Ahumadaet al.2012). The cooperative proposes a rotation schedule for the farmer members with several types of vegetables, though the combination of multiple farmers and various vegetables makes developing rotation schedules that satisfy clients a difficult combinatorial task. The optimization of the rotation schedule has been proven to be a strongly non-deterministic polynomial (NP)-hard problem (Reddy and Kumar 2008;Tanget al. 2012). Alfandariet al. (2015) proposed a 0-1 linear programming formulation for sustainable crop rotation planning. In the past decade, mathematical formulations have been proposed in the literature to optimize rotation schedules(Diaset al. 2015; Santoset al. 2015; Ashworthet al. 2016;Ghimireet al. 2017). Bochtiset al. (2012) developed a DSS to optimize route planning for agricultural vehicles. Many researchers studied the productivity of different rotation schedules through biological models (Stanger and Lauer 2008; Sindelaret al. 2016). Additionally, simulation methods to study the optimization of the rotation schedules were proposed primarily for large vegetable producers (Bachinger and Zander 2007). This is different in China where farmers own small areas of land (0.5–1.5 ha). Another difference seen in previous studies is that market dynamics are ignored.The vegetable market in China experiences large pricefluctuations between and within years (Ma and Meng 2008).The reasons for this fluctuation have been previously studied(Saha 1994a, b; Osaki and Batalha 2014; Maoet al. 2015)but they had not been used to optimize the design of rotation schedules until now.

A number of methods have been applied to solve similar optimization problems, e.g., simulation and mixed multi-objective programming models (Münchet al. 2014),interactive multiple goal linear programming models(Nidumolu 2007), and portfolio theory (Radulescuet al.2014). Liet al. (2014, 2017) used a self-adaptive algorithm in combination with an agent-based model to study a similar problem. Agent-based simulations have been used in many areas (Buchmannet al. 2016), such as biological sequence comparison (Sandeset al. 2014), crowd evacuation (Wagner and Agrawal 2014), marketing strategies (Serrano and Iglesias 2015), land use change (Bellet al. 2015; Tayyebiet al. 2016), water management (Isernet al. 2012; Van der Walet al. 2016), and agricultural policy strategies (Berger and Troost 2014; Troostet al. 2015). In general, agentbased modeling studies assume that agents (farmers) react autonomously and cognitively to signals from the external environment (Murray-Rustet al. 2011).

In this work, we present an example of how agentbased modeling and simulation can be used to design rotation schedules that maximize profits and the equity of the farmers’ profits, for all farmer-members of a vegetable producing cooperative in China. We previously studied the optimal rotation schedule (unchangeable schedule) for contract farming with a stable contract selling price (Liet al.2015b). In this study, we introduce the case of farmers who do not have a fixed-price contract and can modify crops based on in-season market prices. Differing from our previous work (Liet al. 2015b), this paper studies the rotation model with dynamic selling prices and proposes dynamic rotation schedules for farmers. The originality in this paper is the agent-based modeling approach used to identify the dynamic rotation schedule considering thefluctuation of market prices. In addition, the optimal rotation schedule can maximize the profits of each individual farmer and the cooperative; and use the “equity” among the farmer members of the cooperative as a constraint of the model.

2. Data and methods

2.1. Problem statement and model formulation

Smallholder farmer members of a vegetable-producing cooperative who own their land grow a diverse range of vegetables. Leaders of the cooperative use prices from the previous year to design a rotation schedule for the vegetables in the current year, although, farmers cannot all follow the same rotation because a diverse supply of vegetables for the market is also required.

At the beginning of each year, leaders of the cooperative design the rotation schedules for all farmers with the objective of maximizing cooperative profits while limiting the difference in profits (i.e., maximizing equity) among farmer members. Given the in-season variations in market prices, the maximum profits and equity among farmers are rarely achieved. Here, we propose that with the objective of maximizing cooperative profits and the equity between farmers, the rotation schedule can be adjusted dynamically according to the real prices of the current year using an agent-based model of all farmers in the cooperative.

