Learning and Decision Making Under Uncertainty

Lei Li, Purdue University

Abstract

In practice, we often make decisions under uncertainties with known distributions or even without knowing distributions. This study explores decision learning and decision making in not-for-profit operations and supply chain management. We first study dynamic staffing under volunteer supply uncertainty, then explore how to dynamically balance uncertain supply with uncertain demand under lost sales, and finally study decision learning with limited data when distributions are unknown. We provide a brief description of the results obtained from the specific problems considered in this study.The dynamic staffing problem under volunteer supply uncertainty is explored in Chapter 2. We model a finite-horizon staffing problem in nonprofit organizations making hiring and assignment decisions for paid workers and volunteer, given a budget constrain, a capacity constraint, and uncertainties of volunteer supply and part-time worker turnover. Although the optimal staffing policy is computationally challenging to identify in general, we show that an intuitive prioritization assignment policy for all staff and a simple hire-up-to policy for part-time workers can be conveniently applied and close to optimal. Based on the theoretical properties of the optimal policy, we further suggest two easy-to-implement heuristics, both of which have low relative optimality gaps. We also provide performance lower bounds of both heuristics.The dynamic problem of balancing uncertain supply with uncertain demand under lost sales is explored in Chapter 3. We study the dynamic inventory replenishment and product pricing policy aiming to mitigate both supply uncertainty and demand loss. Since the dynamic planning problem is highly non-concave and thus intractable, we propose an approach that focuses on a class of intuitively appealing and practically plausible policies that require the amount of stock allocated for meeting the demand to be increasing and the product price to be decreasing in the available inventory level. We show that, under general conditions for the stochastic supply and demand functions, over a restricted monotone policy class, the dynamic problem become a concave optimization problem . We further reduce the restricted class to a refined class which can be easily computed, and appropriately selected refined policies produce optimal or close-to-optimal profits.The decision learning with limited data problem is explored in Chapter 4. We study how to utilize the data from related systems for decision making with limited data, which underscores the role of domain knowledge, the statistical similarity among the related systems and the structural relationships between inputs and outputs. When a related system has ample data, we demonstrate, through the application of newsvendor systems, that transfer learning can improve decision performance in the focal system, and cross-learning solutions can significantly improves the performance of the focal system over the transfer-learned solution and are asymptotically optimal. When there are multiple related systems with limited data, we transform the data from different systems to create a generic stochastic environment for the decision making problem, and show that the derived co-learning solution is asymptotically optimal for each involved system, as well as the aggregate system.

Degree

Ph.D.

Advisors

Shanthikumar, Purdue University.

Subject Area

Labor relations|Organizational behavior

COinS