zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A multivariate adaptive regression splines cutting plane approach for solving a two-stage stochastic programming fleet assignment model. (English) Zbl 1237.90133
Summary: The fleet assignment model assigns a fleet of aircraft types to the scheduled flight legs in an airline timetable published six to twelve weeks prior to the departure of the aircraft. The objective is to maximize profit. While costs associated with assigning a particular fleet type to a leg are easy to estimate, the revenues are based upon demand, which is realized close to departure. The uncertainty in demand makes it challenging to assign the right type of aircraft to each flight leg based on forecasts taken six to twelve weeks prior to departure. Therefore, in this paper, a two-stage stochastic programming framework has been developed to model the uncertainty in demand, along with the Boeing concept of demand driven dispatch to reallocate aircraft closer to the departure of the aircraft. Traditionally, two-stage stochastic programming problems are solved using the L-shaped method. Due to the slow convergence of the L-shaped method, a novel multivariate adaptive regression splines cutting plane method has been developed. The results obtained from our approach are compared to that of the L-shaped method, and the value of demand-driven dispatch is estimated.

MSC:
90B80Discrete location and assignment
90C15Stochastic programming
WorldCat.org
Full Text: DOI
References:
[1] Abara, J.: Applying integer linear programming to the fleet assignment problem, Interface 19, 20-28 (1989)
[2] Adams, W.; Sherali, H.: Mixed-integer bilinear programming problems, Mathematical programming 59, 279-305 (1993) · Zbl 0801.90085 · doi:10.1007/BF01581249
[3] Barnhart, C.; Boland, N.; Clake, L.; Johnson, E.; Nemhauser, G.; Shenoi, R.: Flight string models for aircraft fleeting and routing, Transportation science 32, 208-220 (1998) · Zbl 0987.90504 · doi:10.1287/trsc.32.3.208
[4] Barnhart, C.; Kniker, T.; Lohatepanont, M.: Itinerary-based airline fleet assignment, Transportation science 36, 199-217 (2002) · Zbl 1134.90316 · doi:10.1287/trsc.36.2.199.566
[5] Berge, M.; Hopperstad, C.: Demand driven dispatch: A method of dynamic aircraft capacity assignment models and algorithms, Operations research 41, 153-168 (1993) · Zbl 0775.90146 · doi:10.1287/opre.41.1.153
[6] Chen, V.: Measuring the goodness of orthogonal array discretizations for stochastic programming and stochastic dynamic programming, SIAM journal of optimization 12, 322-344 (2001) · Zbl 1017.90067 · doi:10.1137/S1052623498332403
[7] Chen, V.; Ruppert, D.; Shoemaker, C.: Applying experimental design and regression splines to high dimensional continuous-state stochastic dynamic programming, Operations research 47, 38-53 (1999) · Zbl 0979.90094 · doi:10.1287/opre.47.1.38
[8] Chen, V. C. P.; G√ľnther, D.; Johnson, E. L.: Solving for an optimal airline yield management policy via statistical learning, Journal of the royal statistical society, series C 52, 1-12 (2003) · Zbl 1111.90333 · doi:10.1111/1467-9876.00386
[9] Chen, V. C. P.; Tsui, K. L.; Barton, R. R.; Meckesheimer, M.: Design, modeling, and applications of computer experiments, IIE transactions 38, 273-291 (2006)
[10] Clarke, L.; Hane, C.; Johnson, E.; Nemhauser, G.: Maintenance and crew considerations in fleet assignment, Transportation science 30, 249-260 (1996) · Zbl 0879.90132 · doi:10.1287/trsc.30.3.249
[11] Friedman, J. H.: Multivariate adaptive regression splines, The annals of statistics 19, 1-141 (1991) · Zbl 0765.62064 · doi:10.1214/aos/1176347963
[12] Geoffrion, A. M.; Graves, G.: Multicommodity distribution system design by benders decomposition, Management science 20, 822-844 (1974) · Zbl 0304.90122 · doi:10.1287/mnsc.20.5.822
[13] Gu, Z.; Johnson, E.; Nemhauser, G.; Wang, Y.: Some properties of the fleet assignment problem, Operations research letters 15, 59-71 (1994) · Zbl 0810.90067 · doi:10.1016/0167-6377(94)90001-9
[14] Hane, C.; Barnhart, C.; Johnson, E.; Nemhauser, G.; Sigismondi, G.: The fleet assignment problem: solving a large scale integer program, Mathematical programming 70, 211-232 (1995) · Zbl 0840.90104
[15] Jacobs, T., Johnson, E., Smith, B., 1999. O-d fam: Incorporating passenger flows into the fleeting process, In: AGIFORS Symposium Proceedings, New Orleans, LA, USA.
[16] Kniker, T., 1998. Itinerary-Based Airline Fleet Assignment. Ph.D. thesis. Massachusetts Institute of Technology. · Zbl 1134.90316
[17] Listes, O.; Dekker, R.: A scenario aggregation-based approach for determining a robust airline fleet composition for dynamic capacity allocation, Transportation science 39, 367-382 (2005)
[18] Pilla, V.; Rosenberger, J.; Chen, V.: A statistical computer experiments approach to airline fleet assignment, IIE transactions 40, 524-537 (2008)
[19] Rockafellar, R.; Wets, R.: Scenarios and policy aggregation in optimization under uncertainty, Mathematics of operations research 16, 119-147 (1991) · Zbl 0729.90067 · doi:10.1287/moor.16.1.119
[20] Rosenberger, J.; Johnson, E.; Nemhauser, G.: A robust fleet assignment model with hub isolation and short cycles, Transportation science 38, 357-368 (2003)
[21] Rushmeier, R.; Kontogiorgis, S.: Advances in the optimization of airline fleet assignment, Transportation science 31, 159-169 (1997) · Zbl 0886.90069 · doi:10.1287/trsc.31.2.159
[22] Savelsbergh, M.: Preprocessing and probing techniques for mixed integer programming problems, ORSA journal on computing 6, 445-454 (1994) · Zbl 0814.90093 · doi:10.1287/ijoc.6.4.445
[23] Sherali, H. D.; Bish, E. K.; Zhu, X.: Airline fleet assignment concepts, models, and algorithms, European journal of operational research 172, 1-30 (2006) · Zbl 1107.90359 · doi:10.1016/j.ejor.2005.01.056
[24] Sherali, H. D.; Zhu, X.: Two-stage fleet assignment model considering stochastic passenger demands, Operations research 56, 383-399 (2008) · Zbl 1167.90387 · doi:10.1287/opre.1070.0476
[25] Shih, D., Kim, S., Chen, V., Rosenberger, J., Pilla, V., 2007. Efficient Computer Experiment-Based Optimization through Variable Selection. Technical Report. The University of Texas at Arlington. · Zbl 1296.90083
[26] Smith, B., 2004. Robust Airline Fleet Assignment. Ph.D. thesis. Georgia Institute of Technology.
[27] Subramanian, R.; Scheff, R.; Quillinan, J.; Wiper, D.; Marsten, R.: Coldstart: fleet assignment at delta airlines, Interfaces 24, 104-120 (1994)
[28] Survajeet, S.; Higle, J.: Stochastic decomposition, (1996)
[29] Talluri, K. T.: Swapping applications in a daily fleet assignment, Transportation science 30, 237-248 (1996) · Zbl 0879.90138 · doi:10.1287/trsc.30.3.237
[30] Tsai, J.; Chen, V.: Flexible and robust implementations of multivariate adaptive regression splines within a wastewater treatment stochastic dynamic program, Quality and reliability engineering international 21, 689-699 (2005)