2.2. Model description

In our model, if farmeriplants a rotation of vegetables using the following sequence of crops: eggplant, turnip and lettuce, this sequence is grown over a period of twelve months beginning in January each year. In the model, we used: (i) a heuristic algorithm to find the optimal rotation schedule based on last year’s prices(i.e., optimization without self-adaptation); and (ii) a selfadaptive optimization algorithm to dynamically adjust the rotation schedules according to the in-season fluctuation in prices. In the model, the target of each virtual farmer was to maximize profits and minimize the difference in profits among farmers (i.e., high equity).

The virtual vegetable is defined by six variables,vegk={bfk,ptk,ck,yk,epk,rpk}, where,k∈{1, 2, 3, ...,n} is the number of vegetables;bfkis the botanical family ofvegk;ptkis the production time ofvegk;ckis the cost of plantingvegk;ykis the yield ofvegk.ep(epk={epk1,epk2,epk3, ...,epk12}) is last year’s price ofvegk; andrpk(rpk={rpk1,rpk2,rpk3, ...,rpk12})is this year’s price ofvegk.

The virtual farmer was defined using two variables,fari={landi,seci}, where,i∈{1, 2, 3, ...,n} is the number of farmers andlandiis the land area offari.seciis the rotation schedule offari, which is defined asseci={vegi1,vegi2, ...,vegini} (niis the length ofseci).

The vegetables and their sequence are defined in the model ofseci, where,vegi1represents the first vegetable to be planted andveginrepresents the last vegetable in the rotation schedule.

The total planting time forfariis defined asaptfariin the following formula:

The objective offariis to find a maximal value ofeppai.The constraints of the model can be defined as follows:

The objective eq. (3) provides the estimated profit per hectare forfari. The goal offariis to achieve maximal profits.This goal should follow the constraints (4), (5), (6) and (7).

Constraint (4) ensures that the production period forfaridoes not exceed the length of the rotation (the maximum production period, twelve months). Constraints (5) and (6)are used to ensure that vegetables from the same botanical family are not planted sequentially byfari.

Constraint (7) is used to limit the differences in profits per hectare among all virtual farmers whereequityiis the difference betweeneppaiand the averageeppaiof all virtual farmers andαis the threshold of equity that is acceptable by the farmers. Ifequityiis larger thanα,fariwill be an unsatisfied farmer in the vegetable cooperative. Here,equityican be calculated by:

2.3. Optimization actions without self-adaptation

Because of soil fertility and nitrate recycling, this paper has defined that vegetables from the same botanical family are not planted in sequence by the same farmer. For random vegetablevegim(mmeans the position ofvegiinseci), all vegetables from different botanical families are defined as a tuple withruledVegm={vegm1,vegm2, ...,vegmnm}, where,nmis the length ofruledVegm. Meanwhile, the sum of the harvest time forvegiand the planting time for any one of vegetable inruledVegmmust not exceed the maximum number of months for a rotation (12 months in this paper). The virtual farmer uses the Boltzmann soft-max distribution (according to the estimated profit of each crop) to select the following vegetablevegifromruledVegm.

Fig. 1 shows the heuristics in the optimization for the virtual farmer to create the rotation schedule. The optimization process consists of selecting vegetables for the first twelve months and modifying the schedule until the average profit is not significantly smaller than the average profit for all farmers. The steps of the optimization action are presented in the following section:

Step 4: If the estimated average profit does not meet the requirement of constraint (7), then delete all vegetables in the rotation schedule, setcurrentVeg=null, and return to Step 1. Otherwise, stop here.

Fig. 1 Optimization actions without self-adaptation. Average profit is the average value of all virtual farmers’ profits. My profit is the profit the virtual farmer using the action in Fig. 1.

2.4. Self-adaptive adjustment actions

Self-adaptive adjustment actions are proposed to virtual farmers to adjust their rotation schedules based on thefluctuation of real market prices. Self-adaptive adjustment actions are used by virtual farmers at the end of each month,differing from optimization actions without self-adaptation(conducted at the beginning of each year). Virtual farmers consider the changes between real market prices and estimated prices from the previous month. Self-adaptive adjustment actions are stimulated by these changes. The process of self-adaptive adjustment actions is shown in Fig. 2.

