Potential of mathematical model-based decision making to promote sustainable performance of agriculture in developing countries: A review article.

In developing countries like Ethiopia, agriculture takes the leading role in the economy and enhancing the efficiency of agriculture resource decision making remains essential to eradicate extreme poverty through promoting sustainable agricultural production. Recent economic growth efforts in agriculture dependent economies are aggravating to further natural resource degradation, environmental pollution, and climate change. One of the main challenges is the use of inefficient conventional land use decision-making. Conventional land use decision making refers to the practice of traditional land use decision-making, which is inefficient to capture spatial and temporal land use decision dynamics and trade-offs. This paper reviewed existing literatures on decision-making models in agriculture targeting to document the potential of mathematical model-based decision making to enhance the sustainable performance of agriculture in developing countries compared to the existing conventional agricultural practice decision approach. From over 400 literatures collected from the Google Scholar search engine; 63 articles were selected for the synthesis. The literatures were screened through inclusion and exclusion criteria. Literatures that used any mathematical model as a decision support tool in agriculture and related sectors, included a clear description of the model type, aim of the study, the key attribute characterizing the application of the model, decision support system, and output were included in the review. The synthesis result uncovered that with varying degrees of impact, flexibility, and complexity, mathematical model-based land use decision making has greater potential to enhance sustainable performance of agriculture and resource use efficiency in developing countries.

Introduction

Literature shows that besides low input use, immature output markets, and inappropriate agricultural policies, agriculture, the main stay of the economy of developing countries suffers from low resource use efficiency that might be attributed to poor resource use decisions. Evidence from many studies uncovers this fact. Resource use inefficiency such as technical inefficiency, distribution inefficiency, and environmental costs are key factors that compromised the performance of agriculture over time in developing regions (Haque, 2006; Mesike et al., 2009; Mussa et al., 2011; Alabdulkader et al., 2012).

Efficiency has long been a topic of empirical research, beginning from the formal practice of Operations Research (OR) during World War II; by the British and US military to assist allocation of scarce war tools. The resulting success of these efforts promoted the use of operations research in various civilian sectors. Several interrelated and computer-aided decision support systems have been developed and used in various sectors like in transportation scheduling, land allocation, and production planning. Since the 1950s, a number of variants mathematical model based decision support tools emerged (Bjørndal et al., 2012), such as linear programming (Dantzig and Thapa, 2003), goal programming, multi-objective programming, fuzzy goal programming, and other computer aided decision support systems that significantly improved resource use efficiency. To date, these models are used in different civilian sectors worldwide, including in agriculture. Moreover, the fourth evolution of the farming technology (Agriculture 4.0) that include use of decision support systems is a topic of research worldwide that targeted to increase productivity, allocating resources efficiently, adapting to climate change, and avoiding food waste (Zhai et al., 2020). However, smallholder farming system in most developing countries is mainly practiced by manpower and animal force using simple tools (Agriculture 1.0). Particularly, the use of mathematical model-based decision support tools is limited in developing countries.

In developing countries, rainfed mixed agriculture is the mainstay of the economy, which accounts for 40–90 % of the employment, 30–60 % of the Gross Domestic Product (GDP), and 25–95% of the foreign exchange (FAO, 2002; Hordofa et al., 2008; Federal Democratic Republic of Ethiopia, 2011; Tedla, 2012; Minot and Sawyer, 2013). Even if developing countries has significant potential for irrigation, the practice of small-scale and large-scale irrigation is immature and the existing practice itself is completely dependent on conventional decision-making of critical resources such as water, land, cropping mix and/or pattern, and other agricultural inputs (Xie et al., 2014, 2021; Nigussie et al., 2020). Supporting this fact, Belete et al. (2011) describes conventional irrigated agriculture as immature that lack both technical and input use efficiency.

In addition to the local and intrinsic challenges, the burden of climate change is significant in developing countries (Anderson et al., 2020) which calls for comprehensive adaptation and mitigation strategy and action to ensure food security and development. In this regard, a study aimed at investigating CO2 emissions’ impact on agricultural performance and household welfare in Ethiopia indicated that CO2 emission is compromising agricultural productivity and household welfare (Eshete and Gatiso, 2020).

