A Sustainable Vegetable Supply Chain Using Plant Factories in Taiwanese

A sustainable vegetable supply chain using plant factories in Taiwanesemarkets: A NashCournot model

Ming-Che Hu a, Yu-Hui Chen b, Li-Chun Huang c,n

a Department of Bioenvironmental Systems Engineering, National Taiwan University, No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwanb Department of Agricultural Economics, National Taiwan University, No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwanc Department of Bio-Industry Communication and Development, National Taiwan University, No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwan

a r t i c l e i n f o

Article history:Received 30 August 2012Accepted 29 January 2014Available online 4 February 2014

Keywords:Plant factorySupply chainTaiwanese vegetable marketNashCournot modelOptimality condition

a b s t r a c t

Sustainable plant factory systems are able to provide steady and high-quality plants to markets whileusing less labor, water, nutrition, and pesticides. A plant factory is a controlled environment for plantproduction systems with articial light, temperature, humidity, carbon dioxide, water supply, andcultivation solution. This paper focuses on the entry and competition of a plant factory supply chain invegetable markets, using a NashCournot model to simulate this competition. The Lagrangian multipliermethod is used to derive KKT optimality conditions for the model. Combining the optimality conditionsyields a linear complementarity problem (LCP), which is solved by GAMS and PATH. A case study of theplant factory supply chain in nine Taiwanese vegetable markets is presented. The research simulates theimpact of the location of plant factories, number of rms, and different market demands. The resultsshow that total production and prots of the plant factory supply chain increase as transportation costsdecrease. In addition, the producer surplus, consumer surplus, and total surplus of the plant factorysupply chain in Taiwanese markets improve when factories are located close to the markets. A sensitivityanalysis is conducted which shows the impact of market share and production cost on the plant factorysupply chain. While the case study focuses on the Taiwanese agricultural commodity production, themethodology and analysis procedures have generalizability to similar plant production industryproblems in other contexts.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

1.1. Background

Plant factories are sustainable and environmental plants grow-ing systems because less water, nutrition, pesticides, and labor areconsumed for plant cultivation. The systems control lighting,temperature, humidity, water, the concentration of carbon dioxide,etc. in order to create an articial and efcient cultivationenvironment in an indoor space (Morimoto et al., 1995; Seginerand Ioslovich, 1999; Alfaro and Rabade, 2009; Winter GreenResearch, 2010; Ahumada and Villalobos, 2011). In plant factorysystems, plants are grown consistently all year round by means ofintegrated high technology systems with efcient energy, natural,and labor resources input. Hence, plant factories are sustainableand articially controlled environment systems which are able tostably produce high-quality vegetables.

Due to the high start-up cost of plant factories, the plant factorysystem is most often used to cultivate crops that have a high-protreturn. High-prot vegetables cultivated by plant factory systemsin Taiwan, Japan, and China include seedlings, herbs, fruits, andvegetables for consumers who are willing to pay the higher pricesfor these goods. In this paper, we analyze the entry of a plantfactory supply chain in vegetable markets and, in addition,simulate competitive behavior among plant factories in thesemarkets.

In this research, we analyze entry into vegetable markets andplant factory production competition in the markets by formulat-ing a NashCournot competition model (Hobbs, 2001; Gabriel andFuller, 2010; Arnold and Minner, 2011; Chung et al., 2012; Shamir,2012). Accordingly, KKT optimality conditions of the NashCournotmodel are derived by applying the Lagrangian multiplier method.Combining KKT equations presents an LCP model. The LCP is amodel that searches a real n-tulip vector variable, x, such that(AxB)Z0, xZ0, and xT(AxB)0, where A is a real nn matrixand B is a real n-tulip vector. When the perpendicular condition of(AxB) and x is denoted by ? , the LCP can be formulated as[0rx]?[(AxB)Z0]. In this paper, the LCP model is solved usingthe PATH solver and the GAMS. GAMS is an optimization modeling

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/ijpe

Int. J. Production Economics

http://dx.doi.org/10.1016/j.ijpe.2014.01.0260925-5273 & 2014 Elsevier B.V. All rights reserved.

n Corresponding author. Tel.: 886 2 33664418; fax: 886 2 23635879.E-mail addresses: [email protected] (M.-C. Hu), [email protected] (Y.-H. Chen),

[email protected] (L.-C. Huang).

Int. J. Production Economics 152 (2014) 4956

language for solving large, complex problems (Rosenthal, 2010).The PATH solver utilizes the most efcient algorithm for solvingthe LCP model (Ferris and Munson, 2000). Finally, we determinethe market equilibrium solution of the NashCournot model usingboth the GAMS and the PATH solver.

This paper is organized in the following manner. Section 2discusses related literature. Section 3 formulates the NashCour-not competition model of plant factory production in vegetablemarkets. Then, KKT conditions are derived using the Lagrangianmultiplier method. Accordingly, the mixed LCP model for plantfactory systems is built and solved by the GAMS and PATH solver.Section 4 presents a case study in Taiwanese vegetable markets,and Section 5 presents the conclusions.