Fig. 2 shows that virtual farmers adjust their estimated selling prices (for future months) based on the real selling prices first. Eq. (10) is used to modify estimated prices,

Fig. 2 Self-adaptive adjustment actions. Average profit is the average value of all virtual farmers’ profits. My profit is the profit the virtual farmer using the action in Fig. 2.

Step 1: Set the current simulation month ascurrentmonthand use eq. (10) to update all estimated prices.

Step 2: Compute the average profit. If the profit meets the requirement of constraint (7), stop here. Otherwise,proceed to Step 3.

2.5. Agent-based model

An agent-based model was developed to determine an optimal rotation schedule based on the objectives and constraints as described above assuming no self-adaptation(Fig. 3) and with self-adaptation (Fig. 4). In the model,simulations were performed until the vegetable cooperative found the optimal result. No self-adaptation action used the same estimated prices in any of the years simulated. In this mode, virtual farmers use a random rotation schedule at the start of the simulation and adjust their rotation schedules at the end of each year.

Assuming self-adaptive adjustment within any single year, virtual farmers adjust their rotation schedules at the end of each month. Because the self-adaptive adjustment runs synchronously with the real world, virtual farmers can adjust the schedule only once each month (Fig. 4). At the beginning of the simulation year, virtual farmers use the optimal schedule produced by the optimization without self-adaptive adjustment, i.e., Fig. 3, and at the end of each month, virtual farmers use a self-adaptive adjustment action to update their rotation schedule according to present (real world) vegetable prices.

JAVA was used to code the agent-based model, and ECLIPSE was used as the simulation platform. In the next section, we provide an example of the agent-based model.

2.6. Case study and simulation experiments

The vegetable production cooperative is located in a rural area between Jurong City and Nanjing City, China. All vegetables produced by the cooperative are sold in Nanjing City. The cooperative has 50 farmers who own their land and live among two neighboring villages. At the beginning of each year, the manager of the cooperative proposes the rotation schedules for all the cooperative farmer members.The planting process is controlled by the cooperative to ensure the quality and time-to-market of all vegetables.The rotation schedules must increase the profits for all farmers and ensure that all farmers have similar profits per unit of hectare. A threshold of equity, i.e., the average profit differenceα=0.1, is assumed and the land area size (ha) of the 50 farms is set as:

Thirteen main vegetables are grown in greenhouses by the farmers of the cooperative. The botanical families and planting data are shown in Table 1. The thirteen vegetables can be planted at any time during the year. Because all seedlings are bought from a seedling company, planting times do not include the time for seedling production.Selling costs are assumed to be the same for all farmers(Table 1). Yields and production costs are provided to the model according to the MOA (2007), Liet al. (2015a) and Wu (2015).

Fig. 3 Simulation process of optimization action without self-adaptation.

We assume that the simulation model was run from January 2014. The managers of the cooperative propose the rotation schedules for all farmers using the monthly prices of the thirteen vegetables from the previous year(2013). The monthly price data of 2013 and 2014 are shown in Appendix A and belong to the website of the Price Bureau of Nanjing, China (http://www.njprice.com/col84/articlecolumn.php?colid=315). The agent-based model was used to model the following six experiments.

2.7. Experiment I: Optimization without self-adaptation

Experiment I was designed to show the validity of the optimization action without self-adaptation. In this experiment, the monthly wholesale prices from 2013 were used as the estimated prices of 2014. Same with previous researches (Hammet al. 2007; Boyeret al. 2015), we used random rotation schedules as the start for the simulation in our paper. The optimization was performed 100 simulation periods and each virtual farmer adjusted the rotation schedule based on the profit-experience of the previous simulations until the optimal schedule was determined(Fig. 3).

Fig. 4 Simulation process of self-adaptive adjustment action.

2.8. Experiment II: Optimization with and without self-adaptation

Experiment I used last year’s prices to propose optimal rotation schedules for all virtual farmers. Experiment II used actual prices in Nanjing to determine the optimal schedule.At the beginning of 2014, one group of virtual farmers used the optimal schedules of Experiment I to produce vegetables. Another group of virtual farmers used the optimal schedules for the first month of 2014 and adjusted the schedule thereafter based on actual monthly prices as in Fig. 4. The results from Experiment II were also compared with those from a third group of virtual farmers for whom the rotation schedule was selected at random.

