Handbook of Operations Research in Agriculture and the Agri-Food Industry

This chapter presents the formulation and resolution of a stochastic mixed integer linear programming model for pig production planning. The aim of the model is to optimize the entire pig supply chain according to the number of farms operating for the same company or cooperative. The model maximizes the total revenue calculated from the income of sales to the abattoir and the production costs. Production cost depends on each type of farm involved in the process. Factors like farm capacity, trucks available, reproduction management policies and transportation costs are taken into account. The proposed model considers a medium-term planning horizon and specifically provides optimal transport planning in terms of animals to be transported and number of trucks needed. Uncertainty in sale prices is explicitly incorporated via a finite set of scenarios. The algebraic modelling software OPL Studio, in combination with the solver CPLEX both from IBM ILOG are used to solve the different instances considered. The results of an averaged single scenario (deterministic instance) are useful in assessing the suitability of the stochastic approach. Finally, the conclusions drawn from the study including an outlook are presented.

Many significant advances have been made in agriculture over the past century; we now have the ability, in theory, to feed the entire world population. Nonetheless, “there still remain great hunger, health and environmental concerns remaining to be addressed” (Hazell and Wood 2008). These are not problems that can be solved simply by increasing agricultural production (Alexandratos and Bruinsma 2006), especially considering the environmental issues that if left unchecked could adversely affect food supply in the future (M.E.A. 2005). Even though increasing agricultural yields and developing better varieties have great importance, a significant breakthrough can be made through better management of agricultural supply chains. The potential for better resource efficiency should not be overlooked, especially in view that one-third of the food produced for human consumption is estimated to be lost or wasted globally; some of the loss can be attributed to a lack of coordination of the different actors of the supply chain (Gustavsson et al. 2011). Thus, the issue of how to efficiently meet the demand with the production available is of utmost importance when high levels of perishability are present in the underlying product, as it is the case in fresh produce. For this reason the planning of supply chain will play an increasingly key role in the definition of those products that are successfully marketed.

This chapter presents optimization approaches based on mathematical programming to support aggregate production and logistics planning in seed corn supply chains. The focus is on linear programming models of the literature that integrate production, inventory, and distribution decisions in practical settings. In the development of these tactical models, besides aiming to minimize production and logistics costs, special efforts have been made to reduce forecasting bias and to incorporate tax planning. Although the models involve thousands of variables and constraints, their solution is reasonably easy to obtain using standard linear programming software. Also, their application to analyze actual situations resulted in important economical and organizational benefits to the studied seed corn companies.

One of the main factors affecting the quality of the apple is the state of maturity at which it is harvested. To help planning agricultural work in apple orchards, this study proposes an optimization model, working through harvest time windows, and that incorporates the fruit ripeness. The model seeks to minimize labor costs, equipment use, and loss of fruit quality, in order to meet the demand of packing plants, considering their processing capacities as well as the production in orchards. This model on three apple orchards in the Maule Region, Chile, led to a 16 % decrease in both labor costs and loss of income for harvesting fruits with poor quality.

In this chapter the authors present and discuss the problem of planning sugarcane harvesting–transportation–delivering to the mill for the supply chain management of the sugarcane. Furthermore, an optimization model for practical use is formulated and embedded into a decision support system (DSS) for planning daily operations. The objective function seeks to minimize transportation costs while assuring cane supply to the sugar mill. The model determines the fields to harvest, the cutting–loading–transport means for such operation, and the roster for each employee. Although the model has been developed and tested under Cuban conditions, it can easily be adapted to different situations updating the parameters of the model and the database of the DSS. Main reported savings represent 8 % of the fuel cost, apart from the workload reduction of mill managers in planning tasks.

The process for agriculture planning starts by delineating the field into site-specific rectangular management zones to face within-field variability. We propose a bi-objective model that minimizes the number of these zones and maximizes their homogeneity with respect to a soil property. Then we use a method to assign the crops to the different plots to obtain the best profit at the end of the production cycle subject to water forecasts for the period, humidity sensors, and the chemical and physical properties of the zones within the plot. With this crop planning model we can identify the best management zones of the previous bi-objective model. Finally, we show a real-time irrigation method to decide the amount of water for each plot, at each irrigation turn, in order to maximize the total final yield. This is a critical decision in countries where water shortages are frequent. In this study we integrate these stages in a hierarchical process for the agriculture planning and empirically prove its efficiency.

This chapter presents a mixed integer linear programming developed to support operational decision making in the transport planning for a fruit logistic centre (FLC). The FLC is part of a fruit supply chain. Associated cooperatives store and supply fruits on demand to fulfil orders received at the logistic centre. The model mitigates the cost of manually managing the planning of trips to transfer fruits from storages at cooperatives to the logistic centre and avoiding idle times in the packaging lines. This is done determining the number of trips to do by available trucks and the load they have to carry to the logistic centre. The model is tested on a real case represented by an important Spanish cooperative during the winter season as a prior test to the more complex. In view of results, the model is ready to be integrated into the ERP of the logistic centre and extended to deal with the more complex case presented during harvest season.