1.2. History of the plant factory systems in Taiwan

In Taiwan, plant factory technology is relatively new but hasattracted interest from both the industry and academia. The rstplant factory was established by Risecare Company in 2010,although they only provide a limited range of leafy vegetables.National Taiwan University installed a new plant factory in thecampus in 2011, providing a facility for experts to conductcultivation experiments in a clean and warm house environment.Furthermore, such techniques are also being tested by NationalYilan University and National Chung Hsing University. The TaiwanPlant Factory Industry Development Association was established inMay 2011, with approximately 40 organization members inter-ested in plant factory technology and derived products. Most ofthese members form a part of the lighting technology, agriculturalautomatics, and agricultural cultivation technology industries,particularly the LED lighting system industry. The members intendextending their business into the eld of plant factory cultivationsystems, albeit using different business strategies. For example,Genesis Photonics Inc. and Everlight Electronics Co. Ltd, both LEDtechnology companies, plan to have their own plant factories. HonHai Precision Ind. Co. Ltd. cooperates with the National TaiwanUniversity for developing plant factory technology in vegetablecultivation. The current goal is to use the vegetables grown fromtheir plant factories to satisfy the dietary need of their employees,a total of 1,300,000 people around the world. Their long-term goalis to commercialize their plant factory-grown vegetables and toobtain a 49% share of the market. Furthermore, Hon Hai PrecisionInd. Co. Ltd. plans to cooperate with a university for developingvegetable cultivation technology for plant factories; the companyhas a long-term goal of obtaining a 49% share of the market forplant factory-grown business. Academic organizations have alsocontributed their resources to the development of plant factorytechnology. National Taiwan University, leading in plant factorytechnology in Taiwan, launches the products, including lettucegrown using the system, into the market. As a result of the highcost of plant factory technology, most investment in Taiwan is inthe cultivation of plants with high economic value, such as lettuce,seedlings, or herbs used as raw material for the bio-technologyindustry. Some horticultural companies in Taiwan are planning touse plant factories to grow cut owers. The high costs also meanthat most plant factory vegetables target consumers who arewilling to pay higher prices for these goods. There are alsocompanies in Taiwan that plan to apply plant factory technologyto urban horticulture. This will allow households in urban areas touse the factories and facilities to grow their vegetables without theneed for soil, which is always in limited supply in these areas.

Five companies from the industries of lighting equipment,building planning, and material service have launched plantfactories. The major products of Wang Yong Hydroponics MaterialsCo. Ltd. are lettuce, pak choi, Lactuca sativa Linn, and so on. WangYong Hydroponics Materials Co. Ltd. already has an enclosed

environmental control plant factory. It also provides LED plantfactory equipment, LED articial light, and 3-D cultivation systems.Zhu Wang Agriculture Corporation focuses on the equipment,cultivation beds, and organic fertilizer, which are essential partsof the plant factory industry. Furthermore, Zhu Wang AgricultureCorporation operates as a direct selling store, assisting farmers toconstruct LED plant factories and accelerating the know-howtransfer of the produce sales procedure in order to expand themarket for LED plant lights. Ting Mao Development Co. Ltd focuseson LED plant-growing lighting, farm and commercial plant fac-tories, medium and large plant factories, small plant factories,family-type layer plate gardens (customized), family balcony-stylegardens, and desktop plant light kits as gifts. Zhan Ye InternationalCo. Ltd. sells equipment for fully enclosed plant factories andgrowing chambers for home leisure planting. The main productsgrown in its plant factories are lettuce, pak choi, baby bok choy,spinach, crown daisy, coriander, and so on. Pacic Life ResortDevelopment Co. Ltd. sells the vegetables grown from the plantfactories. As mentioned earlier, the main crops cultivated by theplant factories of these ve companies in Taiwan focus mainly onvegetables that have a high economic value.

The cultivation technology for plant factories has been devel-oped in Taiwan and the relevant products are ready to launch tothe market. However, most published research concentrates ontechnology development of the plant factory itself, while onlylimited reports focus on investment benets. This paper analyzesthe strategy for entering the plant factory industry. Technologyalone is not enough to encourage investment in the industry.There also needs to be a market benet to back up the total input(Kruseman and Bade, 1998).

2. Literature review

In this paper, we formulate NashCournot and LCP models foranalyzing the competitive interaction between plant factories inTaiwanese vegetable markets. NashCournot and LCP models havebeen used in other research to simulate competition in economicand energy markets. Gabriel and Fuller (2010) formulated astochastic LCP model to simulate quantity competition in uncer-tain energy markets. They modied the Benders decompositionmethod in order to solve the stochastic LCP model. Hobbs (2001)established a NashCournot competition model to analyze bilat-eral and POOLCO electric power markets. This model examined theinteractive behavior among power generation rms, transmissiongrid owners, and market clearing conditions in the energy mar-kets. In addition, a NashCournot model was built to determinethe impact of biomass co-ring on market equilibrium in theTaiwanese power market (Hu et al., 2011).

With respect to plant factory production systems, optimizationmodels and algorithms have been utilized for determining optimalcontrolling strategies (Tzilivakis et al. 2005; Pandey et al., 2007;McGuire, 2008; Amorim et al., 2012; Eben-Chaime et al., 2011;Flores and Villalobos, 2013). In addition, economic analyses havealso been conducted to analyze plant factory production perfor-mance. Van Straten et al. (2000) analyzed optimal strategies oftemperature, moisture, and carbon dioxide control for crop grow-ing in greenhouses. Canakci and Akinci (2006) developed adynamic optimal control model for greenhouse production inTurkey. Their model determined optimal strategies for cost andenergy consumption for vegetable production in greenhouses. Jande Wit Company analyzed strategies for the production andtrading of lily owers and built a linear programming model fordecision support (Caixeta-Filho et al., 2002). Morimoto et al.(2003) established a dynamic optimization model to maintainwater content in fruit during storage; their research used a neural

M.-C. Hu et al. / Int. J. Production Economics 152 (2014) 495650

network and genetic algorithm to determine the best temperaturefor tomato storage. Francisco and Ali (2006) formulated a multi-objective problem and their model calculated the tradeoffbetween price-induced risk, yield-induced risk, labor employ-ment, and net return. Morimoto et al. (1995) established adynamic optimization with a Kalman lter model and presentedthe optimal water controlling strategies for plant physiologicalprocesses.

