You Are What You Eat: A Preference-Aware Inverse Optimization Approach

A key challenge in the emerging field of precision nutrition entails providing diet recommendations that reflect both the (often unknown) dietary preferences of different patient groups and known dietary constraints specified by human experts. Motivated by this challenge, we develop a preference-aware constrained-inference approach in which the objective function of an optimization problem is not pre-specified and can differ across various segments. Among existing methods, clustering models from machine learning are not naturally suited for recovering the constrained optimization problems, whereas constrained inference models such as inverse optimization do not explicitly address non-homogeneity in given datasets. By harnessing the strengths of both clustering and inverse optimization techniques, we develop a novel approach that recovers the utility functions of a constrained optimization process across clusters while providing optimal diet recommendations as cluster representatives. Using a dataset of patients' daily food intakes, we show how our approach generalizes stand-alone clustering and inverse optimization approaches in terms of adherence to dietary guidelines and partitioning observations, respectively. The approach makes diet recommendations by incorporating both patient preferences and expert recommendations for healthier diets, leading to structural improvements in both patient partitioning and nutritional recommendations for each cluster. An appealing feature of our method is its ability to consider infeasible but informative observations for a given set of dietary constraints. The resulting recommendations correspond to a broader range of dietary options, even when they limit unhealthy choices

Inventory management in the face of a limited storage capacity

One of the most important measurements of supply chain performance is inven-tory costs associated with the material and product flow within the whole supply chain. While there exists a large body of inventory management literature, the restriction imposed by a limited storage capacity has not been given due atten-tion. Limited storage capacity, coupled with a traditional warehousing approach, often makes it tough to match inventory with fluctuating demands. In this thesis, we build a stochastic inventory management model subject to storage capacity restrictions. By coordinating inbound and outbound flows, incoming goods are allocated to retail outlets before the leftover goods, if any, are stored to the warehouse. Our Markov Decision Process model differs from other existing work in that the storage capacity does not limit the ordering quantity. We derive optimal inventory policies under different cost structures. For different cases, managerial insights based on computational analysis are highlighted. We also study a problem of water purchasing management under the context of limited storage space, which is motivated by Hong Kong's water purchasing practice from Guangdong. We restrict our attention to the importing side's opti-mal decisions. We build a regulated Brownian motion model to describe various issues of the problem. We provide analysis that helps optimize not only the annual purchasing amount, but also the storage capacity of the reservoir

A game theoretic queueing approach to self-reflection in decentralized human-robot interaction systems

This paper presents a queueing model that addresses robot self-assessment in human-robot-interaction systems. We build the model based on a game theoretic queueing approach, and analyze four issues: 1) individual differences in operator skills/capabilities, 2) differences in difficulty of presenting tasks, 3) trade-off between human interaction and performance and 4) the impact of task heterogeneity in the optimal service decision-making and system performance. The subsequent analytical and numerical exploration helps understand the way the decentralized decision-making scheme is affected by various service environment

Service level differentiation in multi-robot teams

Abstract-In this paper we explore the effects of service level differentiation on a multi-robot control system. We examine the premise that although long interaction time between robots and operators hurts the efficiency of the system, as it generates longer waiting time for robots, it provides robots with longer neglect time and better performance benefiting the system. In the paper we address the problem of how to choose the optimal service level for an operator in a system through a service level differentiation model. Experimental results comparing system performance for different values of system parameters show that a mixed strategy is a general way to get optimal system performance for a large variety of system parameter settings and in all cases is no worse than a pure strategy