Discrete Stochastic Programming Research Articles

Review And Synthesis of Sustainable Land Management on Small Family Farms in Developing Countries

Despite efforts to restore land and fight food insecurity, sustainable land management (SLM) technologies are not yet widely adopted in developing countries. This article reviews and synthesizes studies that have been conducted in developing countries over the last few decades. A total of 145 documents were used in this synthesis. A key finding of this paper is the identification of a theoretical gap that provides information for future studies on SLM practices.Another one is that, studies focusing on adoption in this synthesis have not considered awareness of technology as a key part of the adoption process. Most econometric studies focus on econometric regression and consider SLM adoption as a dichotomous choice. The use of mathematical models such as existing dynamic Discrete Stochastic Programming (DSP) models could provide more robust results to overcome this limitation observed in statistical regression results. Additionally, it would be interesting to analyze smallholder farmers’ preferences for SLM practices because very little is currently known about their preferences.

A stochastic programming model for dynamic portfolio management with financial derivatives

Stochastic optimization models have been extensively applied to financial portfolios and have proven their effectiveness in asset and asset-liability management. Occasionally, however, they have been applied to dynamic portfolio problems including not only assets traded in secondary markets but also derivative contracts such as options or futures with their dedicated payoff functions. Such extension allows the construction of asymmetric payoffs for hedging or speculative purposes but also leads to several mathematical issues. Derivatives-based nonlinear portfolios in a discrete multistage stochastic programming (MSP) framework can be potentially very beneficial to shape dynamically a portfolio return distribution and attain superior performance. In this article we present a portfolio model with equity options, which extends significantly previous efforts in this area, and analyse the potential of such extension from a modeling and methodological viewpoints. We consider an asset universe and model portfolio set-up including equity, bonds, money market, a volatility-based exchange-traded-fund (ETF) and over-the-counter (OTC) option contracts on the equity. Relying on this market structure we formulate and analyse, to the best of our knowledge, for the first time, a comprehensive set of optimal option strategies in a discrete framework, including canonical protective puts, covered calls and straddles, as well as more advanced combined strategies based on equity options and the volatility index. The problem formulation relies on a data-driven scenario generation method for asset returns and option prices consistent with arbitrage-free conditions and incomplete market assumptions. The joint inclusion of option contracts and the VIX as asset class in a dynamic portfolio problem extends previous efforts in the domain of volatility-driven optimal policies. By introducing an optimal trade-off problem based on expected wealth and Conditional Value-at-Risk (CVaR), we formulate the problem as a stochastic linear program and present an extended set of numerical results across different market phases, to discuss the interplay among asset classes and options, relevant to financial engineers and fund managers. We find that options’ portfolios and trading in options strengthen an effective tail risk control, and help shaping portfolios returns’ distributions, consistently with an investor’s risk attitude. Furthermore the introduction of a volatility index in the asset universe, jointly with equity options, leads to superior risk-adjusted returns, both in- and out-of-sample, as shown in the final case-study.

Feeding Management Optimization in Livestock Farms with Anaerobic Digestion Plant: A Discrete Stochastic Programming (DSP) Model

Abstract Biogas-based energy production has become a successful strategy for many livestock farms around the world. However, raw materials production is threatened by a growing uncertainty due to effects of climate change on crops cultivation. The aim of this paper is to propose a tool for the optimal design of the biogas mixture, considering respectively the nutritional needs of livestock and the parameters of the biogas process. Within a context of climate variability, a three-stage Discrete Stochastic Programming (DSP) model is applied in a dairy cattle farm with anaerobic digestion plant. This state-contingent approach (DSP model) considers, as uncertain parameters, the watering needs and the yields of forage and energetic crops. The DSP model is compared with equivalent models of expected values to verify the benefits derived from the explicit inclusion of climatic states. The results showed a remarkable improvement in the efficiency of feedstock management, reflecting in a significant reduction in farm costs (11.75 %) compared to the baseline scenario. Whereas, the comparison between the state-contingent approach and the expected value model, showed only slight benefits (0.02 %). This confirms that the DSP model’s ability to offer a better hedged solution increases when high climate variability affects crop yields and irrigation needs.