The horticulture industry in Australia, valued at $3.6 billion per annum, is cyclically subjected to extreme weather events (EWE) that impact on greenhouse gas (GHG) emissions and fuel costs. These EWE threaten the viability of the industry, and a better understanding of these factors is required to improve the industry’s response to these vulnerabilities. This chapter describes the Supply Chain Database Tool (SCDT), a deterministic model that maps distances, GHG emissions, and other parameters during transport and distribution of fruits and vegetables for consumption in Victoria. The model enabled the calculation of relative measures of GHG emissions for a base (business-as-usual) scenario and for EWE scenarios that simulated the effect of catastrophic flooding in northern Victoria in 2011. The model calculated the net increase/decrease of GHG emissions, as a result of switching suppliers from affected areas to suppliers in non-affected areas to meet demand. We highlight opportunities for the SCDT to be used in conjunction with mathematical programming to improve the supply chain resilience to EWE.

Optimization techniques inspired by swarm intelligence (SI) have become increasingly popular during the last two decades. These techniques are based on the idea that groups of extremely simple agents with little or no organization can exhibit complex and intelligent behavior by using simple local rules and communication mechanisms. Thanks to this intelligent behavior, a group of social agents can carry out actions on a complex level and form decentralized and self-organizational systems. The advantage of these optimization approaches over traditional techniques is their robustness and flexibility, making SI especially appropriated to deal with complex optimization problems. In this chapter we introduce the concept of computational swarm intelligence; we present an overview of the most important optimization techniques inspired by swarm intelligence and examine the research contributions to the application of SI metaheuristics in different problems related to optimal management of aquaculture farms. As example of application we will present a particle swarm optimization (PSO) algorithm based on a bioeconomic model that helps managers of aquaculture enterprises in the process of decision-making, maximizing gross margin and minimizing operational risk.

African agriculture is one of the less productive owing to an inefficient use of available fertilizer and water resources using one-tenth of the world average. The largest increase in agricultural output will most likely come from the intensification of the production of existing agricultural land. This will require widespread adoption of sustainable land management practices and a more efficient use of irrigation and fertilization (http://​www.​fao.​org/​docrep/​013/​i2050e/​i2050e.​pdf). The largest increase in agricultural output will most likely come from the intensification of the production of existing agricultural land.

Reaching an efficient management of natural resources often leads to a difficult and challenging multi-objective optimization problem, in which finding the trade-off strategy solutions is necessary, each solution being no better or worse than the other. Multi-objective optimization methods provide a systematic approach to search and compare trade-offs and to select alternatives that best satisfy the decision-maker’s criteria.

In this context, we integrate a biophysical model with a multi-objective evolutionary algorithm (MOEA). The biophysical model adopted is EPIC, a model that allows to predict the effects of candidate modified agricultural management practices of different land use and land management scenarios. The integrated GIS-EPIC multi-objective analysis tool has been applied to identify optimum crop and land management patterns in different African countries, demonstrating the ability to provide trade-off Pareto solutions which simultaneously minimize total nitrate pollution through runoff and leaching, at the same time maximizing the exploitation benefits by choosing the adequate crop, fertilization, and irrigation management sequences. Knowledge of these sets helps the decision-makers to choose optimum alternative patterns of agricultural management specifically adapted to African countries characterized by multiple soil types and different climate and crops.

The results prove how this optimization method is powerful and operational, an essential tool for taking management decisions. This methodology would be a valuable tool for policy makers and water managers, providing information about cost-effectiveness of different agricultural practices in African countries.

This paper compares alternative ways of conducting a farm risk analysis using sparse data with a special reference to catastrophe events. For this purpose kernel and multivariate normal smoothing procedures are proposed and applied to generate (simulate) the joint distributions of crop yields and prices. The analysis showed that the functional forms chosen to generate the joint distribution substantially impacted the density in the tail of the distribution, although they were parameterised with the same data. The differences in the optimal farm plan (i.e. activity levels) resulting from the optimisation of net farm income, obtained from a utility-efficient programming model, were less profound.

Projected climatic changes in Australia for the next 50 years indicate a likely increase in the frequency, intensity, and duration of extreme weather events such as heatwaves. The wine and grape industry has intensified calls for more effective methods of managing viticulture activities before, during, and after these events in order to ensure the future viability of the industry. This paper presents MatPred, a maturation forecasting tool developed by CSIRO as part of the VitiForecaster package for grape intake logistics. The discussion details the extension of MatPred’s forecasting methodology to account for heat stress and describes the selection of a recommended regression model to forecast daily change in grape maturity.