2.9. Experiment III: Optimization actions considering one vegetable with a price decrease

It was observed that the price of some of the vegetables changed by more than 50% during 2015, e.g., cucumbers in China (Yimutian 2015). The price of hot peppers (Beijing market) increased by 70% compared with the 2014 price(Xinjingbao 2015). Experiments III and VI were used to test the influence of large price fluctuations in one or more than one vegetable. Based on reports for vegetable prices in China for 2015 (Xinjingbao 2015; Yimutian 2015),this experiment assumed a half reduction in the price of cucumbers during 2014. Prices for this experiment are shown in Table 2.

2.10. Experiment IV: Optimization considering two vegetables with a decrease in price

Based on the market reports (Xinjingbao 2015; Yimutian2015), we assumed that the prices of cucumbers and hot peppers underwent substantial price reductions (half) during 2014 in this experiment. Prices for this experiment are shown in Table 2.

Table 1 Data of the thirteen typical vegetables (Nanjing City, China)

2.11. Experiment V: Optimization considering one vegetable with an increase in prices

Experiments III and IV showed the significance of optimal actions when considering vegetables with substantial price increases (double). The significance of the actions considering substantial price increases was explored in Experiments V and VI. Based on market reports, we assumed that the real wholesale prices for cucumbers in Nanjing during 2014 increased by 100% in Experiment V.

2.12. Experiment VI: Optimization considering two vegetables with increases in prices

This experiment assumed a double increase in the prices of cucumbers and hot peppers at the same time (Table 2).The performance of the different actions was tested considering two vegetables with substantial increases in prices.

3. Results

In this paper, all experiments were simulated five times so that the average values and standard errors could be calculated. Since we found the average results of five-times simulations were similar, all results in the following were the average values of five experiments.

3.1. Experiment I: Optimization without selfadaptation

The results from Experiment I are shown in Figs. 5 and 6.Fig. 5 shows the average simulated profit (CNY ha–1) for all virtual farmers during 2014. The average profit increased with the number of optimization cycles and stabilized after 53 cycles. After the 53rd round of simulations, all virtual farmers also met the requirement of equity (constraint (7))in Fig. 6, i.e., none of the farmers were unsatisfied with the derived rotation schedule. It is found that all experiments(Experiment I to VI) could achieve the stable results no more than 100 simulation periods. This paper use the stable results as the experiment results. Figs. 5 and 6 showed the optimum results without self-adaptation. The simulations were performed each time with a different random initial rotation schedule where error bars could be calculated.

3.2. Experiment II: Optimization with and without self-adaptation

Experiment II considered the real market prices and studied the performances of two optimization actions. The results are shown in the first row of Table 3 (results of Experiment II).

Table 3 (first row) shows that the random schedule produced the lowest average profit. The optimal schedules with and without self-adaptive had similar average profits.The percentages of unsatisfied farmers are shown in the first row of Table 3. The self-adaptive action obtained the best results for these virtual farmers. However, because of thefluctuation in real prices, the model was not able to reduce the number of unsatisfied farmers to zero.

3.3. Experiment III: Optimization actions considering one vegetable with a price decrease

Table 3 (the second row) shows the average profits and percentage of unsatisfied virtual farmers in Experiment III. The random rotation schedule obtained the poorest results while the self-adaptive action achieved the best results, both in terms of profits and proportion of unsatisfied farmers. Virtual farmerscould use the self-adaptive action to adjust their optimal schedules based on the fluctuation of wholesale prices.

