Invited Session Thu.2.H 3021

Thursday, 13:15 - 14:45 h, Room: H 3021

Cluster 2: Combinatorial optimization [...]

Combinatorial optimization under uncertainty


Chair: Bo Chen



Thursday, 13:15 - 13:40 h, Room: H 3021, Talk 1

Xiuli Chao
Dynamic pricing decision for a monopoly with strategic customers and price adjustment

Coauthor: Beryl B. Chen


We consider a monopoly firm selling a product over a finite planning horizon to a finite customer base. Each customer requires at most one product and decides whether and when to purchase the product. The customers are strategic and forward looking in making their purchasing decisions. The firm's objective is to set the selling price in each period to maximize its total discounted revenue. We analyze the effect and benefit for the firm's strategy to offer a price adjustment. Our research questions are the following: How does the price adjustment strategy affect the optimal selling price in each period and the consumer behavior, who benefits and who is hurt by this price adjustment strategy? The problem is modeled as a dynamic game and we obtain Markov subgame perfect equilibrium. We show that, depending on the system parameters, the optimal pricing strategy has several interesting patterns. These results are then applied to answer the research questions raised above. We also offer the managerial insights yielded from this model.



Thursday, 13:45 - 14:10 h, Room: H 3021, Talk 2

Mahdi Noorizadegan
A branch and cut approach for some heterogeneous routing problems under demand uncertainty

Coauthors: Bo Chen, Laura Galli


The Capacitated Vehicle Routing Problem (CVRP), with its many variants, is one of the most widely studied NP-hard problems in combinatorial optimisation due to its wide practical applications and tough computational challenges. An important generalisation of the classical CVRP is the so-called Heterogeneous Vehicle Routing Problem (HVRP), where a heterogeneous fleet of finite vehicles is stationed at the depot. In this study, we first consider the stochastic HVRP, and then move to a new and even more general variant known as (stochastic) Capacitated Multi-Depot Heterogeneous VRP. In the stochastic versions it is assumed that customer demands are not known for certain. There are many ways to deal with uncertainty. We present three models: two robust counterparts according to Ben-Tal & Nemirovski (1999) and Bertsimas & Sim (2004) and one chance-constrained. Our first step is to formulate the (deterministic) problems in such a way that the corresponding stochastic ones, according to the three frameworks, remain tractable. The second step is to solve the resulting models using a Branch-and-Cut approach. We present heuristic separation algorithms for some classes of valid inequalities.



Thursday, 14:15 - 14:40 h, Room: H 3021, Talk 3

Zhichao Zheng
Least square regret in stochastic discrete optimization

Coauthor: Chung Piaw Teo


We describe an approach to find good solution to combinatorial optimization problem, when the objective function is random. We use the notion of least square regret, i.e., the expected squared deviation from the optimal solution with perfect hindsight, to measure the performance of the proposed solution. This mimics the tracking error minimization approach often used in the portfolio optimization literature


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