Pig production is very important in Spain and increasing competition has led the pig industry to look for ways of improving the efficiency of the production process. This chapter presents the analysis of technical efficiency in sow farms vertically integrated into the same company comparing parametric and non-parametric approaches. Empirical data from 96 Spanish sow farms classified into 2 groups depending on the final product, that is, farms producing weaned piglets (FPP) or feeder pigs (FPFP) were available. The results for the stochastic frontier production function for feeder pigs and weaned piglets exhibit problems related to multicolinearity. Even though, the observed trends of technical efficiencies calculated from both approaches were consistent. The results revealed considerable efficiencies in this study being FPP more efficient that FPFP (0.99 vs. 0.87 with the parametric approach, and 0.93 vs. 0.91 with VRS-DEA model). Scale efficiency was also very high showing that 58 % of FPP and 45 % of FPFP are small farms in which efficiency gains would be expected by increasing the size. In addition, farm-specific factors affecting productive inefficiencies from CRS–DEA and VRS–DEA models were explored using a Tobit model. The output, number of sow, feed consumed, and artificial insemination were the variables showing significant coefficients at the 5 % level. Finally, the efficiency measures presented in this study are similar to other European studies and demonstrate the higher technical efficiency of the pig sector in Spain.

This chapter presents an empirical application of Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) models to measure the sustainability of olive farms in Andalusia, Spain. The Analytic Hierarchy Process is used to assess the weights of sustainability dimensions and the weights of each indicator when developing the TOPSIS model. In addition, an additive approach based on weighted sum is applied to compare sustainability results of olive farms. Taking into account the weights given to each indicator and to each of the sustainability dimensions, results show that ‘intensive olive farms’ are the most sustainable olive farms.

The importance of food production is ever increasing. Livestock production represents a complex logistics problem where agistment, transport conditions, storage, seasonality, time to market, and road infrastructure play a significant role. We present an overview of commonly-used logistic tools that reflect how Operational Research models and methods can be used in beef supply chains for strategic and operational planning purposes. As part of our contribution, we present a case study of beef production in northern and western Australia and introduce a framework to assist planners in taking optimal capital investments. The case study we present is interesting because it is highly sensitive to external environmental and economic factors. The proposed model is formulated as a facility location problem which simultaneously considers selection of segments of the road network to upgrade as well as the selection of abattoirs from a set of potential sites in the Rangelands of Western Australia as well as for Queensland and the Northern Territory. The model captures transport accessibility and abattoir set up costs and provides insight on the fundamental question of resource allocation between facilities and links. We present results on abattoir selection and outline directions of research.

Pig farmers depend on the income they get from the delivering of fattened pigs to the abattoir. Pigs are fattened in batches and all-in-all-out management strategy is common in commercial farms. This chapter presents a mixed-integer linear programming model describing a fattening pig unit delivering pigs to the same abattoir. The interest of the model is mainly to maximise the revenue from deliveries of pigs to the abattoir that pays according to a carcass classification. Carcass classification is affected by the heterogeneous growth of animals determining the weight and body composition (percent of fat and/or lean) changing over time. The delivery of all pigs of a batch at a time is shown to be less profitable than two or three within a time window of around 4 weeks. Our contribution corroborates the findings of past studies and demonstrates the benefit of homogeneous weights. It is also shown how a time window of 4 weeks delivering animals to the abattoir is optimal. However, the optimal result per batch does not correspond to the optimal result per day. The latter would imply saving 1 week in the marketing time window and increments of 5 % in the daily or annual revenue.

This study concerns feed composition and planning and is mainly focused in reducing feeding costs. We also estimate the excretion of nutrients that can be harmful to the environment when applied in excess but without trying to reduce them. The diets are formulated to satisfy or exceed the animal’s requirements, so their growth will not be affected. Under these conditions, we can apply linear programming models. The resulting models are variations on the classical linear programming models. We study three types of feeding: traditional feeding, fixed energy density feeding with phases, and variable energy density feeding with phases. We will develop models corresponding to each feeding type. In a first time, the models established are linear mathematical problem. Introducing premixes for practical reasons, the models using variable or unknown premixes become bilinear. We will apply the developed models more specifically in the pigs growing context. This study shows that the feeding costs can be substantially reduced using variable energy density model with daily phases and variable premixes.

Livestock farming problems are often sequential in nature. For instance at a specific time instance the decision on whether to replace an animal or not is based on known information and expectation about the future. At the next decision epoch updated information is available and the decision choice is re-evaluated. As a result Markov decision processes (MDPs) have been used to model livestock decision problems over the last decades. The objective of this chapter is to review the increasing amount of papers using MDPs to model livestock farming systems and provide an overview over the recent advances within this branch of research. Moreover, theory and algorithms for solving both ordinary and hierarchical MDPs are given and possible software for solving MDPs are considered.