Table 2 Price (CNY kg–1) fluctuation of two vegetables in 2014

To show the influence of different actions, Appendix B shows the results of a random schedule, an optimal schedule without self-adaptation, and an optimal schedule with selfadaptive adjustment from one run time of Experiment III.Appendix B shows that almost all random schedules were different when the optimal action without self-adaptation was simulated (Farmers 6, 10, 13, 33, and 40 were not adjusted).Meanwhile, 13 farmers’ optimal schedules were modified by self-adaptive action. Table 4 shows this modification in the 13 farmers’ optimal schedules. It also shows that 9 farmers increased their average profits because of the self-adaptive action, while 4 farmers’ average profits were decreased by the action (Farmers 7, 41, 43 and 47). The reason for the failure of the 4 farmers was that some vegetables had different fluctuations (compared with the prices of 2013) in the first and second half of 2014. For example, Farmer 7 used potatoes to substitute hot peppers in his rotation schedule according to the self-adaptive action.Unfortunately, potatoes had a different price fluctuation in the second half of the year. The prices for potatoes from Appendix A are illustrated in Fig. 7.

Compared with 2013, the prices for potatoes clearly increased in the first half of 2014 in Fig. 7. According to selfadaptive actions, virtual farmers had believed that potatoes would have obtained good prices in the second half of the year. However, potato prices decreased during the second half of the year compared with the prices in 2013. This was the reason for Farmer 7’s failure.

Fig. 5 Average profit (CNY ha–1 yr–1) of farmers based on estimated prices.

Fig. 6 Count of unsatisfied farmers in the simulation model.

Table 3 Average simulation results of five experiments

3.4. Experiment IV: Optimization considering two vegetables with a decrease in prices

The results of Experiment IV are shown in the third row of Table 3. Similar to Experiment III, the self-adaptive adjustment action improved the performance of the virtual farmers. The percentage of unsatisfied farmers was similar between the two optimal schedules, even though there were two vegetables with larger price decreases. Because of the significant disruption in prices, i.e., the two vegetable prices,the self-adaptation action did not decrease the percentage of unsatisfied farmers. The reason for this was because the profits were related to the percentage of virtual famers planting cucumbers and hot peppers in Table 2.

3.5. Experiment V: Optimization considering one vegetable with an increase in price

Results from Experiment V are shown in Table 3 (the fourth row). Table 3 shows that the self-adaptive adjustment action resulted in the maximum average profit for the virtual cooperative. At the same time, the action could reduce the number of unsatisfied farmers (proposed in Table 3).The optimal schedule (from the optimal action without self-adaptation) provided better results than the random schedule.

3.6. Experiment VI: Optimization considering two vegetables with increases in prices

The results of this experiment are shown in Table 3 (the fifth row). The optimal schedule without self-adaptive adjustment achieved the best performance in terms of profits. The reason was the unseasonable increase in the prices of two vegetables in Table 2. The self-adaptation action eliminated two vegetables from the rotation. Table 3 shows that the self-adaptive adjustment action could improve the equity of the cooperative even when considering two vegetables with large price increases. However, the self-adaptive action may cause a reduction in profits due to the unintentional removal of the vegetables with the large price increases (Table 3).

Table 3 presents the results of all five experiments and shows that the self-adaptive adjustment of the rotation schedule was particularly beneficial for improving profits in scenarios that included larger price fluctuations. This result provides quantitative evidence of how farmers can achieve larger profits by acting on additional market information.

4. Discussion

Burt and Allison (1963) were first to consider the problem of crop rotation schedules in a dynamic programming framework. However, most of the existing work on optimal crop rotation schedules used linear programming techniques to identify optimal sequencings of crops based on a number of objectives and constraints on single or typical farm case studies (Santoset al. 2015). The virtual farmers used a“heuristic rule-based model” (Gibonet al. 2010) to find the optimal results. The objective of each virtual farmer was to maximize their profits while decreasing the profit gaps between the farmer members of the cooperative.The benefits and trade-offs of the scenarios in the rotation schedule was decided once at the start of the year based on January prices. In addition, a price-contingent self-adaptive rotation schedule that was decided for each month during the cropping year was evaluated.

