By: Jacob Andreesen, Miao Xu, Yiyi Wang, Chengyi (Jeff) Chen

In Project 1, we designed a restaurant recommendation application that utilizes a mixed integer program to find the five best restaurants based on a group’s collective preferences. During the project we scraped data from Yelp, allowed for user inputs, and outputted a decision of 5 restaurants as well as a secondary cocktail bar recommendation. The app performed as expected with accurate results outputted. A range of additional features are currently being implemented.

In Project 2, we wanted to utilize simulation methods in coordination with stochastic optimization to solve problems with distributed uncertainty. We set out to solve the “multilocation transshipment problem” where a supply chain relies operates with transshipments, which is the practice of shipping inventory between retailers of the same class rather than the retailers relying on inventory from the central supplier alone. In order to solve the linear program, we developed, we used two alternate optimization algorithms (Stochastic Gradient Descent (SGD) and Bender’s Decomposition) and compared their performance. Results showed that Bender’s operated more efficiently in this formulation however we hypothesized that the outcome may be different when more scenarios are introduced.

In Project 3, we set out to investigate the behavior and performance of Predictive Stochastic Programming (PSP) where informed predictions of uncertainty can be made based on “covariate” sets of responses and predictors. During this project, a PSP formulation wthat the Simple Recourse model performs better than the Deterministic model in the long run.as applied to the popular ‘Wyndor Glass Company’ production problem. To solve the Wyndor PSP, a methodology referred to as Learning Enabled Optimization (LEO) was applied and is walked through in the Technical Architecture Section. To understand the benefit of the LEO protocol as applied to PSPs, two statistical models were utilized and compared: Deterministic Forecast (DF) and SAA-Empirical Additive Error (EAE/SAA). Ultimately, we determined that LEO-PSP poses a number of modeling advantages, the validation approach established is useful and accurate in assessing model validity, and the EAE/SAA model is appropriate for PSP models whereas Deterministic is not due to respective error considerations

In project 4, we try to implement the Deterministic and Simple Recourse model in stochastic optimization to find the optimal allocation of ventilators among U.S. During the COVID-19 pandemic, many states in the U.S. have faced a shortage of medical resources, so if the medical resources(ventilators) can be transferred across states and the Strategic National Stockpile, ventilators will be allocated to the states in need, and the shortage of ventilators will be alleviated. The objective of our problem is to minimize the unmet demand for ventilators by optimally distributing them across all states. We build two models to solve this problem, one is the deterministic (point-forecast) model without data uncertainty, and another is the two-stage simple recourse model considering three different scenarios for each state’s demand. The result shows the simple recourse model performs better than the deterministic model in the long run, which means the simple recourse model can meet the actual demand with a smaller shortfall after considering three possible low, mean, and high expected demand for each state. Also, unlike stochastic optimization we did in project 2&3, in this project, we observe that the decision of one period will affect the start point of the next period. Therefore, the simple recourse model performs better over time.