Besides the challenges, agriculture has untapped potential for economic growth, poverty reduction, and rural development in developing countries. The International consultative conference held in Addis Ababa, Ethiopia, entitled “Advancing Agriculture in Developing Countries through Knowledge and Innovation” pronounced that advancing agricultural performance through knowledge and innovation is key for growth and poverty reduction in developing countries (Research Institute (IFPRI), 2009). However, agriculture is continuing to suffer from resource use inefficiency due to limited technology and innovation that include inefficient agricultural resource decision-making practices in addition to natural and environmental factors (Federal Democratic Republic of Ethiopia, 2011; Mussa et al., 2011; Geta et al., 2013). Hence, the purpose of this paper is to review and document the significance of mathematical model-based decision making to unlock challenges associated with agricultural resource use efficiency and to promote sustainable performance of agriculture. The finding will have significant contribution for decision makers, researchers, and policy makers in the field of agriculture, particularly in developing countries.

Method and materials

Scoping review design was used to thoroughly examine and synthesize existing literature with the aim to understand the potential of mathematical model-based decision making to enhance the sustainable performance of agriculture. Scoping review technique was preferred from other methods of review by the fact that this technique suits to address the aim of the review study through classifying, evaluating, synthesizing, and summarizing.

Organization of the review

In this paper, a review of relevant literatures (empirical research and previous reviews) on mathematical model-based decision making in agriculture and summary of these models with possible implications for sustainable planning to enhance the performance of agriculture in the face of climate change was made. Literature search made advanced back from March 2020 on mathematical model-based decision making in agriculture were made in the Google Scholar search engine. The terms mathematical model, mathematical programming, agricultural production, agricultural resource allocation, and a combination of these with “AND” and “OR” were used to browse literatures.

The broad search passed through title and abstract screening resulted in the collection of over 400 studies including journal articles, conference papers, master's and doctoral dissertations, and unpublished papers and reports. These literatures were then screened through inclusion and exclusion criteria. Literatures that:

involved one of the mathematical models as a decision support system in agriculture and related sectors,

included a clear description of model type, aim of the study, the key attribute characterizing the application of the model, decision support system, and possible output outlined,

was carried out in any country from around the world but published/written in English language, and/or

is a review study of studies employing one or more of mathematical model-based decision systems in agriculture and related sectors were included in the review.

The studies were then synthesized and summarized into mathematical model groups as linear programming, multi-objective programming, goal programming, fuzzy goal programming, and mathematical models integrated with GIS. Details of reviewed articles, author(s) name and publication year, country, model name, application area (crop, livestock, fishpond, tree lots, farm, grassland, landscape, watershed, and basin), aim of the study, key attribute, decision-making model type, and outlined output, are annexed in appendix A. Based on the screening first 50 articles were selected for the synthesis. In order to widen the search scope, an iterative technique that involved examining the reference sections of the pre-accessed articles were also used and additional 13 articles were collected for the synthesis. Including 23 literatures used to strengthen argument in the review, a total of 86 literatures are used in the review.

Result and discussion

The screening resulted the following categories of the literature: single objective mathematical models (Linear programming), multi-objective mathematical models (Goal programming), fuzzy goal programming (FGP), and GIS-based mathematical models. Thus, the review discussion part is subtitled based on these categories of the literature. While the detail of the articles is given in appendix A, the number of literatures per year of publication per model type is illustrated as shown in Figure 1.

Figure 1

Number of literatures reviewed per model type per year of publication.

The application area and the objectives of the models used in the articles reviewed are summarized per model type in Table 1 below.

Table 1

Application area and major objectives of the models per model type.