Jensen (2007) concluded that farmers cannot make effective production decisions without considering information about future market prices. Tanget al. (2015)also proposed that market information could be used to increase farmers’ profits. In this paper, we proposed three types of schedules that assume different availabilities of market information. The results in Table 3 show that the schedules that use more market information achieve higher profits. When the price of two vegetables varied significantly during the cropping season (Experiment VI),not even the schedule with the most information achieved maximum profits. This is the first time that “equity” among the farmers’ income was included as an objective in defining optimality. Optimality without self-adaptation was studied in previous work (Liet al. 2015b). Equity in farmers’ profit was shown to be a particularly important concern for farmers when operating in a network of connected farms, e.g., as members of a cooperative (Palsule-Desai 2015). It has been suggested that profit equity can impact the competitiveness and stability of the entire network of farmers (Jackson 2005).A random schedule (ignoring market information) in Table 3 produced the worst profit in “equity”. The percentage of unsatisfied farmers further increased when the price of vegetables was assumed to vary significantly during the year. Table 3 shows that a self-adaptive adjustment action can significantly reduce the number of unsatisfied farmers across all scenarios. The rotation schedule using more market information provided higher equity between the farmers’ incomes. However, when facing large pricefluctuations (Experiment IV, V, and VI) equity remained low.

Results demonstrated that our approach was valid for use in situations where market information was available during the cropping season to improve the rotation schedule of vegetables. If these prices can be available, the cooperative can implement optimal crop rotation schedules that account for the farmers’ objectives and the actual market conditions.

Table 4 Self-adaptive adjustment based on optimal rotation schedules

Fig. 7 Prices of potatoes in 2013 and 2014.

5. Conclusion

From the discussion above, we draw three conclusions:First, the random rotation schedule, i.e., without using any market information, offered the worst results across all scenarios. Second, the self-adaptive adjustment action(i.e., using historic and current market information) was optimal at achieving the objectives of the farmers across all scenarios except for large market-fluctuation. Third, the self-adaptive adjustment method was the most effective at identifying rotation schedules that maximized profits and profit equity for farmers in most scenarios except when a higher increase in prices was encountered.

This study is the first to optimize rotation schedules using an agent-based model. The proposed approach has room for improvement, namely the need to account for real-world situations involving different types of cooperatives and produced commodities. The use of different constraints for different vegetables is also another topic for further research.Optimal rotation schedules that consider specific agronomic requirements is also an interesting topic for future studies,particularly linking agent-based models with dynamic whole farm models, e.g., Rodriguezet al. (2011, 2014).

Acknowledgements

This research was supported by the National Natural Science Foundation of China (NSFC, 71301077).

Appendicesassociated with this paper can be available on http://www.ChinaAgriSci.com/V2/En/appendix.htm

Ahumada O, Villalobos J R, Mason A N. 2012. Tactical planning of the production and distribution of fresh agricultural products under uncertainty.Agricultural Systems, 112,17–26.

Alfandari L, Plateau A, Schepler X. 2015. A branch-and-priceand-cut approach for sustainable crop rotation planning.European Journal of Operational Research, 241, 872–879.

Ashworth A J, Allen F L, Saxton A M, Tyler D D. 2016. Long-term corn yield impacted by cropping rotations and bio-covers under no-tillage.Agronomy Journal, 108, 1495–1502.

Bachinger J, Zander P R. 2007. A tool for generating and evaluating crop rotations for organic farming systems.European Journal of Agronomy, 26, 130–143.

Bell A R, Robinson D T, Malik A, Dewal S. 2015. Modular ABM development for improved dissemination and training.Environmental Modelling and Software, 73, 189–200.

Berger T, Troost C. 2014. Agent-based modelling of climate adaptation and mitigation options in agriculture.Journal of Agricultural Economics, 65, 323–348.

Bochtis D D, Sørensen C G, Green O A. 2012. DSS for planning of soil-sensitive field operations.Decision Support Systems,53, 66–75.

Boyer C N, Brorsen B W, Fain J R. 2015. Private-value auction versus posted-price selling: An agent-based model approach.Intelligent Systems in Accounting,Finance and Management, 22, 249–262.

Buchmann C M, Grossmann K, Schwarz N. 2016. How agent heterogeneity model structure and input data determine the performance of an empirical ABM - A real-world case study on residential mobility.Environmental Modelling and Software, 75, 77–93.

Burt O R, Allison J R. 1963. Farm management decisions with dynamic programming.Journal of Farm Economics, 45,121–136.

Dias T, Dukes A, Antunes P M. 2015. Accounting for soil biotic effects on soil health and crop productivity in the design of crop rotations.Journal of the Science of Food and Agriculture, 95, 447–454.