Paths of adaptation to climate change in major Italian agricultural areas: Effectiveness and limits in supporting the profitability of farms

Climate change requires Mediterranean farms to maintain adequate profitability, while adapting to the increase in water needs of crops, the growth of water demand for non-agricultural users and the reduction of resource availability. We use discrete stochastic programming models of three Italian farming areas to simulate the adaptation paths of their farm types to changes in yields and irrigation needs of crops that climate change could generate at 2030. This is done in a context of progressive decrease of water availability. We condense the adaptation choices attributed by the optimization process to the farm types by means of indicators of value produced per water cubic meter and per hectare. We use those indicators in a quadratic regression analysis to explain the change in the hourly wages of family labour, which represents the farm resources’ profitability. The examination of the resulting elasticity indices outlines the adaptation paths impact on farm profitability. This integrated analysis of optimization models and econometric regression shows that the core of Italian cow milk production, based on medium-high intensity forage systems, adapts better. Instead, available technologies and structural features provide much narrower margins to livestock farms based on intensive forage production and, conversely, to more extensive livestock systems. Crop farms adapt by reducing labour use in less profitable activities, which boosts family hourly wages but increases unemployment. Furthermore, the surface of some crops can be expanded because their cycle takes place in months in which the availability of water decreases less and their irrigation requirement increases less; however, the low productivity of these crops does not allow to increase wages for family labour. The results on farms overall profitability derive from an integrated analysis of changes in water resources productivity, soil and labor. Mathematical programming outlines the adaptation paths that maximize farming incomes; the econometric analysis indicates whether those paths support profitability, favouring farm economic sustainability.

Dynamic expediting of an urgent order with uncertain progress

A supplier manages an urgent order with uncertain progress for which her client has set a deadline for its completion. The supplier observes in real time the order progress and chooses dynamically the effort level, such as manpower level, to expedite the order. Her problem is to identify expediting policies to minimise her expected cost, given by two costs in trade-off with each other: an effort level cost and a one-time penalty cost for late completion of the order. We formulate this problem using a discrete stochastic dynamic programming framework and obtain an optimal expediting policy for it.By conducting a worst-case analysis, we show that decreasing the level of flexibility, interpreted as the supplier’s ability to update effort levels more often, may lead to a large increase in the costs of managing the order. We refine the problem formulation by modelling the case in which the supplier takes into account the negative effects of late order completion on her client using a penalty cost charged every period the order is delayed. We find an optimal policy for this case, by solving two dynamic programming problems sequentially. For both problems, we show that in presence of certain assumptions, there is an optimal expediting policy for which effort levels are non-increasing in the order progress. Finally, using a simulation study based on a car seat assembly case, we compare the performance of the two policies.

Approximate group context tree

We study a variable length Markov chain model associated with a group of stationary processes that share the same context tree but each process has potentially different conditional probabilities. We propose a new model selection and estimation method which is computationally efficient. We develop oracle and adaptivity inequalities, as well as model selection properties, that hold under continuity of the transition probabilities and polynomial $\beta$-mixing. In particular, model misspecification is allowed. These results are applied to interesting families of processes. For Markov processes, we obtain uniform rate of convergence for the estimation error of transition probabilities as well as perfect model selection results. For chains of infinite order with complete connections, we obtain explicit uniform rates of convergence on the estimation of conditional probabilities, which have an explicit dependence on the processes’ continuity rates. Similar guarantees are also derived for renewal processes. Our results are shown to be applicable to discrete stochastic dynamic programming problems and to dynamic discrete choice models. We also apply our estimator to a linguistic study, based on recent work by Galves et al. [Ann. Appl. Stat. 6 (2012) 186–209], of the rhythmic differences between Brazilian and European Portuguese.

Time-of-Day Pricing in Taxi Markets

For a regular weekday in New York City, the number of taxi trips at 8 P.M. may be 10 times greater than that at 5 A.M., while passengers are charged under the same pricing scheme. Motivated by temporally non-stationary demand and supply in the taxi market, the time-of-day (TOD) pricing scheme for taxi industry is framed to vary trip cost dynamically over time, so that total market revenue is maximized. Temporal market dynamics is modeled as a semi-Markov process, which captures leftover of drivers, spillover of passengers, and restoration of drivers in service along the time horizon. The TOD pricing scheme is therefore formulated as discrete time stochastic dynamic programming with the goal to find the optimal sequence of price multipliers. The approximate dynamic programming (ADP) approach is introduced to solve the curse of dimensionality. Numerical experiments are conducted using New York City taxi trip data to illustrate the effectiveness of TOD price in real-world taxi market. The results suggest that TOD price may increase daily market revenue by over 10% using the ADP approach. Our experiments also show that TOD price may be even more effective if sudden surges in demand take place in the market.