No.	Model type	Application area	Objectives
1.	LP	Arable crops and fishBotanical farmCrop mix or cropping patternsCropland planningCrop and livestock mixCrop-livestock integrationCrop yieldsCrop and land use planningDairy farmFood and cash cropsLand and water useLand allocationMaize productionWater, crop, and livestock integration	Economic impact or performanceEnhancing livelihood or food securityMaximum profit levelMaximize net return or net benefitMaximize gross margin or gross returnsMaximise net farm incomeMaximize revenueOptimize net profit or incomeOptimize productivityEnhance productivity and technical efficiency
2.	GP	Crop production and cropping patternDairy production/milk productionLivelihood enhancementOptimal land usePerishable products productionResource allocationVegetable productionWater and Nutrient ManagementWater/irrigation PlanningWatershed management	Control priceEconomic and ecological performanceEnhance productivity and environmental impactIncome maximisationMaximize net profitMaximization of gross marginMaximize gross marginsNutrition valueNutrient managementOptimize productionOptimize monetary benefitsOvercome environmental changes
	GP & LCA
	GP, USLE
	MCDM
	MCDM
	MOEO
	MOFLP
	MOP
3.	FGP	Crop planning or cropping mixVegetable productionCropping patternCrop productionLand and water use planning	Maximize incomeMaximize net profitMaximize net returnEnhance livelihoodOptimize gross marginOptimize productionOptimize resource allocationOptimize monetary benefits
	FMOFP
	FMOP
	FLP
4.	GIS-MCDM	Crop/pineappleLand use planningLand use allocationDifferent purposeAquaculture	Different valuesEnhance economic and ecological performanceMaximize economic contributionMaximize net returnMaximize productivitySystem effectiveness
	GIS-LP
	GIS- MCDA
	GIS-MCDM

Agricultural decision making using single objective mathematical models: linear programming (LP)

In this section, 27 study articles conducted in 16 countries which employed linear programming decision support tool for agricultural resource decision making were reviewed. Most of the literatures reviewed here are articles that used linear programming decision support systems for crop mix and cropping pattern (65%) while the remaining are articles that employed linear programming to promote the performance of dairy farms, crop-livestock integration, land and water resource use, arable crops and fisheries enterprises, botanical farm, and other forms of land use with the aim of maximizing net income, maximizing gross income, improving food security, and enhancing livelihood performance. Outlined results suggested that using LP as decision making tool in agriculture provides maximum annual return (Sarker et al., 1997; Hassan et al., 2005; Fallah Shamsi, 2010; Mohamad and Said, 2011; Alabdulkader et al., 2012; Felix et al., 2013; Geta et al., 2013; Andreea and Adrian, 2013; Gadge et al., 2014; Mugabe et al., 2014; Buzuzi and Buzuzi, 2018; Muhammed Jaslam et al., 2018).

To optimize the cropping pattern that result efficient allocation of scarce water resources and arable land among competing crops and to maximize the net annual return from agriculture in Saudi Arabia Alabdulkader et al. (2012) formulated and used linear programming mathematical model. The result disclosed that the approach was suitable to optimize the benefits of crop production through determining optimal cropping patterns and improving the utilization of scarce natural resources. Particularly, the finding of the study indicated that the use of a linear programming decision support system has the potential to create additional benefit equivalent of 2.42 billion US$ per year net return for Saudi Arabia. Besides, the finding of the study revealed that optimizing cropping patterns using linear programming has the potential to improve the efficiency of scarce natural resources. Accordingly, about 53% and 48% of water use and arable land use saving were gained respectively when linear programming-based decision support systems were used as compared to the conventional cropping pattern decision making approach.

As income depends on expenditure, determining the optimal structure of crops that minimize expenditure and maximize income per available land size is essential. Andreea and Adrian (2013) used the LP model aiming to assess the possible effect of the optimal structure of crops to minimize expenditure and maximize profit in Romania. Accordingly, linear programming based land use decision making resulted reduction of expenditure by 81% and enhancement of profit by 143%. Buzuzi and Buzuzi (2018) in Zimbabwe also conducted a similar study aiming to analyze the agricultural efficiency using LP model on a small-scale farm. The finding disclosed that in the conventional practice, the available resources were used sub-optimally and the use of linear programming model decision support system to optimize the crop production pattern was found to have the potential to enhance the profit margin by 76%.