3. Methodology

In this section, we formulate a NashCournot quantity compe-tition model for the sustainable plant factory supply chain inTaiwanese vegetable markets. The model assumes that there areseveral companies in the market and each company owns multipleplant factories. The NashCournot model establishes the protmaximizing problem for each company. Then, the LCP model andKKT conditions are derived using the Lagrangian multipliermethod. Then, the LCP model is established on the GAMS platformand solved using the PATH solver.

In the vegetable market, a company f produces xfj vegetables ina plant factory j. The company f delivers tj from plant factory j tomarket i, and sells s in market i. The total sales of vegetables inmarket i is gsgi. Inserting the total sales into the linear inversedemand curve yields the market price (Aigsgi Ai=Bi),where Ai and Bi are the price and demand intercepts of the lineardemand curve for market i. Then, the total revenue of company f isisf i Aigsgi Ai=Bi. In addition, the total transportationcost and production cost are ijtf ij C1f ij and jxf j C2f j,respectively. Hence, the total prot for company f is calculated inEq. (1). We denote the production capacity of plant factory j forcompany f as Pfj. The production capacity constraint of plantfactory j for company f is formulated in Eq. (2). The transportationcost of the vegetables from the plants to the market is calculated inEq. (3). The total sales of company f in market i are estimated inEq. (4) and the non-negativity constraints are listed in Eq. (5).Therefore, the prot maximizing problem for company f in thevegetable production market is formulated in Eqs. (1)(5), wherethe indices, variables, and coefcients are as given below

max i sf i Aigsgi

Ai=Bi

!# "

ijtf ij C1f ij

jxf j C2f j 1

s:t: xf jPf jr0 8 j 2

xf jitf ij 0 8 j 3

itf ijsf i 0 8 i 4

xf j; tf ij; sf iZ0 8 i; j 5Indices

f, g companies, f, g1,,Fi markets, i1,,ij plant factories, j1,,J

Variables

xfj production of the plant factory j for company f [Mg]tj transportation from the plant factory j to market i for

company f [Mg]s sales in market i for company f [Mg]

Coefcients

Ai price intercept of linear demand curve for market i [NTD/Mg]

Bi quantity intercept of linear demand curve for marketi [Mg]

C1j transportation cost from plant factory j to market i forcompany f [NTD/Mg]

C2fj production cost of plant factory j for company f [NTD/Mg]

Pfj production capacity of plant factory j for company f [Mg]

In order to solve the prot maximizing problem, KKT optimalityconditions are derived using the Lagrangian method and optimalsolutions are calculated. We denote fj, fj, and fj as the Lagrangianmultipliers for production capacity, factory transportation, andmarket transportation constraints in the model, respectively. TheLagrangian function is established in Eq. (6). Taking the derivativeof the Lagrangian function with respect to each variable yields theKKT conditions. The KKT conditions displayed in Eqs. (7)(12)establish an LCP model for simulating the NashCournot competi-tion of plant factory companies in the vegetable productionmarket. In order to obtain an equilibrium solution in the markets,the LCP model is formulated on the GAMS software and analyzedusing the PATH solver. The model demonstrates the competitionbetween plant factory production companies. Each companymaximizes total prot by selecting optimal production and trans-portation plans. The market equilibrium is derived and a casestudy is conducted in next section. In this research, the competi-tion model, production constraints, transportation constraints, andmarket equilibrium are general and can be applied to otherdifferent business situations

max Lxf j; tf ij; sf i; f j; f j; f i

i

sf i Ai

gsgi

Ai=Bi

!#

ij

"tf ij C1f ij

#

j

"xf j C2f j

#"

f j xf jPf j

!f j

xf j

itf ij

!f i

jtf ijsf i

!

xf j; tf ij; sf i; f jZ0 8 i; jf j; f i unrestricted 8 i; j 6

KKT conditions of company f for xfjZ0 are"f jf jC2f j

#Z0 8 j

xf j "f jf jC2f j

# 0 8 j 7

KKT conditions of company f for tjZ0 are"f if jC1f ij

#Z0 8 i; j

tf ij "f if jC1f ij

# 0 8 i; j 8

KKT conditions of company f for sZ0 are

f iAi gsgisf i Ai=Bi

!" #Z0 8 i

sf i "f iAi

gsgisf i

! Ai=Bi

# 0 8 i

9

M.-C. Hu et al. / Int. J. Production Economics 152 (2014) 4956 51

KKT conditions of company f for fjZ0 are

xf jPf jZ0 8 jf j xf jPf j 0 8 j 10

KKT conditions of company f for fj are

xf jitf ij

# 0 8 j

"11

KKT conditions of company f for are

jtf ijsf i

# 0 8 i

"12

Variables

fj Lagrangian multipliers of production capacity constraintof plant factory j for company f [NTD/Mg]

fj Lagrangian multipliers of factory transportation con-straint of plant factory j for company f [NTD/Mg]

Lagrangian multipliers of market transportation con-straint of market i for company f [NTD/Mg]

The model can be applied to specic market of plant factoryproduction and other general situations. Eq. (1) calculates totalprot for a single company and the structure can be applied tosimilar situations. However, the high installation, energy, andtransportation cost for agricultural commodity production con-sidered in Eq. (1) is specic for plant factory production markets.In addition, the basic structure of production capacity and trans-portation constraints in Eqs. (2)(5) is general to other industries.Notice that the data of existing capacity and the investment of newplant factory are specic and should be provided for solving Eqs.(2)(5). Furthermore, the model presents a general framework toanalyze the production competition in the market. Eqs. (1)(5)establish the prot maximizing problem for each participating

company. The associate KKT optimality conditions are derived andpresented in Eqs. (6)(12). The procedures are general and can beapplied to all production competition scenarios.