Determining the optimal selling time of cattle: A stochastic dynamic programming approach

The world meat market demands competitiveness and optimal livestock replacement decisions can help to achieve this goal. We introduce a novel discrete stochastic dynamic programming framework to support a manager’s decision-making process of whether to sell or keep fattening animals in the beef sector. In particular, our proposal uses a non-convex value function, combining both economic and biological variables, and involving uncertainty with regard to price fluctuations. Our methodology is very general, so practitioners can apply it in different regions around the world. We illustrate the model’s convenience with an empirical application, finding that our methodology generates better results than actions based on empirical experience.

An Approach to Financial Planning of Retirement Pensions with Scenario-Dependent Correlation Matrixes and Convex Risk Measures

The article describes an approach to asset–liability modeling using discrete time stochastic linear programming. The model uses future scenarios and optimizes the asset–liability mix subject to various constraints and is applicable to insurance companies, bank trading departments, overall bank asset–liability management, and other financial institutions. An application to the Siemens Austria pension fund, where the model has been in use since 2000, is described. The model has had considerable success and has been used by regulators to determine the effect of various possible pension fund policy changes. It has also been used by pension fund advisors who deal with uncertain assets and liabilities subject to various legal and policy constraints.

Winners and losers from climate change in agriculture: Insights from a case study in the Mediterranean basin

The Mediterranean region has always shown a marked inter-annual variability in seasonal weather, creating uncertainty in decisional processes of cultivation and livestock breeding that should not be neglected when modeling farmers' adaptive responses. This is especially relevant when assessing the impact of climate change (CC), which modifies the atmospheric variability and generates new uncertainty conditions, and the possibility of adaptation of agriculture. Our analysis examines this aspect reconstructing the effects of inter-annual climate variability in a diversified farming district that well represents a wide range of rainfed and irrigated agricultural systems in the Mediterranean area. We used a Regional Atmospheric Modelling System and a weather generator to generate 150 stochastic years of the present and near future climate. Then, we implemented calibrated crop and livestock models to estimate the corresponding productive responses in the form of probability distribution functions (PDFs) under the two climatic conditions. We assumed these PDFs able to represent the expectations of farmers in a discrete stochastic programming (DSP) model that reproduced their economic behaviour under uncertainty conditions. The comparison of the results in the two scenarios provided an assessment of the impact of CC, also taking into account the possibility of adjustment allowed by present technologies and price regimes. The DSP model is built in blocks that represent the farm typologies operating in the study area, each one with its own resource endowment, decisional constraints and economic response. Under this latter aspect, major differences emerged among farm typologies and sub-zones of the study area. A crucial element of differentiation was water availability, since only irrigated C3 crops took full advantage from the fertilization effect of increasing atmospheric CO2 concentration. Rainfed crop production was depressed by the expected reduction of spring rainfall associated to the higher temperatures. So, a dualism emerges between the smaller impact on crop production in the irrigated plain sub-zone, equipped with collective water networks and abundant irrigation resources, and the major negative impact in the hilly area, where these facilities and resources are absent. However intensive dairy farming was also negatively affected in terms of milk production and quality, and cattle mortality because of the increasing summer temperatures. This provides explicit guidance for addressing strategic adaptation policies and for framing farmers' perception of CC, in order to help them to develop an awareness of the phenomena that are already in progress, which is a prerequisite for effective adaptation responses.

Multiyear Discrete Stochastic Programming with a Fuzzy Semi-Markov Process

Drought conditions at a given location evolve randomly through time and are typically characterized by severity and duration. Researchers interested in modeling the economic effects of drought on agriculture or other water users often capture the stochastic nature of drought and its conditions via multiyear, stochastic economic models. Three major sources of uncertainty in application of a multiyear discrete stochastic model to evaluate user preparedness and response to drought are: (1) the assumption of independence of yearly weather conditions, (2) linguistic vagueness in the definition of drought itself, and (3) the duration of drought. One means of addressing these uncertainties is to re-cast drought as a stochastic, multiyear process using a “fuzzy” semi-Markov process. In this paper, we review “crisp” versus “fuzzy” representations of drought and show how fuzzy semi-Markov processes can aid researchers in developing more robust multiyear, discrete stochastic models.

