Min-max regret versus gross margin maximization in arable sector modeling

"A sector model presented in this article, uses about 200 representative French cereal-oriented farms to estimate policy impacts by means of mathematical modeling. Usually, such models suppose that farmers intend to maximize expected gross margin. This rationality hypothesis however seems hardly justifiable, especially these days, when gross margin variability due to European Common Agricultural Policy changes may become significant. Increasing uncertainty introduces bounded rationality to the decision problem so that crop gross margins may be better approximated by interval rather than by expected (precise) values. The initial LP problem is specified as an “Interval Linear Programming (ILP)”. We assume that farmers tend to decide upon their surface allocation prudently in order to get through with minimum loss, which is precisely the rationale underlying the minimization of maximum regret decision criterion. Recent advances in operations research, namely Mausser and Laguna algorithms, are exploited to implement the min-max regret criterion to arable agriculture ILP. The validation against observed crop mix proved that as uncertainty increases about 40% of the farmers adopt the min-max regret decision rule instead of the gross margin maximization."Interval Linear Programming, Min-Max Regret, Common Agricultural Policy, Arable cropping, France

Energy Crop Supply in France: A Min-Max Regret Approach

This paper attempts to estimate energy crop supply using an LP model comprising hundreds of representative farms of the arable cropping sector in France. In order to enhance the predictive ability of such a model and to provide an analytical tool useful to policy makers, interval linear programming (ILP) is used to formalise bounded rationality conditions. In the presence of uncertainty related to yields and prices it is assumed that the farmer minimises the distance from optimality once uncertainty resolves introducing an alternative criterion to the classic profit maximisation rationale. Model validation based on observed activity levels suggests that about 40% of the farms adopt the min-max regret criterion. Then energy crop supply curves, generated by the min-max regret model, are proved to be upward sloped alike classic LP supply curves.interval linear programming, min-max regret, energy crops, France, Crop Production/Industries, Resource /Energy Economics and Policy, C61, D81, Q18,

Hybrid linear programming to estimate CAP impacts of flatter rates and environmental top-ups

This paper examines evolutions of the Common Agricultural Policy (CAP) decoupling regime and their impacts on Greek arable agriculture. Policy analysis is performed by using mathematical programming tools. Taking into account increasing uncertainty, we assume that farmers perceive gross margin in intervals rather than as expected crisp values. A bottom-up hybrid model accommodates both profit maximizing and risk prudent attitudes in order to accurately assess farmers’ response. Marginal changes to crop plans are expected so that flatter single payment rates cause significant changes in incomes and subsidies. Nitrogen reduction incentives result in moderate changes putting their effectiveness in question.Interval Linear Programming, Min-Max Regret, Common Agricultural Policy, Arable cropping, Greece

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

Minmax regret combinatorial optimization problems: an Algorithmic Perspective

Candia-Vejar, A (reprint author), Univ Talca, Modeling & Ind Management Dept, Curico, Chile.Uncertainty in optimization is not a new ingredient. Diverse models considering uncertainty have been developed over the last 40 years. In our paper we essentially discuss a particular uncertainty model associated with combinatorial optimization problems, developed in the 90's and broadly studied in the past years. This approach named minmax regret (in particular our emphasis is on the robust deviation criteria) is different from the classical approach for handling uncertainty, stochastic approach, where uncertainty is modeled by assumed probability distributions over the space of all possible scenarios and the objective is to find a solution with good probabilistic performance. In the minmax regret (MMR) approach, the set of all possible scenarios is described deterministically, and the search is for a solution that performs reasonably well for all scenarios, i.e., that has the best worst-case performance. In this paper we discuss the computational complexity of some classic combinatorial optimization problems using MMR. approach, analyze the design of several algorithms for these problems, suggest the study of some specific research problems in this attractive area, and also discuss some applications using this model

Robust optimization criteria: state-of-the-art and new issues

Uncertain parameters appear in many optimization problems raised by real-world applications. To handle such problems, several approaches to model uncertainty are available, such as stochastic programming and robust optimization. This study is focused on robust optimization, in particular, the criteria to select and determine a robust solution. We provide an overview on robust optimization criteria and introduce two new classifications criteria for measuring the robustness of both scenarios and solutions. They can be used independently or coupled with classical robust optimization criteria and could work as a complementary tool for intensification in local searches

Mathematical Optimization of the Tactical Allocation of Machining Resources in Aerospace Industry

