Food hubs are of interest in regional and local food system development because they potentially enhance the sustainability of food supply chains. Expanding on earlier literature, this study introduces economies of scale into an aggregation hub location model and disaggregates production into four seasons to account for geographic and seasonal variation of US fresh produce production. A mixed integer linear programming model is formulated with the objective of minimizing total costs of assembly and first-handler operations. Results suggest scale economies have significant effects on the optimal number, locations, and sizes of aggregation hubs. We model regional and local food systems in a manner more consistent with economic theory and provide a richer framework for policy analysis.

We propose a new adaptive and composite Barzilai–Borwein (BB) step size by integrating the advantages of such existing step sizes. Particularly, the proposed step size is an optimal weighted mean of two classical BB step sizes and the weights are updated at each iteration in accordance with the quality of the classical BB step sizes. Combined with the steepest descent direction, the adaptive and composite BB step size is incorporated into the development of an algorithm such that it is efficient to solve large-scale optimization problems. We prove that the developed algorithm is globally convergent and it R-linearly converges when applied to solve strictly convex quadratic minimization problems. Compared with the state-of-the-art algorithms available in the literature, the proposed step size is more efficient in solving ill-posed or large-scale benchmark test problems.