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 12 unattainable means to optimize their processes. However, the value they provide is only as good as their capacity to 13 capture the process domain. This information can only be obtained from stakeholders, i.e., clients or users, who can 14 hardly communicate the requirements clearly and completely. Besides, existing conceptual models of mathematical 15 programming models are not standardized, nor is the process of deriving the mathematical programming model from 16 the concept model, which remains ad hoc. In this paper, we propose an agile methodology to construct mathematical 17 programming models based on two techniques from requirements engineering that have been proven effective at 18 requirements elicitation: the language extended lexicon (LEL) and scenarios. Using the pair of LEL + scenarios allows 19 to create a conceptual model that is clear and complete enough to derive a mathematical programming model that 20 effectively captures the business domain. We also define an ontology to describe the pair LEL + scenarios, which has 21 been implemented with a semantic mediawiki and allows the collaborative construction of the conceptual model and 22 the semi-automatic derivation of mathematical programming model elements. The process is applied and validated in 23 a known fresh tomato packing optimization problem. This proposal can be of high relevance for the development and 24 implementation of mathematical programming models for optimizing agriculture and supply chain management 25 related processes in order to fill the current gap between mathematical programming models in the theory and the 26 practice.