4. Results and discussion

This section analyzes the NashCournot competition of thesustainable plant factories production system in Taiwanese vege-table markets. A case study of the plant factory supply chain innine Taiwanese vegetable markets is also presented. The marketdemand curves of a plant factory in nine representative Taiwanesevegetables market are derived. We assume organic vegetableconsumers are the potential buyers for plant factory product inthe market. According the survey of this research, the averageprice of organic vegetables is approximately 150220 NTD/kg inthe market. In addition, the annual consumption of organicvegetables in Taiwanese markets is collected. The model is rununder the assumption that plant factories supply 25% of organicvegetable consumption. Then, the total vegetable demand of plantfactories is calculated for nine Taiwanese markets. Given that thelinear demand elasticity is 0.15 in the Taiwanese organicvegetable market, the linear inverse demand functions of plantfactories are established. Furthermore, this research assumes theproduction cost of vegetables in plant factories to be 100 NTD/kg.

The model assumes symmetric plant factory companies in themarket; scenarios with different numbers of companies are alsosimulated. In Table 1, the results show that revenue and produc-tion costs of each company are 15.96 billion NTD and 3.55 billionNTD in a duopoly scenario. The revenue and production costdecrease to 1.89 billion NTD and 0.97 billion NTD in a ten-company scenario. The prot for each company decreases from12.42 billion NTD (duopoly case) to 0.92 billion NTD (ten-companycase) because of the increasing number of companies in themarket. Accordingly, the producer surplus decreases from 24.83

Table 1Market equilibrium of plant factory production without transportation cost.

Total number of rms Revenue (NTD) Production cost (NTD) Prot (NTD) Producer surplus (NTD) Consumer surplus (NTD) Total surplus (NTD)

2 15,964,500,000 3,547,664,000 12,416,836,000 24,833,672,000 24,833,600,000 49,667,272,0003 9,645,212,000 2,660,748,000 6,984,464,000 20,953,392,000 31,430,100,000 52,383,492,0004 6,598,655,000 2,128,598,000 4,470,057,000 17,880,228,000 35,760,500,000 53,640,728,0005 4,878,038,000 1,773,832,000 3,104,206,000 15,521,030,000 38,802,600,000 54,323,630,0006 3,801,069,000 1,520,427,000 2,280,642,000 13,683,852,000 41,051,500,000 54,735,352,0007 3,076,490,000 1,330,374,000 1,746,116,000 12,222,812,000 42,779,800,000 55,002,612,0008 2,562,202,000 1,182,555,000 1,379,647,000 11,037,176,000 44,148,700,000 55,185,876,0009 2,181,813,000 1,064,299,000 1,117,514,000 10,057,626,000 45,259,300,000 55,316,926,00010 1,891,110,000 967,544,800 923,565,200 9,235,652,000 46,178,300,000 55,413,952,000

Table 2Sensitivity analysis for market share of plant factory production.

Total number of rms 15% of market share 35% of market share

Prot (NTD) Producer surplus (NTD) Total surplus (NTD) Prot (NTD) Producer surplus (NTD) Total surplus (NTD)

2 3,920,450,000 7,840,901,000 15,681,800,000 25,679,500,000 51,358,900,000 102,718,000,0003 2,205,253,000 6,615,760,000 16,539,400,000 14,444,700,000 43,334,100,000 108,335,000,0004 1,411,362,000 5,645,449,000 16,936,300,000 9,244,605,000 36,978,400,000 110,935,000,0005 980,112,600 4,900,563,000 17,152,000,000 6,419,864,000 32,099,300,000 112,348,000,0006 720,082,700 4,320,496,000 17,282,000,000 4,716,635,000 28,299,800,000 113,199,000,0007 551,313,300 3,859,193,000 17,366,400,000 3,611,174,000 25,278,200,000 113,752,000,0008 435,605,600 3,484,845,000 17,424,200,000 2,853,273,000 22,826,200,000 114,131,000,0009 352,840,500 3,175,565,000 17,465,600,000 2,311,151,000 20,800,400,000 114,402,000,00010 291,603,800 2,916,038,000 17,496,200,000 1,910,042,000 19,100,400,000 114,603,000,000


billion NTD (duopoly case) to 9.24 billion NTD (ten-company case).On the other hand, the consumer surplus rises from 24.83 billionNTD (duopoly case) to 46.18 billion NTD (ten-company case).The rise of consumer surplus is because of the result of theincreasing competition among the companies and the decreasingequilibrium price. Consequently, the total surplus of the marketgrows from 49.67 billion NTD to 55.41 billion NTD.