In the aerospace industry, efficient management of machining capacity is crucial to meet the required service levels to customers (which includes, measures of quality and production lead-times) and to maintain control of the tied-up working capital. We introduce a new multi-item, multi-level capacitated planning model with a medium-to-long term planning horizon. The model can be used by most companies having functional workshops where costly and/or time- and resource demanding preparations (or qualifications) are required each time a product needs to be (re)allocated to a machining resource. Our goal is to identify possible product routings through the factory which minimizes the maximum excess resource loading above a given loading threshold, while incurring as low qualification costs as possible. In Paper I (Bi-objective optimization of the tactical allocation of jobtypes to machines), we propose a new bi-objective mathematical optimization model for the Tactical Resource Allocation Problem (TRAP). We highlight some of the mathematical properties of the TRAP which are utilized to enhance the solution process. Another contribution is a modified version of the bi-directional $\epsilon$ -constraint method especially tailored for our problem. We perform numerical tests on industrial test cases generated for our class of problem which indicates computational superiority of our method over conventional solution approaches. In Paper II (Robust optimization of a bi-objective tactical resource allocation problem with uncertain qualification costs), we address the uncertainty in the coefficients of one of the objective functions considered in the bi-objective TRAP. We propose a new bi-objective robust efficiency concept and highlight its benefits over existing robust efficiency concepts. We also suggest a solution approach for identifying all the relevant robust efficient (RE) solutions. Our proposed approach is significantly faster than an existing approach for robust bi-objective optimization problems

Mathematical optimization models for reallocating and sharing health equipment in pandemic situations

In this paper we provide a mathematical programming based decision tool to optimally reallocate and share equipment between different units to efficiently equip hospitals in pandemic emergency situations under lack of resources. The approach is motivated by the COVID-19 pandemic in which many Heath National Systems were not able to satisfy the demand of ventilators, sanitary individual protection equipment or different human resources. Our tool is based in two main principles: (1) Part of the stock of equipment at a unit that is not needed (in near future) could be shared to other units; and (2) extra stock to be shared among the units in a region can be efficiently distributed taking into account the demand of the units. The decisions are taken with the aim of minimizing certain measures of the non-covered demand in a region where units are structured in a given network. The mathematical programming models that we provide are stochastic and multiperiod with different robust objective functions. Since the proposed models are computationally hard to solve, we provide a divide-et-conquer math-heuristic approach. We report the results of applying our approach to the COVID-19 case in different regions of Spain, highlighting some interesting conclusions of our analysis, such as the great increase of treated patients if the proposed redistribution tool is applied.Spanish Ministerio de Ciencia e Innovacion, Agencia Estatal de Investigacion/FEDER PID2020-114594GB-C21Junta de Andalucia SEJ-584 FQM-331 P18-FR-1422 US-1256951 P18-FR-2369Spanish Government PEJ2018-002962-ADoctoral Program in Mathematics at the Universidad of GranadaProyect NetMeetData (Fundacion BBVA - Big Data)IMAG-Maria de Maeztu grant CEX2020-001105-M/AEICenter for Forestry Research & Experimentation (CIEF)European Commission CIGE/2021/16

Dynamic Pricing through Sampling Based Optimization

In this paper we develop an approach to dynamic pricing that combines ideas from data-driven and robust optimization to address the uncertain and dynamic aspects of the problem. In our setting, a firm off ers multiple products to be sold over a fixed discrete time horizon. Each product sold consumes one or more resources, possibly sharing the same resources among di fferent products. The firm is given a fixed initial inventory of these resources and cannot replenish this inventory during the selling season. We assume there is uncertainty about the demand seen by the fi rm for each product and seek to determine a robust and dynamic pricing strategy that maximizes revenue over the time horizon. While the traditional robust optimization models are tractable, they give rise to static policies and are often too conservative. The main contribution of this paper is the exploration of closed-loop pricing policies for di fferent robust objectives, such as MaxMin, MinMax Regret and MaxMin Ratio. We introduce a sampling based optimization approach that can solve this problem in a tractable way, with a con fidence level and a robustness level based on the number of samples used. We will show how this methodology can be used for data-driven pricing or adapted for a random sampling optimization approach when limited information is known about the demand uncertainty. Finally, we compare the revenue performance of the di fferent models using numerical simulations, exploring the behavior of each model under diff erent sample sizes and sampling distributions.National Science Foundation (U.S.) (Grant 0556106-CMII)National Science Foundation (U.S.) (Grant 0824674-CMII)Singapore-MIT Allianc