Ghimire R, Lamichhane S, Acharya B S, Bista P, Sainju U M. 2017. Tillage, crop residue, and nutrient management effects on soil organic carbon in rice-based cropping systems: A review.Journal of Integrative Agriculture, 16,1–15.

Gibon A, Sheeren D, Monteil C, Ladet S, Balent G. 2010.Modelling and simulating change in reforesting mountain landscapes using a social-ecological framework.Landscape Ecology, 25, 267–285.

Hamm L, Brorsen B W, Hagan M T. 2007. Comparison of stochastic global optimization methods to estimate neural network weights.Neural Processing Letters, 26, 145–158.

He C, Guo X, Wang W, Wu J. 2007. Study on the optimum N rates under spring cabbage-maize-winter cabbage rotation system.Journal of Integrative Agriculture, 6, 1322–1329.

Isern D, Abelló S. Moreno A. 2012. Development of a multiagent system simulation platform for irrigation scheduling with case studies for garden irrigation.Computers and Electronics in Agriculture, 87, 1–13.

Jackson M. 2005.A Survey of Network Formation Models,Stability and Efficiency. Cambridge University Press,Cambridge, United Kingdom.

Jensen R. 2007. The digital provide information (technology),market performance, and welfare in the south Indianfisheries sector.Quarterly Journal of Economics, 122,879–924.

Li J, An Q, Wang J. 2015a. Dynamic analysis of cost and efficiency for Chinese vegetable, based on the data from 2011 to 2014.Price Theory and Practice, 4, 65–67. (in Chinese)

Li J, Ding C, Liu W. 2014. Adaptive learning algorithm of selforganizing teams.Expert Systems with Applications, 41,2630–2637.

Li J, Rodriguez D, Tang X. 2017. Effects of land lease policy on changes in land use, mechanization and agricultural pollution.Land Use Policy, 64, 405–413.

Li J, Rodriguez D, Zhang D, Ma K. 2015b. Crop rotation model for contract farming with constraints on similar profits.Computers and Electronics in Agriculture, 119, 12–18.

Liang Q, Hendrikse G, Huang Z, Xu X. 2015. Governance structure of chinese farmer cooperatives evidence from Zhejiang Province.Agribusiness, 31, 198–214.

Ma Y, Meng C. 2008. The dual-agency relations in farmer cooperatives in China - The problem and improvement ideas.Issues in Agricultural Economy, 5, 55–60. (in Chinese)

Mackrell D, Kerr D, Hellens L V. 2009. A qualitative case study of the adoption and use of an agricultural decision support system in the Australian cotton industry, the socio-technical view.Decision Support Systems, 47, 143–153.

Mao L, Zhang L, Zhang S, Evers J B, van der Werf W, Wang J, Spiertz H. 2015. Resource use efficiency, ecological intensification and sustainability of intercropping systems.Journal of Integrative Agriculture, 14, 1542–1550.

MOA (Ministry of Agriculture of China). 2007. Yield of vegetables in 2005.China Vegetables, 1, 40–41. (in Chinese)

Münch T, Mirschel B W, Nendel W C. 2014. Considering cost accountancy items in crop production simulations under climate change.European Journal of Agronomy, 52, 57–68.

Murray-Rust D, Dendoncker N, Dawson T P, Acostamichlik L, Karali E. 2011. Conceptualising the analysis of socioecological systems through ecosystem services and agent based modelling.Journal of Land Use Science, 6, 83–99.

Nidumolu U B, van Keulen H, Lubbers M, Mapfumo A. 2007.Combining multiple goal linear programming and interstakeholder communication matrix to generate land use planning options.Environmental Modelling Software, 22,73–83.

Osaki M, Batalha M O. 2014. Optimization model of agricultural production system in grain farms under risk, in Sorriso Brazil.Agricultural System, 127, 178–188.

Palsule-Desai O D. 2015. Cooperatives for fruits and vegetables in emerging countries rationalization and impact of decentralization.Transportation Research(Part E: Logistics and Transportation Review), 81, 114–140.