The sensitivity analyses of market share and production costare performed. In Table 2, the results show that the decrease ofmarket share lowers rm prot and producer surplus. On theother hand, increase of market share rises rm prot and producersurplus. For example of duopoly case, lowering market share from25% to 15% deducts rm prot by 8.50 (12.423.92) billion NTDand producer surplus (from 24.33 to 7.84 billion NTD). Whilemarket share expands from 25% to 35%, rm prot increases from12.42 to 25.68 billion NTD and producer surplus grows from 24.33to 51.36 billion NTD for higher market share rises. Table 3 showsthe result of sensitivity analysis for production cost. The rmprot, producer surplus, and total surplus rise while productioncost drops. Meanwhile, the increase of production cost decreasesrm prot, producer surplus, and total surplus.

Next, we discuss the payback period of investment in a plantfactory. If we assume a plant factory company earns a uniformseries of annual prots, then Eq. (13) calculates the payback periodof the present investment

PIAP 1 IRPPAP

=

IR 1 IRPP

; 13

where PI, AP, IR, and PP are the present investment, annual prot,interest rate, and payback period, respectively. Table 4 shows thepayback periods of factory investment ranges from 0.5 years(a two-company scenario) to 5 years (a ten-company scenario).

Next, we analyze the impact of transportation costs by simulat-ing different locations of plant factories in a ve-rm scenario inTaiwanese vegetable markets. In order to compare different

production locations, three factory locations of Firm 1 are scat-tered uniformly in Northern Taiwan (Taipei), Central Taiwan(Taichung), and Southern Taiwan (Tainan). Firms 2, 3, 4, and5 are assumed to be located separately in Northern Taiwan, CentralTaiwan, Southern Taiwan, and Eastern Taiwan, respectively. Thedetailed locations of Firms 1, 2, 3, 4, and 5 are displayed in Table 5and Fig. 1. Hence, the location of plant factory production in thevegetable markets of the ve major cities is addressed in Table 6.Furthermore, the location of plant factory production in county-level markets is compared in Table 7.

Because Firm 1 has three plant factories in the North, Central,and South, Firm 1 is able to deliver its produce easily to eachmarket. Vegetables sold by Firm 1 in Taipei city, New Taipei city,northern county, and eastern county markets are grown in theplant factory in the Taipei area. The vegetables of Taichung city andcentral county markets are provided by the central factory in theTaichung area. Furthermore, the Tainan factory supplies vegetablesto Tainan city, Kaohsiung city, and the southern county markets.Since the factories of Firm 2 are located in the north, vegetablessold by Firm 2 in the markets of Taipei city, New Taipei city, thenorthern county, and the eastern county are delivered fromfactories in Taipei and Taoyuan. Otherwise, the markets inTaichung city, Tainan city, Kaohsiung city, the central county, andthe southern county are supplied by factories in Hsinchu. Firm3 delivers vegetables fromMiaoli to the markets in Taipei city, NewTaipei city, the northern county, and the eastern county. Further-more, vegetables transported to Taichung city and the centralcounties are produced in the plant factories of Taichung; theremainder is provided by factories in Nantou. Because the factoriesof Firm 4 are in southern Taiwan, the vegetable demand of Tainancity, Kaohsiung city, the southern county, and the eastern countyare met by factories in Tainan and Kaohsiung. Furthermore, thefactories of Chiayi contribute the majority of the vegetableproduction in order to meet the remainder of the market demand.Firm 5 owns eastern plant factories; thus, demand in Taipei city,New Taipei city, Taichung city, the northern county, and the centralcounty is met by the factories in Yilan. The factories of Taitunggrow vegetables for Taichung city, Kaohsiung city, and the south-ern county markets; the factories of Hualien supply the easterncounty.

Table 3Sensitivity analysis for production cost of plant factory production.

Total number of rms 90 NTD/kg production cost 110 NTD/kg production cost

Prot (NTD) Producer surplus (NTD) Total surplus (NTD) Prot (NTD) Producer surplus (NTD) Total surplus (NTD)

2 12,654,500,000 25,308,900,000 50,617,800,000 12,181,400,000 24,362,900,000 48,725,800,0003 7,118,135,000 21,354,400,000 53,386,000,000 6,852,060,000 20,556,200,000 51,390,400,0004 4,555,606,000 18,222,400,000 54,667,300,000 4,385,318,000 17,541,300,000 52,623,800,0005 3,163,615,000 15,818,100,000 55,363,300,000 3,045,360,000 15,226,800,000 53,293,800,0006 2,324,289,000 13,945,700,000 55,782,900,000 2,237,407,000 13,424,400,000 53,697,800,0007 1,779,534,000 12,456,700,000 56,055,300,000 1,713,015,000 11,991,100,000 53,960,000,0008 1,406,051,000 11,248,400,000 56,242,100,000 1,353,493,000 10,827,900,000 54,139,700,0009 1,138,902,000 10,250,100,000 56,375,600,000 1,096,330,000 9,866,966,000 54,268,300,00010 941,240,900 9,412,409,000 56,474,500,000 906,057,500 9,060,575,000 54,363,500,000

Table 4Payback periods for different numbers of companies in the vegetable market(years).

Number of companies Interest rate

0% 1% 2% 3% 4%

2 0.4855 0.4891 0.4927 0.4963 0.50003 0.8035 0.8108 0.8181 0.8255 0.83294 1.1745 1.1873 1.2003 1.2135 1.22695 1.5888 1.6095 1.6306 1.6522 1.67416 2.0389 2.0703 2.1024 2.1353 2.16917 2.5191 2.5641 2.6105 2.6585 2.70808 3.0247 3.0868 3.1512 3.2182 3.28809 3.5521 3.6348 3.7213 3.8120 3.907310 4.0981 4.2054 4.3185 4.4381 4.5649

Table 5Location of plant factories in Taiwanese markets.

