Behavioral portfolio selection with loss control

In this paper we formulate a continuous-time behavioral (à la cumulative prospect theory) portfolio selection model where the losses are constrained by a pre-specified upper bound. Economically the model is motivated by the previously proved fact that the losses occurring in a bad state of the world can be catastrophic for an unconstrained model. Mathematically solving the model boils down to solving a concave Choquet minimization problem with an additional upper bound. We derive the optimal solution explicitly for such a loss control model. The optimal terminal wealth profile is in general characterized by three pieces: the agent has gains in the good states of the world, gets a moderate, endogenously constant loss in the intermediate states, and suffers the maximal loss (which is the given bound for losses) in the bad states. Examples are given to illustrate the general results.     

Resource constraint scheduling with a fractional shared resource

We consider a scheduling problem motivated by mining in remote off-grid areas. In this model, mines have pre-assigned mineral processing jobs and their own machine for executing these jobs. Each job also needs a certain amount of electricity in order to get completed. The electricity, on the other hand, is of limited supply and must be shared between the mines. We present a mathematical formulation of the problem and a Lagrangian relaxation based heuristic. Computational results which compares our heuristic with genetic algorithm and simulated annealing are also presented.     

Bilinear approach for a symmetry constraint of the modified KdV equation

The paper investigates the mKdV equation with the potential under symmetry constraint through bilinear approach, i.e., Hirota method and Wronskian technique. We show that the potential can be a summation of squares of wave functions and these wave functions can precisely be described as Wronskians.     

Defocus and binocular vision based stereo particle pairing method for 3D particle tracking velocimetry

We propose a new method, based on the depth-from-defocus technique and binocular vision, for solving the stereo particle pairing problem in 3D particle tracking velocimetry (PTV). Firstly, the apparent particle depth is measured with a single camera, using the depth-from-defocus technique. Secondly, a strict mathematical model of the particle-to-particle correspondence relationship between the left and right images, taking into account the refractions at the interfaces in the optical path, is presented, with the assumption that the apparent particle depth is measured. Thirdly, based on the apparent particle depth and particle-to-particle correspondence relationship, the epipoplar line is truncated into a short line segment by cutting off, where the apparent particle depth extends beyond its estimated range. For the first time, the range of the blur circle radius is employed as an additional stereo particle pairing constraint. Finally, the optimal pairing particle is selected by applying the epipolar line segment and blur circle radius constraints. The experimental results show that the rate of correct pairing is significantly improved compared with the epipolar line nearest neighbor analysis, especially when the particle density is increasing.     

The complexity of recursive constraint satisfaction problems

We investigate the complexity of finding solutions to infinite recursive constraint satisfaction problems. We show that, in general, the problem of finding a solution to an infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through a recursive tree. We also identify natural classes of infinite recursive constraint satisfaction problems where the problem of finding a solution to the infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through finitely branching recursive trees or recursive binary trees. There are a large number of results in the literature on the complexity of the problem of finding an infinite path through a recursive tree. Our main result allows us to automatically transfer such results to give equivalent results about the complexity of the problem of finding a solution to a recursive constraint satisfaction problem.     

Numerical methods for portfolio selection with bounded constraints

This work develops an approximation procedure for portfolio selection with bounded constraints. Based on the Markov chain approximation techniques, numerical procedures are constructed for the utility optimization task. Under simple conditions, the convergence of the approximation sequences to the wealth process and the optimal utility function is established. Numerical examples are provided to illustrate the performance of the algorithms.     

Revisiting the shelf life constrained multi-product manufacturing problem

A multi-product manufacturing problem generally consists of the total cost minimization. In case where the shelf life constraint is imposed, various options to deal with the situation are widely discussed in the literature. These options include a reduction in the production rate and cycle time separately, and the simultaneous reduction of production rate and cycle time. When the production rate is decreased, the unit manufacturing cost increases and because of this the inventory holding costs need modification. In the existing literature, this has been ignored in the computation of cost and therefore a revisit to the problem has been justified. The present paper modifies the holding cost and this problem has been reformulated for the basic case. This has also been extended for an inclusion of shortages that are backordered completely or partially.     

Star partitions on graphs

Given an undirected graph, a star partition is a partition of the nodes into subsets with at least two nodes so that the subgraph induced by each subset has a spanning star. Star partitions are related to well-known problems concerning domination in graphs and edge covering. We focus on the Constrained Star Partition Problem (CSP) that asks for finding a star partition of given cardinality. The problem is new and presents interesting peculiarities. We explore the relation between the cardinalities of star partitions and domatic bipartitions, showing that there are star partitions of any cardinality between minimum and maximum values, and that a similar but weaker result holds for domatic bipartitions. We study the computational complexity of different versions of star partition and domatic bipartition problems, proving that most of them, in particular CSP, constrained domatic bipartition and balanced domatic bipartition, are NP-complete. We also show that star partition problems are polynomial on trees and, more generally, on bounded treewidth graphs. We introduce an integer linear programming formulation that defines a polytope containing all the star partitions of a graph, showing that its vertices have only integral components for trees, which implies that linear programming can be used to solve weighted star partition problems on trees.     

A {(\frac 4 3) -} approximation algorithm for a special case of the two machine flow shop problem with several availability constraints

In this paper, we deal with a special case of the two-machine flow shop scheduling problem with several availability constraints on the second machine, under the resumable scenario. We develop an improved algorithm with a relative worst-case error bound of 4/3.     

A problem in enumerating extreme points, and an efficient algorithm for one class of polytopes

We consider the problem of developing an efficient algorithm for enumerating the extreme points of a convex polytope specified by linear constraints. Murty and Chung (Math Program 70:27–45, 1995) introduced the concept of a segment of a polytope, and used it to develop some steps for carrying out the enumeration efficiently until the convex hull of the set of known extreme points becomes a segment. That effort stops with a segment, other steps outlined in Murty and Chung (Math Program 70:27–45, 1995) for carrying out the enumeration after reaching a segment, or for checking whether the segment is equal to the original polytope, do not constitute an efficient algorithm. Here we describe the central problem in carrying out the enumeration efficiently after reaching a segment. We then discuss two procedures for enumerating extreme points, the mukkadvayam checking procedure, and the nearest point procedure. We divide polytopes into two classes: Class 1 polytopes have at least one extreme point satisfying the property that there is a hyperplane H through that extreme point such that every facet of the polytope incident at that extreme point has relative interior point intersections with both sides of H; Class 2 polytopes have the property that every hyperplane through any extreme point has at least one facet incident at that extreme point completely contained on one of its sides. We then prove that the procedures developed solve the problem efficiently when the polytope belongs to Class 2.