scholarly journals An Approach to Stochastic Integer Programming Problem with Simple Recourse via Dynamic Slope Scaling Procedure

2010 ◽  
Vol 22 (2) ◽  
pp. 257-265
Author(s):  
Ayumi NISHIOKA ◽  
Takayuki SHIINA ◽  
Jun IMAIZUMI ◽  
Susumu MORITO
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Stochastic Integer Programming ◽  
Integer Programming Problem ◽  
Scaling Procedure ◽  
Dynamic Slope Scaling ◽  
Simple Recourse ◽  
Dynamic Slope Scaling Procedure

scholarly journals Recourse in Kidney Exchange Programs

2021 ◽  
Author(s):  
Bart Smeulders ◽  
Valentin Bartier ◽  
Yves Crama ◽  
Frits C. R. Spieksma
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Cycle Length ◽  
Stochastic Integer Programming ◽  
Integer Programming Problem ◽  
Expected Number ◽  
Two Stage ◽  
Exchange Programs ◽  
Kidney Exchange ◽  
Algorithmic Approaches

We introduce the problem of selecting patient-donor pairs in a kidney exchange program to undergo a crossmatch test, and we model this selection problem as a two-stage stochastic integer programming problem. The optimal solutions of this new formulation yield a larger expected number of realized transplants than previous approaches based on internal recourse or subset recourse. We settle the computational complexity of the selection problem by showing that it remains NP-hard even for maximum cycle length equal to two. Furthermore, we investigate to what extent different algorithmic approaches, including one based on Benders decomposition, are able to solve instances of the model. We empirically investigate the computational efficiency of this approach by solving randomly generated instances and study the corresponding running times as a function of maximum cycle length, and of the presence of nondirected donors. Summary of Contribution: This paper deals with an important and very complex issue linked to the optimization of transplant matchings in kidney exchange programs, namely, the inherent uncertainty in the assessment of compatibility between donors and recipients of transplants. Although this issue has previously received some attention in the optimization literature, most attempts to date have focused on applying recourse to solutions selected within restricted spaces. The present paper explicitly formulates the maximization of the expected number of transplants as a two-stage stochastic integer programming problem. The formulation turns out to be computationally difficulty, both from a theoretical and from a numerical perspective. Different algorithmic approaches are proposed and tested experimentally for its solution. The quality of the kidney exchanges produced by these algorithms compares favorably with that of earlier models.

TWO BI-OBJECTIVE OPTIMIZATION MODELS FOR COMPETITIVE LOCATION PROBLEMS

2006 ◽  
Vol 05 (03) ◽  
pp. 531-543 ◽  
Author(s):  
FENGMEI YANG ◽  
GUOWEI HUA ◽  
HIROSHI INOUE ◽  
JIANMING SHI
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Efficient Solutions ◽  
Integer Program ◽  
Location Problems ◽  
Optimization Models ◽  
Competitive Location ◽  
Integer Programming Problem ◽  
Single Objective ◽  
Parametric Integer Programming

This paper deals with two bi-objective models arising from competitive location problems. The first model simultaneously intends to maximize market share and to minimize cost. The second one aims to maximize both profit and the profit margin. We study some of the related properties of the models, examine relations between the models and a single objective parametric integer programming problem, and then show how both bi-objective location problems can be solved through the use of a single objective parametric integer program. Based on this, we propose two methods of obtaining a set of efficient solutions to the problems of fundamental approach. Finally, a numerical example is presented to illustrate the solution techniques.

scholarly journals The Magnetic Bead Computing Model of the 0-1 Integer Programming Problem Based on DNA Cycle Hybridization

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Rujie Xu ◽  
Zhixiang Yin ◽  
Zhen Tang ◽  
Jing Yang ◽  
Jianzhong Cui ◽  
...  
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Magnetic Beads ◽  
Specific Binding ◽  
Optimal Solution ◽  
High Sensitivity ◽  
Magnetic Bead ◽  
Integer Programming Problem ◽  
Computing Model ◽  
Dna Strands

Magnetic beads and magnetic Raman technology substrates have good magnetic response ability and surface-enhanced Raman technology (SERS) activity. Therefore, magnetic beads exhibit high sensitivity in SERS detection. In this paper, DNA cycle hybridization and magnetic bead models are combined to solve 0-1 integer programming problems. First, the model maps the variables to DNA strands with hairpin structures and weights them by the number of hairpin DNA strands. This result can be displayed by the specific binding of streptavidin and biotin. Second, the constraint condition of the 0-1 integer programming problem can be accomplished by detecting the signal intensity of the biological barcode to find the optimal solution. Finally, this model can be used to solve the general 0-1 integer programming problem and has more extensive applications than the previous DNA computing model.

Solving the multi-objective stochastic interval-valued linear fractional integer programming problem

2021 ◽  
pp. 2250022
Author(s):  
Leila Younsi-Abbaci ◽  
Mustapha Moulaï
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Probabilistic Constraints ◽  
Chance Constrained Programming ◽  
Integer Programming Problem ◽  
Objective Functions ◽  
Programming Technique ◽  
Multi Objective ◽  
Weighted Sum Method ◽  
Interval Valued

In this paper, we consider a Multi-Objective Stochastic Interval-Valued Linear Fractional Integer Programming problem (MOSIVLFIP). We especially deal with a multi-objective stochastic fractional problem involving an inequality type of constraints, where all quantities on the right side are log-normal random variables, and the objective functions coefficients are fractional intervals. The proposed solving procedure is divided in three steps. In the first one, the probabilistic constraints are converted into deterministic ones by using the chance constrained programming technique. Then, the second step consists of transforming the studied problem objectives on an optimization problem with an interval-valued objective functions. Finally, by introducing the concept of weighted sum method, the equivalent converted problem obtained from the two first steps is transformed into a single objective deterministic fractional problem. The effectiveness of the proposed procedure is illustrated through a numerical example.

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