Thursday, March 9, 2017

Game Theory and Fresh Produce Supply Chains - It's About the Fruits and Veggies

Is there anything more delicious than a ripe peach or mango? Or, perhaps, you love biting into a sweet, crisp apple? I love my fresh fruit and veggies and, frankly, we are spoiled, in a sense, in the US, where we can savor berries and cherries even in the winter. You probably also enjoy a variety of vegetables and I am not speaking of just French fries.

At the same time, when the "fresh" produce is not so fresh, one gets quite disappointed and the wastage associated with this industry is vast. Quality of fruits and vegetables is a topic, hence, of great research and practical interest and not only for food scientists and economists,  but operations researchers as well.

The first paper that my group published on fresh produce supply chains was: Competitive Food Supply Chain Networks with Application to Fresh Produce, Min Yu and Anna Nagurney, European Journal of Operational Research 224(2): (2013) pp 273-282, a paper that is highly cited and was even recognized by the Editors of the journal in a special session last July at the fabulous EURO conference in Poznan, Poland. You can read my blogpost, which even has photos of delicious pierogies here.

In this paper, we utilized game theory to capture competition among food firms, who differentiate their products, which are perishable, and we applied the model to a case study of cantaloupes, subject also to a disruption. Indeed, there have been some major quality issues resulting in food-borne illnesses in this sector. Quality in this paper was modeled using a generalized network framework with link multipliers and it was assumed that as the fresh produce "moved" over links in the supply chain that a certain percentage would "perish" and would, hence, be discarded.

More recently, we turned to short fresh produce supply chains in the form of farmers' markets.  In the paper, Quality in Competitive Fresh Produce Supply Chains with Application to Farmers’ Markets,
Deniz Besik and Anna Nagurney, which is now in press in Socio-Economic Planning Sciences, we used kinetic formulae to model quality deterioration over time and under temperature conditions. I think that this is super cool and very much enjoy bringing scientific disciplines from chemistry to physics to operations research supply chain modeling.  We then applied the model to apple farms in western Massachusetts, and, since one of the farms was Apex Orchards (one of my favorites), below I have photos of their relatively new store in Shelburne Falls.
And I can't resist sharing the photo below of the bridge of flowers in neighboring Shelburne.
In Amherst, we have a farmers' market from May through October in downtown, which is very enjoyable and also highly social. The Farmers' Market then moves indoors for the winter and whenever we are in town we always visit and purchase produce. You know where it is coming from and when it was picked. Our paper we dedicated to Robert Colnes, who owned an orchard in New Salem and who was a fellow Brown University alumnus. Deniz had interviewed him multiple times. He passed away a few months ago at age 96 and before we could share with him the good news that our paper had been accepted for publication. He was so generous in answering questions.

Last spring/summer I spent several months as a Visiting Fellow at All Souls College at Oxford University (a simply heavenly intellectual and aesthetic experience that will be very hard to top). While at Oxford I would regularly go to the Farmers' Market in the center of Oxford and the photos below capture some of the spirit of it.
The food stalls at the Oxford Farmers' Market are fabulous and there is a wide variety of ethnic cuisines for purchase.

In the paper, Supply Chain Network Capacity Competition with Outsourcing: A Variational Equilibrium Framework, Anna Nagurney, Min Yu, and Deniz Besik, in press in the Journal of Global Optimization, we used game theory, but the governing equilibrium concept was a Generalized Nash Equilibrium (rather than a Nash Equilibrium as in the above papers), since the producers' constraints, and not just their utility functions, depended on the strategies of the other producers.  The case study was to apples in western Massachusetts. We used variational equilibrium to formulate the problem.

What I find so special about the discipline of Operations Research is that you can work on what you love and that includes food supply chains!