A Dynamic Stochastic Programming model of crop rotation choice to test the adoption of long rotation under price and production risks

This article investigates the role played by both production and market risks on cash crop farmers’ decision to adopt long rotations considered as innovative cropping systems. We build a multi-period recursive farm model with Discrete Stochastic Programming. The model arbitrates each year between conventional and innovative, longer rotations. Yearly farming operations are declined according to a decision tree, so that production risk is an intra-year risk. Market risk is considered as an inter-year risk influencing crop successions. Simulations are performed on a specialized French cash crop farm. They show that when the long rotation is subsidized by an area premium, farmers are encouraged to remain in longer rotations. They also show that a high level of risk aversion tends to slow down the conversion towards longer rotations.

Efficient water management policies for irrigation adaptation to climate change in Southern Europe

This paper evaluates economic and environmental effects of two incentive-based water management policies to address climate change impacts on irrigated agriculture: water markets and irrigation subsidies. A Southern European case study assesses farmers' long and short-run adaptation responses under climate change and policy interventions with a discrete stochastic programming model. Results indicate that climate change will likely have negative impacts on irrigation activities and water-dependent ecosystems in Southern Europe. However, the severity of impacts depends on government policy settings and farmers' adaptation responses. The comparison between water market and irrigation subsidy policies shows the advantages of water markets over irrigation subsidies in terms of both private and social benefits. These findings could guide policymakers on the design of efficient water institutions and policies to address climate change in the irrigated agriculture of Southern Europe.

Self-insurance and multi-peril grassland crop insurance: the case of French suckler cow farms

Purpose – From the perspectives of the probable replacement of the national calamity funds by multi-peril grassland insurance, the purpose of this paper is to estimate demand for grassland production insurance. Design/methodology/approach – A discrete stochastic programming model with a three-year planning horizon was used to run simulations for farms raising suckler cows primarily with grasslands. In this model, the annual area insured and some production decisions are optimized under grasland yield uncertainty, with possible ex post production-system adjustments. The effects of insurance loading cost (14 levels), insurance coverage level (three levels), risk aversion (two levels) and stock levels (forage and animal stocks vary according to grassland yields and to farm management of the previous years) were analyzed. Findings – The results show that grassland insurance could be used as a flexible risk management tool, when farm becomes vulnerable to fodder shortfall. According to previous years’ grassland yields and to the subsequent states of hay stock and animal liveweight, the area insured could vary between nearly the none and full. Farmers with low-average stocking rate and important hay storage capacity have less incentive to buy grassland insurance. The author also demonstrates that for a given loading cost, more insurance is purchased at a coverage level of 70 percent of average yield than at higher coverage levels. The cost of self-insurance increases for important and rare losses while multi-peril grassland insurance premium decreases. Higher levels of risk aversion also raise the quantity of insurance subscribed. Eventually, insurance price is a key factor. Almost no insurance is bought for loading costs greater than 1.1 under low-risk aversion and for loading costs greater than 1.3 under moderate risk aversion. Research limitations/implications – The willingness to pay for insurance could have been overestimated for different reasons. First, basis risks have not been introduced in the simulation framework. Although the Forage Production Index performed quite well, basis risks are high enough to trigger inappropriate indemnifications in some cases. Consequences of these risks should be estimated in further research. Second, other self-insurance options and public emergency measures such as subsidized loan or reduction in social security contributions should also be considered to assess and reduce farmers vulnerability to risks. Practical implications – The launching of the multi-peril grassland insurance is likely to be successful thanks to the 65 percent of public subsidies on insurance premiuml. However, considering that the loading cost is likely to be high and that demand for grassland production insurance is rather low, multi-peril grassland production insurance may struggle to continue unsubsidized. Originality/value – This paper provides a framework that enables to estimate demand for grassland production insurance factoring in substitution with self-insurance and taking into account successive risks.

Determining the Optimal Selling Time of Cattle: A Stochastic Dynamic Programming Approach

The world meat market demands competitiveness and optimal livestock replacement decisions can help to achieve this goal. We introduce a novel discrete stochastic dynamic programming framework to support a manager’s decision-making process of whether to sell or keep fattening animals in the beef sector. In particular, our proposal uses a non-convex value function, combining both economic and biological variables, and involving uncertainty with regard to price fluctuations. Our methodology is very general, so practitioners can apply it in different regions around the world. We illustrate the model’s convenience with an empirical application, finding that our methodology generates better results than actions based on empirical experience.

Will cotton make a comeback in Mali?