Common problems that most farmers encountered when thinking of maximizing profit is the selection of crop mix that is what and how much to plant. With this regard, the literature is full of evidence on the significance of the LP model to decide profit maximizing crop mix (Sarker et al., 1997; Hassan et al., 2005; Mohamad and Said, 2011; Rani and Rao, 2012; Collins et al., 2013; Felix et al., 2013; Otoo et al., 2015; Matsyapal, 2017). For instance, a study conducted by Hassan et al. (2005) aiming to maximize gross income through proper crop planning in Pakistan disclosed that the difference in gross income using the LP model was 2.91% higher when compared to the conventional crop mix decision approach. Considering the problem associated with the mismatch between the choices of the crop type appropriate for the type of land, Sarker et al. (1997) used LP model to resolve the mismatch in Bangladesh. The results of the study emphasized that crop planning using the LP model1 unquestionably enhances production and the socio-economic performance. A study conducted by Paramjita et al. (2018) that aimed to design an approach which enhance efficiency of water, crop, and livestock resource use using the LP also revealed that LP decision support model was helpful to enhance the utilization of water and maximization of the return from crop and livestock production.

Ahmed et al. (2011) applying LP model with objective of maximizing gross margin from the production of field crops using irrigation scheme in River Nile State (RNS), North Sudan, under the constraints of land, labor, water, and capital, concluded that the gross margin from the practice of irrigation and resource use efficiency has been significantly improved compared to the conventional decision-making practice. In addition, the study also uncovered that the use of the LP optimization model gives additional opportunity to stretch the irrigation field to a wider area by saving important resources such as water in addition to a selection of crop mix that should be cultivated to maximize gross margin. Similarly, a study in Saline track of Murtizapur Tahsil district Akola of Maharashtra in India that employed LP with the objective of maximization of net profit under the constraints of meeting expected yield, fixed labor, fixed machine-hours, cost of pesticide, seed, and fertilizer on fixed land size concluded that the model is appropriate for cropland allocation when compared to the existing conventional land use decision making (Wankhade and Lunge, 2012).

Extending the use of the LP model for cropland allocation, Igwe and Onyenweaku (2013) employed the LP optimization model to determine the possible combination of crops, monogastric farm animals, and fish enterprise in Ohafia agricultural zone Abia state, Nigeria. The study revealed that the profit without the use of the LP model of decision-making is very much low when compared to the profit obtained when using the LP model to make decision to select the proper mix of agricultural practice. Similar studies by Jayasuriya and Das (2018) and Minh et al. (2007) also confirmed that the application of the LP model enables to make optimal crop-livestock combination decisions that maximize farm income without creating excessive pressure on land resources.

The study on cropland allocation using LP by Mohamad and Said (2011) pronounces the role of LP to promote the performance of agriculture. The study boldly disclosed that cropland allocation using the LP gives more promising output in a short planning time horizon that promotes commercialization. In addition, many studies including Glen and Tipper (2001), Val-Arreola et al. (2004), Ahmed et al. (2011), Igwe et al. (2011), Igwe and Onyenweaku (2013), and Delgado-Matas and Pukkala (2014) revealed that LP provides an alternative production opportunity in addition to optimizing desired outcomes and Louhichi et al. (2004), Das et al. (2015), and Sofi et al. (2015), pronounced that LP provides objective criteria for land and other resource use allocation to meet desired goals.

In addition to maximization of return from agriculture, animal, and crop production, Felix et al. (2013) used the LP model on a small farm livelihood system to select cropping patterns by communal farmers to ensure sustainable production in Bindura, Zimbabwe. Applying the LP model with the objective of maximizing cash income under constraints of meeting the minimum requirement for consumption (minimum level store of maize for family consumption), land, labor, and crop budget (cash available for production) revealed that it is an important decision-making tool to ensure sustainability. The study revealed that the maximum cash income that can be made employing the LP model is more superior to the cash income from current conventional farm decision practice without the use of LP.

A case study on the application of optimization models for sustainable agriculture and water resource planning by Mutnuru et al. (2013) uncovered the significance of the LP model for decision-making to promote performance of agriculture. The study employing LP with the objective of maximizing net benefit under constraints of fixed water quantity, land size, keeping water cycle (groundwater draft always less than the recharge), and emission pattern kept below total emission from current practice proved that LP is an important tool for sustainable agricultural practice. Solving the LP model in four scenarios, varying the number of constraints included in the model, the case study proved that the model output gives various options to planners than the conventional current planning such as providing optimal cropping patterns and operational policies that can achieve desired results of maximum benefits promoting sustainable agriculture. A study on soil loss minimization through land use optimization in Iran also pronounced the role of LP for sustainable agriculture and natural resource management. The optimal combination of land allocation to different land uses using LP showed a significant effect on the minimization of the amount of soil erosion and the conversion of forestland into agriculture (Vafakhah and Mohseni, 2011).

