Contributed Session Thu.2.H 2036

Thursday, 13:15 - 14:45 h, Room: H 2036

Cluster 4: Conic programming [...]

Conic relaxation approaches for scheduling and selection problems


Chair: Yuan Yuan



Thursday, 13:15 - 13:40 h, Room: H 2036, Talk 1

Karthik Natarajan
On theoretical and empirical aspects of marginal distribution choice models

Coauthors: Vinit Kumar Mishra, Dhanesh Padmanabhan, Chung-Piaw Teo


In the discrete choice context, two recently proposed models are the marginal distribution model (MDM) and marginal moment model (MMM), using only limited information of joint distribution of random utilities (marginal distributions
and first two marginal moments, respectively). In this paper, we show that multinomial logit (MNL) and MMM choice probabilities are special cases of MDM for exponential and t-distributions. The choice probabilities obtained using the generalized extreme value (GEV) models is also a special case of the MDM with generalized exponential distributions. The convexity of the maximum loglikelihood estimation
problem is established for a class of distributions from the theory of constrained optimization. We show that the seller’s problem of determining the prices of multiple differentiated products to maximize the expected profit can be formulated as a concave maximization problem for the class of logconcave density functions. Conjoint choice data set on technological features for automotives, provided by General Motors is used to test the performance of the models.



Thursday, 13:45 - 14:10 h, Room: H 2036, Talk 2

Yuan Yuan
Integrated ship plan of strip coil consolidation and stowage

Coauthor: Tang Lixin


In iron and steel industry, finished products such as strip coils are mainly transported by ship. The planning of ship transportation includes consolidation planning and stowage planning. Consolidation planning is to determine which coils to be loaded on a given ship according to the delivery dates, destinations and storage locations of the coils. Stowage planning is to allocate exact position to each coil based on the constraints about the ship's stability. Ordinary researches divided the problem into two subproblems, and discussed them sequentially. The solution obtained by solving the two problems may not be very good or there may be many shifts, or even not all the coils in consolidation plan could be loaded. This is because the size of coils is irregular and the constraints for balance are rigorous, but the frame of ship was not considered by consolidation planning. The situation motivates us to integrate the two subproblems. We formulate the problem and relax it by a second order cone programming approach. An approximate solution is obtained by a heuristic method.


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