Invited Session Fri.2.MA 141

Friday, 13:15 - 14:45 h, Room: MA 141

Cluster 22: Stochastic optimization [...]

Target oriented optimization under uncertainity


Chair: Melvyn Sim and Jin Qi



Friday, 13:15 - 13:40 h, Room: MA 141, Talk 1

Zhuoyu Long
Managing operational and financing decisions to meet consumption targets

Coauthors: Lucy Gongtao Chen, Melvyn Sim


We study dynamic operational decision problems where risky cash flows are resolved over a finite planning horizon. Financing decisions via lending and borrowing are available to smooth out consumptions over time with the goal of achieving prescribed consumption targets. Our target-oriented decision criterion has salient properties of subadditivity, convexity and respecting second-order stochastic dominance. We show that if borrowing and lending are unrestricted, the optimal policy is to finance consumptions at the target levels for all periods except the last. Moreover, the optimal policy has the same control state as the optimal risk neutral policy and could be achieved with relatively modest computational effort. Under restricted financing, the optimal policies correspond to those that maximize expected additive-exponential utilities, and can be obtained by an efficient algorithm. We also analyze the optimal policies of joint inventory-pricing decision problems under the target-oriented criterion and provide optimal policy structures. With a numerical study, we report favorable computational results for using targets in regulating uncertain consumptions over time.



Friday, 14:15 - 14:40 h, Room: MA 141, Talk 3

Jin Qi
Routing optimization with deadlines under uncertainty

Coauthors: Patrick Jaillet, Melvyn Sim


We study a routing problem with deadlines imposed at a given subset of nodes, and uncertain arc travel times characterized by distributional information set. Our model is static in the sense that the routing decision is made prior to the realization of uncertain travel times.
To find an optimal routing policy such that arrival times at the nodes "effectively'' respect deadlines, we first introduce a new measure named Lateness Index to evaluate the performance of meeting deadlines. It is defined as the minimum risk tolerance parameter such that its worst-case certainty equivalent arrival time is no larger than the deadline presumed at the corresponding node. Instead of specifying the exact probability distribution of the uncertain arc travel time, we assume its true distribution lies in a family of distributions, which is characterized by some descriptive statistics.
We show that some special cases of our problem, such as when only one node has a deadline requirement, are polynomially solvable. And for the general case, we can develop computationally more "efficient'' algorithms to find exact optimal routing policy by only solving a series of deterministic routing problems.


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