Studies like Bjørndal et al. (2012) also suggest that LP and related optimization tools can make significant contributions to support sustainable environmental and natural resource management through enhancing the performance of agriculture. Moreover, evidences from other many literatures uncovered that LP models are essential decision support tools that can be applied in many sectors that result remarkable outputs. For example, the work of Sarker et al. (1997), Collins et al. (2013), and Jayasuriya and Das (2018) are evidences from Bangladesh, Sri Lanka, and Nepal respectively that proved the role of LP models for better performance. A study by Collins et al. (2013) also concluded that LP is a potential tool to exercise crop diversification. In general, LP model-based decision making is a powerful tool as compared with traditional or conventional decision-making to improve the performance of agriculture.

Agricultural decision making using multi-objective mathematical models: goal programming (GP)

In this section twelve literatures from ten countries that used multi-objective mathematical models for decision making in agriculture are reviewed. The application areas were land allocation, dairy production, rainfed and irrigated crop production, resource allocation, water management, nutrient management, and livelihood. These literatures employed multi-objective mathematical model targeting to enhance economic and ecological performance, productivity and environmental impact, maximization of gross margins, and nutrition value.

Latinopoulos (2009), employing multi-objective mathematical model for efficient water and land resources allocation in irrigated agriculture in Northern Greece, has uncovered that the existing land allocation practice is in favor of farmers' welfare at the expense of water resources quality and quantity. The model was articulated based on two classes of objectives, socio-economic objectives (maximizing farmer's income, reducing risk on farmer's income, getting of human labor, preserving the current cropping pattern, maintenance of the current revenues of water agencies, and maximizing total labor efficiency) and the environmental objective (maximizing water use efficiency and alignment of fertilizer utilization to the European Union legislation). The outlined results demonstrated that the current agricultural resource decision practice is skewed to the economic objectives. Thus, the multi-objective mathematical model referred as multi-criteria decision-making in the study revealed that the current irrigation water pricing approach does not meet the sustainability criteria. In conclusion, it uncovered that multi-objective mathematical model is better to be used for policy analysis to consider multiple goals of agricultural practice. Besides, the model was found to allow flexibility for decision makers (Leung and Ng, 2007).

Another study that used multi-objective linear programming was the one conducted by Walangitan et al. (2012) in the catchment of Lake Todano, Indonesia for land allocation to meet four different objectives. The objectives were generating income, creating employment opportunity, minimizing land erosion, and securing forest areas. The study uncovered that the model is essential tool for multi-objective land allocation. While it is not easy to treat multiple objectives at a time using the existing conventional land use decision practice, this study revealed that it is possible to meet all except the employment. Thus, this shows that multi-objective mathematical model is essential tool that may enhance sustainability of agriculture through considering multiple social economical and sustainability objectives. Moreover, Jeyavanan et al. (2017) used goal programming to enhance crop production for different levels of resource utilization in Sri Lanka and concluded that the use of goal programming reduces production cost by about 14%. Masoumi et al. (2016) also confirmed that GP is valuable to identify cropping pattern that enhance water utilization efficiency.

The literature reviewed in this section reveals that multi-objective mathematical programming decision making is a potential decision support tool for agricultural decision making that might significantly contribute to profit or revenue optimization, ensure food security, and minimize environmental degradation. An optimum production plan with a greater gross return, fewer fertilizers use, and less irrigated water use than the existent production plan was observed using goal programming as compared to the existing practice. In addition, many literatures such as the work of Val-Arreola et al. (2006) in Mexico, Hassan et al. (2013) in Malaysia, Manos et al. (2013) in Greece, Arzamendia et al. (2015) in Paraguay, Pastori et al. (2017) in Africa, and Galan-Martin et al. (2017) in Spain pronounces the role of goal programming for multi-criteria decision-making in agriculture. Generally, literatures reviewed emphasize the role of multi-objective mathematical models for significantly improving the performance of agricultural production gross margin while preserving the environmental influence and dwindling of resources.