With the decline of cotton especially in the marginal cotton areas, farmers have been using more of the cotton-financed inputs on the cereals. The cotton para-statal company (CMDT) has made a virtue out of this recommending diversification for these regions. Following the world price spike in 2010, the Malian government responded with a substantial price increase for cotton in 2011 of 38% to rejuvenate the Malian sector. This article looks at the impact of this price policy in the cotton economy and the potential of new cereal technology and marketing strategy to raise incomes and facilitate the diversification. Given the importance of the marketing decision of selling later after the recovery of cereal prices from the harvest collapse, a discrete stochastic programming model was developed for three-stage decision making. Then, the recent changes in the cotton economy and government fertilizer subsidies were analyzed along with the introduction of the new technology marketing of sorghum. Cotton and maize continue to dominate the economy but the combined sorghum technology marketing increases farmers’ incomes by 16% to 21% and eases the return to normal cotton prices, after the 2011 price spike, as well as the removal of the fertilizer subsidies.

Stochastic Optimization of Grid to Vehicle Frequency Regulation Capacity Bids

This paper investigates the application of stochastic dynamic programming to the optimization of charging and frequency regulation capacity bids of an electric vehicle (EV) in a smart electric grid environment. We formulate a Markov decision problem to minimize an EV's expected cost over a fixed charging horizon. We account for both Markov random prices and a Markov random regulation signal. We also propose an enhancement to the classical discrete stochastic dynamic programming method. This enhancement allows optimization over a continuous space of decision variables via linear programming at each state. Simple stochastic process models are built from real data and used to simulate the implementation of the proposed method. The proposed method is shown to outperform deterministic model predictive control in terms of average EV charging cost.

Valuing seasonal climate forecasts in a state‐contingent manner

We applied state‐contingent theory to climate uncertainty at a farm level to assess the value of seasonal climate forecasts in the Central West region of NSW. We find that modelling uncertainty in a state‐contingent manner results in a lower estimate of forecast value than the typical expected value approach. We attribute this finding to a more conservative long‐term farm plan in the discrete stochastic programming (DSP) model, which is better balanced for climate uncertainty. Hence, a climate forecast, even though it still revises probabilities held by farmers, does not call forth such large changes in farm plans and associated farm incomes. We then use the DSP model to assess how attributes of a hypothetical forecasting system, particularly its skill and timeliness, as well as attributes of the decision environment, influence its value. Lastly, we assess the value of current operational forecast systems and show that the value derived from seasonal climate forecasts is relatively limited in the case study region largely because of low skill embodied in forecasts at the time when major farm decisions are being made.

Representing climatic uncertainty in agricultural models - an application of state-contingent theory

The state-contingent approach to production uncertainty presents a more general model than the conventional stochastic production approach. Here we investigate whether the state-contingent approach offers a tractable framework for representing climatic uncertainty at a farm level. We developed a discrete stochastic programming (DSP) model of a representative wheat–sheep (mixed) farm in the Central West of NSW. More explicit recognition of climatic states, and associated state-contingent responses, led to optimal farm plans that were more profitable on average and less prone to the effects of variations in climate than comparable farm plans based on the expected value framework. The solutions from the DSP model also appeared to more closely resemble farm land use than the equivalent expected value model using the same data. We conclude that there are benefits of adopting a state-contingent view of uncertainty, giving support to its more widespread application to other problems.

An Integrated Assessment of the Impacts of Changing Climate Variability on Agricultural Productivity and Profitability in an Irrigated Mediterranean Catchment

Climate change is likely to have a profound effect on many agricultural variables, although the extent of its influence will vary over the course of the annual farm management cycle. Consequently, the effect of different and interconnected physical, technical and economic factors must be modeled in order to estimate the effects of climate change on agricultural productivity. Such modeling commonly makes use of indicators that summarize the among environmental factors that are considered when farmers plan their activities. This study uses net evapotranspiration (ETN), estimated using EPIC, as a proxy index for the physical factors considered by farmers when managing irrigation. Recent trends suggest that the probability distribution function of ETN may continue to change in the near future due to changes in the irrigation needs of crops. Also, water availability may continue to vary due to changes in the rainfall regime. The impacts of the uncertainties related to these changes on costs are evaluated using a Discrete Stochastic Programming model representing an irrigable Mediterranean area where limited water is supplied from a reservoir. In this context, adaptation to climate change can be best supported by improvements to the collective irrigation systems, rather than by measures aimed at individual farms such as those contained within the rural development policy.