Using LEL and scenarios to derive mathematical programming models. Application in a fresh tomato packing problem

Abstract

Mathematical programming models are invaluable tools at decision making, assisting managers to uncover otherwise unattainable means to optimize their processes. However, the value they provide is only as good as their capacity to capture the process domain. This information can only be obtained from stakeholders, i.e., clients or users, who can hardly communicate the requirements clearly and completely. Besides, existing conceptual models of mathematical programming models are not standardized, nor is the process of deriving the mathematical programming model from the concept model, which remains ad hoc. In this paper, we propose an agile methodology to construct mathematical programming models based on two techniques from requirements engineering that have been proven effective at requirements elicitation: the language extended lexicon (LEL) and scenarios. Using the pair of LEL + scenarios allows to create a conceptual model that is clear and complete enough to derive a mathematical programming model that effectively captures the business domain. We also define an ontology to describe the pair LEL + scenarios, which has been implemented with a semantic mediawiki and allows the collaborative construction of the conceptual model and the semi-automatic derivation of mathematical programming model elements. The process is applied and validated in a known fresh tomato packing optimization problem. This proposal can be of high relevance for the development and implementation of mathematical programming models for optimizing agriculture and supply chain management related processes in order to fill the current gap between mathematical programming models in the theory and the practice.

Multidimensional modeling driven from a domain language

“…Garrido et al [37] derive models of mathematical problems. Barbosa et al [38] consider the LEL as a shared communicative artifact during software design, so they propose an extension of the LEL to act as an interlingua that captures the shared understanding of both stakeholders and designers.…”

An Improved Linear Complementarity Solver for the Dynamic Analysis of Blast Loaded Structures

“…From this precedent, mathematical programming provides an approach to incorporate the rigid-plastic theory into a unified formalism that is not specific and problem-oriented. Furthermore, mathematical programming (Dantzig, 1998;Dantzig et al, 1955;Guzas & Earls, 2011;Lemke, 1978;Murty, 1983) has a broader application in various specialized fields of engineering, such as robotics (Nuseirat & Stavroulakis, 2000), fluid simulation (Andersen et al, 2017), and agriculture (Garrido et al, 2020). It has the potential to proffer a finite element-based numerical formulation (Maier, 1984;Martin, 1964) that facilitates any distribution of mass, spatial placement of applied loading, and temporal variation of the associated load pulses.…”