Firm Location of plant factories

Firm 1 Taipei Taichung TainanFirm 2 Taipei Taoyuan HsinchuFirm 3 Miaoli Taichung NantouFirm 4 Chiayi Tainan KaohsiungFirm 5 Yilan Hualien Taitung


Table 8 shows the market equilibrium of the ve plant factories.Firm 1 is expected to sell the highest amount of vegetables and earnthe highest prot of 3.13 billion NTD. The reason is that Firm 1, withfactories in northern, central, and southern Taiwan, has the lowesttransportation cost of 12.80 million NTD. In addition, the resultsshow that Firms 2 and 3 make second highest prot of 3.10 billionNTD. Since the population and market demand are concentrated inthe northern part of Taiwan, the factories of Firm 2 located inthe north have lower transportation costs of 28.49 million NTD.In contrast, the three factories of Firm 3 are located in the middleof Taiwan, so transportation to all markets is convenient andtherefore their transportation costs are also low (28.40 millionNTD). Firms 4 and 5 are located in southern and eastern Taiwan, andso the factories are relatively far from most vegetable markets.Accordingly, Firms 4 and 5 pay the highest transportation costs of35.29 million NTD and 42.61 million NTD, respectively. Hence,Firms 4 and 5 earn the lowest prots of 3.08 billion NTD and 3.07billion NTD, respectively.

Tables 9 and 10 compare the impact of the number of plantfactories on market equilibrium, consumer surplus, producersurplus, and total surplus. A producer surplus is the benetto a producer for selling products at a price that is higher than

consumers are normally willing to pay. A consumer surplus is themonetary gain to consumers when the market price is lessthan they would be willing to pay. The total surplus is thetotal welfare, which is the sum of the producer surplus andconsumer surplus. As the number of plant factories increases,the transportation costs and production costs decrease. Thenconsumer surplus, producer surplus, and total surplus increase.Specically, when each rm has only one factory, the producersurplus is 15,450,200,000 NTD; the consumer surplus is 38,623,500,000 NTD; and the total surplus is 54,073,700,000 NTD. Thesegures rise to 15,476,600,000 (producer surplus); 38,690,500,000(consumer surplus); and 54,167,100,000 (total surplus) when thenumber of factories increases to four per company.

5. Conclusions

In this research, we analyzed the quantity of competition forsustainable supply chain of plant factory in vegetable markets.Combining the prot maximizing problems of plant factorycompanies yields a NashCournot competition model. In themodel, every company seeks to maximize prot subject to pro-duction, transportation, and market demand constraints. Then,KKT conditions of prot maximizing problems were derived usingthe Lagrangian multiplier method. Accordingly, merging the KKTconditions and the model establishes an LCP model. The model isformulated on GAMS software and solved using the PATH solver.Furthermore, we conducted a case study for Taiwanese vegetablemarkets. Nine markets were considered, including markets in vemajor cities and four county-level areas.

The results simulated sustainable plant factory production mar-ket, compared different locations for plant factories in a ve-rmscenario, and then quantied the impact of transportation costs inthe Taiwanese vegetables markets. First, increasing competitionshrinks rm prots from 12.42 billion NTD (two-rm case) to 0.92billion NTD (ten-rm case). The producer surplus decreases by 15.59billion NTD and the consumer surplus increases by 21.35 billion NTD.Therefore, the total surplus increases by 5.76 billion NTD, and thepayback periods of factory investment increase from 0.5 years (two-rm scenario) to 5 years (ten-rm scenario). Next, under marketequilibrium when each rm has ve plant factories, Firm 1withfactories in northern, central, and southern Taiwanhas the lowesttransportation costs of 12.80 million NTD and therefore the highestprot of 3.13 billion NTD. Firm 5, with the highest transportation costof 42.61 million NTD, earns the lowest prot of 3.07 billion NTD. Inaddition, the results show that increasing the number of plantfactories reduces transportation distance and transportation costsand therefore yields higher social welfare. In this case, the producersurplus, consumer surplus, and total surplus rise by 26 million NTD,67 million NTD, and 93 million NTD, respectively.

The signicant contribution of this paper contains three parts,including geospatial analysis of LCP model, investigation of newemerging and important industry of plant factory production, andcase study and sensitivity analysis of plant factory production inTaiwanese vegetable markets. The transportation cost and manage-ment of plant factory production are important factors and must beconsidered. In previous studies, LCP models were used to simulatemarket competition but few of them discussed spatial relationshipof the LCP model. Hence, the rst major contribution of our researchis to analyze the geospatial relationship between plant factorysupply and demand by formulating the spatial LCP model of plantfactory production. In the model, the transportation cost and spatiallocation are considered. In the results, the locational and strategicdelivery management of plant factory systems is presented. Plantfactories are articially controlled environment systems which areable to stably produce high-quality vegetables with less water,

Fig. 1. Location of cities and plant factories in Taiwanese markets.


nutrition, pesticides, and labor consumption. Plant factories areemerging and sustainable production systems for future plantcultivation. In Asia, plant factory systems in Taiwan, Japan, andChina already cultivated high-prot seedlings, herbs, fruits, andvegetables for consumers. However, previous studies focused oncontrolling technologies and strategies of plant factories; few of

them concerned the entry of the plant factory supply chain invegetable markets. The second major contribution of this paper is toanalyze the penetration of plant factory systems in the agriculturalcommodity markets and then assess the potential of the plantfactory production industry. Plant factory systems are emergingplant production industry in the future. None of the previous

Table 6Production of plant factories in the markets of Taiwan's ve major cities.