Agricultural decision making using fuzzy multi-objective linear programming (FMOLP) models: fuzzy goal programming (FGP)

Earlier mathematical models discussed in this paper, both single and multi-objective linear programming models, were based on deterministic model parameter estimation, which, however, does not reflect the reality predominantly in agriculture (Pal and Moitra, 2004). Besides volatile market demand and prices of the futures market predicted climate variables are subject to change in the field of agricultural practice. Therefore, the impossibility of access to perfect information in the field of agriculture implies that exact estimation of model parameters is hardly possible. Hence, a new method that reflect the level of uncertainty in model parameter estimation named fuzzy multi-objective programming or fuzzy goal programming (FGP) has evolved (Pal and Moitra, 2004; Sharma et al., 2007).

Fuzzy goal programming (FGP)

In this section of the review, seventeen articles that employed FGP were used. The articles were results of studies conducted in four different countries aimed to maximize farmers’ income, optimize monetary benefits, enhance the livelihood, and enhance the socio-economic and environmental performance of the agriculture in general and the land use practice in particular.

Mohaddes and Mohayidin (2008) employing FGP with the objective of profit maximization, labor employment maximization, and erosion minimization for agricultural production planning in Atrak watershed, Iran concluded that the FGP model-based agricultural decision-making is

“…an effective tool for generating a set of more realistic and flexible solutions in dealing with and attempting to solve the complex real world land development issues particularly in the context of sustainable agricultural production planning with consideration for the economic, social and environmental targets.”

The FGP model has been found to uplift the benefit of farmers and employment opportunities better than the current practice meeting the environmental performance objectives (Wang et al., 2006; Kakhki et al., 2009; Garg and Singh, 2010).

Pal and Moitra (2004) employing FGP as a multi-objective mathematical model decision making for long-range production in agricultural systems with five goals, meeting land utilization, productive resources use (which include workforce, water consumption, and fertilizer requirement sub-goals), production level, cash requirement, and profit goals, pronounced the significance of FGP for agricultural resource decision making to promote sustainable performance of agriculture. The result of the study indicated that the model was advantageous over other deterministic goals by the fact that it is more realistic and flexible which gives the opportunity to explore the risk level of each goal that may arise from imprecise climate information. A similar study, that employed FGP for land allocation for annual crop production confirmed the same fact that the model is able to give better results not only as compared to the conventional decision making approach but also when compared to linear programming and deterministic goal programming decision models (Sharma et al., 2007; Rezayi et al., 2017).

Most of the resources in agriculture are depletable natural resources as compared to the rate of population growth. Thus, efficient resource utilization is a concern around the globe. In this regard, literatures suggest the significance of the FGP approach for efficient utilization of agricultural resources. For instance, the work of Mohaddes and Mohayidin (2008), Safavi and Alijanian (2011), Ghaderzadeh et al. (2011), and Amini (2015) from Iran, Biswas and Pal (2005) and Lone et al. (2019) from India, and El Sayed (2012) from Egypt support the fact. The studies suggested that the use of the FGP approach is not only significant for efficient resource utilization but also to identify land allocation strategies.

Moreover, many other studies also uncovered that FGP model-based decision making is a reliable decision support tool to maximize net return, to offer potential solution to the model constraints, to obtain more realistic and promising result (Regulwar and Gurav, 2011; Soltani et al., 2011; Vivekanand. & Kumar, 2016; Rezayi et al., 2017). Joolaie et al. (2017) also using the FGP to determine sustainable cropping patterns in Iran considering certain economic, environmental, and social goals composed together, revealed that the FGP decision-making model provides a new perspective for analyzing multiple objectives and making precise decisions for crop planning. Wang et al. (2006) and Safavi and Alijanian (2011) also documented that FGP is a powerful tool for integrated watershed management planning that has the potential to provide a solid base for sustainable watershed management.

