Lambert W Function in Mathematical Models of Intra-year Pricing, Storage and Manipulation of Perishable Agricultural Goods
Tomislav Došlić
Department of Mathematics, Faculty of Civil Engineering,University of Zagreb, Kaciceva ulica 26, 10 000 Zagreb, Croatia.
Biserka Kolarec *
Department of Information Science and Mathematics, Faculty of Agriculture, University of Zagreb, Svetošimunska cesta 25, 10000 Zagreb, Croatia.
*Author to whom correspondence should be addressed.
Abstract
Mathematical modelling has increasingly shifted towards computational and numerical methods, resulting in less emphasis on exactly solvable models and closed-form analytical solutions. This study presents Lambert W function solutions to models of the pricing, storage, and handling of agricultural goods with lifespans extending over two intra-year periods. The original linear pricing model given by Helmberger is extended to two semi-exponential models, both of which are explicitly solvable in terms of the Lambert W function. In addition, the Lambert W function solution is provided for determining the optimal time to transfer harvested goods into cool storage under specified agro-technical and managerial constraints.
Keywords: Lambert W function, Helmberger linear pricing model, semi-exponential models, optimal transfer time