Firm Location of plant factories Taipei city (kg) New Taipei city (kg) Taichung city (kg) Tainan city (kg) Kaohsiung city (kg)

Firm 1 Taipei 2,661,111 5,018,095Firm 1 Taichung 1,995,739Firm 1 Tainan 1,776,431 2,197,500Firm 2 Taipei 1,303,329 2,481,821Firm 2 Taoyuan 1,357,782 2,536,274Firm 2 Hsinchu 1,985,511 1,753,199 2,165,625Firm 3 Miaoli 2,647,475 4,992,381Firm 3 Taichung 1,995,739Firm 3 Nantou 1,763,805 2,177,500Firm 4 Chiayi 2,626,263 4,952,381 1,985,511Firm 4 Tainan 1,776,431Firm 4 Kaohsiung 2,201,250Firm 5 Yilan 2,642,172 4,982,381 1,966,193Firm 5 HualienFirm 5 Taitung 1,753,199 2,173,750Total 13,238,131 24,963,333 9,928,693 8,823,064 10,915,625

Table 8Market equilibrium of ve plant factories, including transportation costs.

Firm Revenue (NTD) Production cost (NTD) Transportation cost (NTD) Total cost (NTD) Prot (NTD)

Firm 1 4,921,639,000 1,780,666,000 12,799,889 1,793,466,000 3,128,174,000Firm 2 4,896,543,000 1,771,591,000 28,488,388 1,800,080,000 3,096,463,000Firm 3 4,896,831,000 1,771,692,000 28,400,823 1,800,093,000 3,096,738,000Firm 4 4,885,678,000 1,767,649,000 35,287,895 1,802,937,000 3,082,741,000Firm 5 4,874,031,000 1,763,440,000 42,614,005 1,806,054,000 3,067,977,000

Table 7Production of plant factories in county-level markets.

Firm Location of plant factories Northern Taiwan (kg) Central Taiwan (kg) Southern Taiwan (kg) Eastern Taiwan (kg)

Firm 1 Taipei 1,463,056 217,813Firm 1 Taichung 878,125Firm 1 Tainan 1,598,788Firm 2 Taipei 704,301 217,813Firm 2 Taoyuan 758,754Firm 2 Hsinchu 873,625 1,577,879Firm 3 Miaoli 1,457,222 217,250Firm 3 Taichung 878,125Firm 3 Nantou 1,587,424Firm 4 Chiayi 1,445,556 873,625Firm 4 Tainan 1,598,788Firm 4 Kaohsiung 216,688Firm 5 Yilan 1,452,639 865,125Firm 5 Hualien 221,063Firm 5 Taitung 1,577,879Total 7,281,528 4,368,625 7,940,757 1,090,625

Table 9The impact of number of plant factories on market equilibrium.

Number ofplantfactories

Marketrevenue (NTD)

Marketproductioncost (NTD)

Markettransportationcost (NTD)

Market totalcost (NTD)

1 24,512,700,000 8,848,667,000 213,875,200 9,062,543,0002 24,485,300,000 8,853,265,000 165,992,700 9,019,258,0003 24,474,700,000 8,855,038,000 147,591,000 9,002,629,0004 24,467,000,000 8,856,338,000 134,001,100 8,990,339,000

Table 10The impact of number of plant factories on economic surplus.

Number of plantfactories

Producer surplus(NTD)

Consumer surplus(NTD)

Total surplus(NTD)

1 15,450,200,000 38,623,500,000 54,073,700,0002 15,466,000,000 38,663,600,000 54,129,700,0003 15,472,100,000 38,679,100,000 54,151,200,0004 15,476,600,000 38,690,500,000 54,167,100,000


studies analyzed or simulated the entry of plant factory systems inagricultural markets. Therefore, the third major contribution of thisresearch is to conduct a case study and sensitivity analysis of plantfactory production for various supply and demand scenarios inTaiwanese vegetable markets. A case study of the plant factorysupply chain in nine Taiwanese vegetable markets is provided.Further, the sensitivity analyses of market share and productioncost are performed. In the results, the geospatial relationshipbetween plant factory supply and demand is presented anddiscussed.

In this research, we formulate a NashCournot competitivemodel and then the model is applied to an interesting applicationdomain plant, factory production systems. Notice that the meth-odology of the competition model can be applied to specicmarket of plant factory production and other general situations.The case study simulated the competition of plant factories,compared different locations for plant factories in a ve-rmscenario, quantied the impact of transportation cost, and thenconducted sensitivity analysis in the Taiwanese vegetables mar-kets. Optimal production strategies for plant factories and green-houses have been determined in the previous studies. However,the economic competition of plant factory production has neverbeen analyzed. Therefore, the signicant contribution of thisresearch is the application of the NashCournot model to thesustainable plant factory supply chain. A NashCournot competi-tive model is formulated for an agricultural commodity productionsystem. Then, rst-order optimality conditions of the optimalmodels are derived using the Lagrangian multiplier method. Next,combining KKT conditions yields an LCP model, which is solvedusing the GAMS and PATH solver. Taiwanese vegetable market datais collected, and a case study of the NashCournot competitivemodel is conducted in Taiwanese markets. Future topics of thestudy include a formulation of a stochastic LCP model for vege-table markets, a multi-objective analysis of plant factory produc-tion, and facility location problems for a plant factory system.