Agricultural decision-making using GIS based mathematical models

Although GIS and mathematical modeling are two distinct areas of research and application, combining data interpretation from both aspects can enhance analysis and problem-solving techniques. As discussed in the previous sub-sections multi-criteria mathematical models (MCDM) like GP and FGP have significant contribution in agricultural decision making. For instance, Ziadat and Al-bakri (2006) and Mazahreh et al. (2019) used GIS to solve land use problems. Ziadat and Al-bakri (2006) used GIS to compare the conventional land use and the potential land utilization in two agricultural sites of Jordan and revealed that the conventional land use in both sites has a deviation from the land use potential. Similarly, Mazahreh et al. (2019) employed GIS to assess land suitability for different land use alternatives in Jordan and discovered that the approach was suitable to identify the potential land purpose and challenges of the land use in the traditional approach. Thus, the question is what will be the significance if both GIS and MCDM approaches are combined to assist the decision-making process? Literature used in this review demonstrated that a combination of linear programming (LP), multi-objective programming (MOP), or goal programming (GP) model with geographic information systems (GIS) to make agricultural decisions is trending topic of research in area of agriculture and land management. And the use of GIS and mathematical model-based decision-making was found useful decision support tool to promote performance of land use decision. For decision making in land use, GIS is used to analyze and assemble data for aggregate land use alternatives based on factors such as bio-physical characteristics of the land, and then the data are used in LP, MOLP, GP, or FGP models to optimize desired objectives of the land use decision using objective criteria.

In this review, five empirical study articles conducted in three countries and one systematic review that used GIS based mathematical programming are used. As in Malczewski (2006), Fallah Shamsi (2010), and Govindrao et al. (2011), the use of GIS integrated with mathematical models for land use decisions is an important decision support tool to advance the efficiency of land use decision making.

According to Feizizadeh and Blaschke (2013) study that aimed to develop MCDM model to optimize land use pattern in Eastern Azerbaijan, Iran, used multi-criteria land allocation using the data from GIS concluded that the models offers extensive alternatives for both economic and ecological land use planning than the conventional practice. The finding also agrees with what Govindrao et al. (2011) found in India that outlined GIS integrated mathematical model provides objective criteria for multi-objective land use decision. Moreover, many literatures documented that the GIS integrated mathematical modelling-based decisions provides not only the potential land use type, but also the type of potential limitation(s) that may be faced during implementation. Furthermore, a study by Attua and Fisher (2010) in Ghana and Vafaie et al. (2015) in Iran indicated that the approach is effective in identifying and allocating appropriate land for cultivation.

The systematic review made by Malczewski (2006) on geographical information system-based multi-criteria decision analysis (GIS-MCDA) using literature published from 1990 to 2004 pronounces the use of GIS in MCDA. The review had discussed the two dimensions of the GIS-MCDA, the GIS component of the GIS-MCDA models (i.e. the geographical data models, the spatial dimension of the evaluation criteria, and the dimension of decision alternatives) and the generic element of the MCDA (i.e. the nature of evaluation criteria, the number of individuals involved in the decision making process, and the number of uncertainties). Besides, the review examined the GIS-MCDA literatures based on the level of combination in the application domain and decision seeking problems. Consequently, the review found that the application domains are environmental, transportation, urban planning, waste management, water resource, forestry, natural hazard, tourism, real estate, geology, manufacturing, and cartography. The evaluation problems include land suitability, scenario evaluation, site search and selection, resource allocation, transportation scheduling, and impact assessment. The review disclosed that the GIS-MCDA is a significant decision support tool not only in agriculture but also in other sectors such as economic, environmental management, natural resource management, and transport scheduling.

Regarding the advantage of the GIS integrated mathematical model based decision support tools, literatures revealed that the technique allows decision makers to compute values; add a value judgment and receive feedback on the overall implication of the decision. In addition, the technique provides an opportunity to make team-based decision and allows flexibility.

Literatures used for this review revealed that, regardless of the type of mathematical model used, the mathematical model-based decisions lead to achieving optimal results compared to the performance of the agricultural practice employing the conventional agricultural resource decision making. Pronouncing this result, a study by Schreinemachers and Berger (2006) that compared heuristic decision trees and optimization techniques (mathematical model-based decision making) for land use decision in developing countries pointed out that land use modeling using optimization is advantageous over heuristic decision modeling for three reasons:

Optimization techniques allow multiple input and output decisions, such as maximizing employment and profit (two outputs) from crop production from multiple inputs such as land, labor, and financial capital, thus relatively easily capturing the heterogeneity of agents;

Optimization techniques permit sensitivity analysis or economic trade-offs that can be easily evaluated to assist decision making; and

The results of optimization models imply clear policy recommendations identifying sources of economic inefficiencies.