Radulescu M, Radulescu C Z, Zbaganu G. 2014. A portfolio theory approach to crop planning under environmental constraints.Annals of Operations Research, 219, 243–264.

Reddy M, Kumar D N. 2008. Evolving strategies for crop planning and operation of irrigation reservoir system using multi-objective differential evolution.Irrigation Science, 26,177–190.

Rodriguez D, Cox H, deVoil P, Power B. 2014. A whole farm modelling approach to understand impacts and increase preparedness to climate change in Australia.Agricultural Systems, 126, 50–61.

Rodriguez D, deVoil P, Power B, Crimp S, Meinke H. 2011. The intrinsic plasticity of farm businesses and their resilience to change.Field Crops Research, 124, 157–170.

Saha A. 1994a. A two-season agricultural household model of output and price uncertainty.Development Economics,45, 245–296.

Saha A. 1994b. Compensated optimal response under uncertainty in agricultural household models.Agricultural Economics, 11, 111–123.

Sandes E F D O, Ralha C G, Melo A C M A D. 2014. An agentbased solution for dynamic multi-node wavefront balancing in biological sequence comparison.Expert Systems with Applications, 41, 4929–4938.

Santos L M R, Munari P, Costa A M. 2015. A branch-priceand-cut method for the vegetable crop rotation scheduling problem with minimal plot sizes.European Journal of Operational Research, 245, 581–590.

Serrano E, Iglesias C A. 2015. Validating viral marketing strategies in twitterviaagent-based social simulation.Expert Systems with Applications, 50, 140–150.

Sindelar A J, Schmer M R, Jin V L, Wienhold B J, Varvel G E. 2016. Crop rotation affects corn, grain sorghum, and soybean yields and nitrogen recovery.Agronomy Journal,108, 1592–1602.

Stanger T F, Lauer J G. 2008. Corn grain yield response to crop rotation and nitrogen over 35 years.Agronomy Journal,100, 643–650.

Tang C S, Wang Y, Zhao M. 2005. The implications of utilizing market information and adopting agricultural advice for farmers in developing economies.Production and Operations Management, 24, 1197–1215.

Tang Q, Ren T, Wilko S, Liu H, Lei B, Lin T, Zhang G. 2012.Study on environmental risk and economic benefits of rotation systems in farmland of Erhai Lake Basin.Journal of Integrative Agriculture, 11, 1038–1047.

Tayyebi A, Meehan T D, Dischler J, Radloff G, Ferris M,Gratton C, Smartscape T M. 2016. A web-based decision support system for assessing the tradeoffs among multiple ecosystem services under crop-change scenarios.Computers Electronics in Agriculture, 121, 916–924.

Troost C, Walter T, Berger T. 2015. Climate, energy and environmental policies in agriculture simulating likely farmer responses in Southwest Germany.Land Use Policy, 46,50–64.

Wagner N, Agrawal V. 2014. An agent-based simulation system for concert venue crowd evacuation modeling in the presence of a fire disaster.Expert Systems with Applications, 41, 2807–2815.

Van der Wal M M, de Kraker J, Kroeze C, Kirschner P A,Valkering P. 2016. Can computer models be used for social learning? A serious game in water management.Environmental Modelling and Software, 75,119–132.

Wu W. 2015. Analysis on cost, benefit and influence factors of vegetable production in China.Journal of Changjiang Vegetable, 12, 53–56. (in Chinese)

Xinjingbao. 2015. Bigger prices increase of Beijing vegetables. [2015-08-02]. http://finance.sina.com.cn/consume/20150731/023022838440.shtml (in Chinese)

Xiong J, Zheng Y. 2008. Analysis on agency cost in famer cooperatives controlled by minority members in China.Agricultural Economy, 11, 76–78.

Xu X. 2005.Institutional Analysis on Farmer Specialized Cooperatives in China. The Publishing House of Economic Science, Beijing, China. (in Chinese)

Yimutian. 2015. Fluctuation of cucumber prices in 2015.[2015-08-02]. http://hangqing.ymt.com/chandi_7799_0_0(in Chinese)

Yin Y, Liang C, Pei Z. 2015. Effect of greenhouse soil management on soil aggregation and organic matter in northeast China.Catena, 133, 412–419.