Acknowledgments

The authors would like to thank the anonymous referees andeditors for their thoughtful comments and suggestions. The authorsare responsible for the accuracy of the information presented in thispaper and for all opinions expressed herein. This research wasfunded by the National Science Council of Taiwan under Grant NSC-102-2313-B-002-054-MY3, NSC-100-2313-B-002-056, and NTU-99R50019-5.

References

Ahumada, O., Villalobos, J.R., 2011. Operational model for planning the harvest anddistribution of perishable agricultural products. Int. J. Prod. Econ. 133 (2),677687.

Alfaro, J.A., Rabade, L.A., 2009. Traceability as a strategic tool to improve inventorymanagement: a case study in the food industry. Int. J. Prod. Econ. 118 (1),104110.

Amorim, P., Gunther, H.O., Almada-Lobo, B., 2012. Multi-objective integratedproduction and distribution planning of perishable products. Int. J. Prod. Econ.138 (1), 89101.

Arnold, J., Minner, S., 2011. Financial and operational instruments for commodityprocurement in quantity competition. Int. J. Prod. Econ. 131 (1), 96106.

Caixeta-Filho, J.V., van Swaay-Neto, J.M., de Padua Wagemaker, A., 2002. Optimiza-tion of the production planning and trade of lily owers at Jan de Wit Company.INFORMS 32 (1), 3546.

Canakci, M., Akinci, I., 2006. Energy use pattern analyses of greenhouse vegetableproduction. Energy 31, 12431256.

Chung, S.H., Weaver, R.D., Friesz, T.L., 2012. Oligopolies in pollution permit markets:a dynamic game approach. Int. J. Prod. Econ. 140 (1), 4856.

Eben-Chaime, M., Bechar, A., Baron, A., 2011. Economical evaluation of greenhouselayout design. Int. J. Prod. Econ. 134 (1), 246254.

Ferris, M.C., Munson, T.S., 2000. GAMS/PATH User Guide Version 4.3. http://www.gams.com/docs/pdf/path.pdf.

Flores, H., Villalobos, J.R., 2013. Using market intelligence for the opportunisticshipping of fresh produce. Int. J. Prod. Econ. 142 (1), 8997.

Francisco, S.R., Ali, M., 2006. Resource allocation tradeoffs in Manila's peri-urbanvegetable production systems: an application of multiple objective program-ming. Agric. Syst. 87, 147168.

Gabriel, S.A., Fuller, J.D., 2010. A Benders decomposition method for solvingstochastic complementarity problems with an application in energy. Comput.Econ. 35 (4), 301329.

Hobbs, B.F., 2001. Linear complementarity models of NashCournot competition inbilaterial and POOLCO power markets. IEEE Trans. Power Syst. 16 (2), 194202.

Hu, M.C., Lin, C.H., Chou, C.A., Hsu, S.Y., Wen, T.H., 2011. Analysis of biomass co-ring systems in Taiwan power markets using linear complementarity models.Energy Policy 39 (8), 45944600.

Kruseman, G., Bade, J., 1998. Agrarian policies for sustainable land use: bio-economic modeling to assess the effectiveness of policy instruments. Agric.Syst. 58 (3), 465481.

McGuire, S.J., 2008. Path-dependency in plant breeding: challenges facing partici-patory reforms in the Ethiopian Sorghum Improvement Program. Agric. Syst.96, 139149.

Morimoto, T., Torii, T., Hashimoto, Y., 1995. Optimal control of physiologicalprocesses of plants in a green plant factory. Control Eng. Pract. 3 (4), 505511.

Morimoto, T., Tu, K., Hatou, K., Hashimoto, Y., 2003. Dynamic optimization usingneural networks and genetic algorithms for tomato cool storage to minimizewater loss. Trans. ASABE 46 (4), 11511159.

Pandey, C.B., Rai, R.B., Singh, L., Singh, A.K., 2007. Homegardens of Andaman andNicobar, India. Agric. Syst. 92, 122.

Rosenthal, R.E., 2010. GAMS: A User's Guide. http://www.gams.com/dd/docs/bigdocs/GAMSUsersGuide.pdf.

Seginer, I., Ioslovich, I., 1999. Optimal spacing and cultivation intensity for anindustrialized crop production system. Agric. Syst. 62, 143157.

Shamir, N., 2012. Strategic information sharing between competing retailers in asupply chain with endogenous wholesale price. Int. J. Prod. Econ. 136 (2),352365.

Tzilivakis, J., Warner, D.J., May, M., Lewis, K.A., Jaggard, K., 2005. An assessment ofthe energy inputs and greenhouse gas emissions in sugar beet (Beta vulgaris)production in the UK. Agric. Syst. 85, 101119.

Van Straten, G., Challa, H., Buwalda, F., 2000. Towards user accepted optimal controlof greenhouse climate. Comput. Electron. Agric. 26, 221238.

Winter Green Research, 2010. Plant Factory Grow Lights and Control SystemsMarket Strategies, Shares and Forecasts, Worldwide, 20102016. Lexington,MA, USA.


A sustainable vegetable supply chain using plant factories in Taiwanese markets: A NashCournot modelIntroductionBackgroundHistory of the plant factory systems in Taiwan

Literature reviewMethodologyResults and discussionConclusionsAcknowledgmentsReferences

Documents

A Sustainable Vegetable Supply Chain Using Plant Factories in Taiwanese