Generally, the mathematical model-based decision support models such as the GIS integrated with mathematical model-based decision making and the fuzzy-logic programming are more practical for landscape/regional agricultural resource planning whereas linear programming, multi-objective programming and goal programming can be suitable for both landscape agricultural planning and agricultural enterprise planning. Landscape and/or regional mathematical model-based decision outcomes might have richer policy decision relevance. The study by Schreinemachers and Berger (2006) supports this fact.

Summary

The main aim of this review study was to document the potential of mathematical model-based decision making to enhance the sustainable performance of agriculture in developing countries. A scoping review of articles that employed different mathematical model-based decision support models that include single objective linear programming, multi-objective linear programming, goal programming, fuzzy logic programming, and GIS integrated with mathematical model programming shown in Figure 1 were made. The scoping review technique was preferred over any other review technique by the fact that the approach was found suitable to achieve the objective of the study, documenting the potential of mathematical model-based decision making to promote the sustainable performance of agriculture in developing countries. The review generally uncovered that mathematical model-based decision is an essential tool to enhance desired decision outcomes and to promote resource use efficiency in many sectors including agriculture. Moreover, it is generally comprehensive and significant decision support tool to inform policy and practice.

Although many studies reported a positive influence of using mathematical modeling in decision-making, there are also concerns on how the farmers use such tools (Collins et al., 2013). Most of the mathematical models that can be used for decision making in agriculture have varied levels of complexity and significance with regard to impact, technical capability to be used by agents, and data requirement. With regard to overall impact, multi-objective programming models goal programming, fuzzy-logic programming, and GIS integrated mathematical models can result in wider impact than single-objective linear programming models. This is by the fact that many sustainability goal/objectives either social, economic, and environmental models can be included in the multi-objective mathematical model-based decision support tool than in the single objective models and can be solved simultaneously given equal or desired weights to the objectives in the models. However, reliable time series/panel data required for mathematical model-based decision systems modelling, particularly for models that incorporate environmental risk variables is limited or costly to acquire. Hence, employing any mathematical model-based decision support model of any form might require the establishment of Geo-Databases in addition to socio-economic data centers to include environmental, social, and economic objectives into mathematical model-based decision-support mathematical models. Finally, with regard to the feasibility of application based on technical requirement and timescale, single objective and multi-objective mathematical decision support models (linear programming and goal programming) are feasible decision support tools that might be used right away at least for optimizing single time decisions outcome by any decision-making agent, firm-level, landscape level, regional level or national level. These mathematical model-based decision support systems can be used to optimize one or a combination of economic objectives such as maximizing profit, maximizing employment, minimizing expenditure and etc. with limited technical skill employing existing socioeconomic data or primary survey data. However, employing single-objective and multi-objective mathematical model-based decision support models for dynamic decision analysis incorporating environmental outcomes require reliable data sources. Besides data and/or information requirements, fuzzy logic and GIS integrated mathematical models require extensive technical skill and expertise when compared to others.

Conclusion

Currently following the emphasis of sustainability and food security problems in developing countries in the face of climate change, the use of these models particularly multi-objective mathematical models such as fuzzy goal programming combined with GIS is well supported by literature being more realistic agricultural decision making models that promote systems approach of decision making. Hence, integrating mathematical model-based decision making in the current land use planning and agricultural decision making in developing countries will significantly improve the efficiency of agricultural production and contribute to achieving the goal of eradicating extreme poverty in the face of climate change. The opportunity of expansion of mobile technology and emerging cluster farming practice plays a prominent role to use mathematical model-based decision making in agriculture if supplemented with reliable national and regional agriculture, climatic, and market information. Mobile applications that make use of updated agronomic, climate, and market information from regional and national system databases can be developed and used by agricultural households that has access to mobile technology. Hence, promoting mathematical model-based decision making through accessible mobile application technology integrated with national and regional agronomy, climate and market information systems is an option to enhance the sustainable performance of agriculture in the face of climate change.

Declarations

Author contribution statement

All authors listed have significantly contributed to the development and the writing of this article.

Funding statement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Data availability statement

No data was used for the research described in the article.

Declaration of interests statement

The authors declare no conflict of interest.

Additional information

No additional information is available for this paper.

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