# Research

• Nondifferentiable Optimization

Nondifferentiable optimization (NDO) involves nondifferentiability in the objective and constraint functions. I have particularly worked on the nondifferentiable optimization problems arising in the context of solving Lagrangian relaxations of large-scale mixed integer programs. Conventional gradient-based optimization methods cannot be employed due to nondifferentiability, and hence, NDO methods are specially designed to guarantee convergence.

• Network Interdiction

Network interdiction problems involve sequential games typically played by two players on a network: a follower who wishes to maximize his or her own interest (or profit), and a leader who wishes to minimize the maximum profit attainable by the follower.  These problems are often observed in applications facing threats of a malignant adversary, and have received much attention in that realm.

• Optimal Stopping

Optimal stopping problem seeks the best timing to take an action that yields the maximum expected rewards when a series of decision-making points are set ahead. A well-known example of this type of problems is a secretary problem, where an open secretary position is filled during a finite sequence of interviews. The interviewer must accept or reject the interviewee right after the interview only based on relative rankings. Although there are numerous variants of the problem that have been introduced in literature, the most common solution approach is to employ dynamic programming, which utilizes recursive decision-making.

• Reverse Bullwhip Effect

The reverse bullwhip effect in pricing (RBP) represents the increase in price variability as we move toward the downstream of the supply chain.  It is known that the price variability is one of the major causes of amplified order-quantity variability that adversely affects the supply chain performance. Hence, identifying the existence of RBP is an important step to properly cope with amplified order-quantity variability.

• Stability in Production Planning

The flexible requirements profile (FRP) is a production planning scheme that is designed to reduce variability in production plans over a certain planning-horizon.  Under FRP, current and future production quantities are subject to a funnel-shaped set of bounds, which typically stipulates a narrower range between lower and upper bounds in the near future while this range increases as we move into the further future.