An extended transportation problem: a DEA-based approach

The transportation problem is an important network structured linear programming problem that arises in several contexts and that has received a great deal of attention in the literature. The existing transportation problems are limited to consideration unit of shipping cost or profit along an arc. However, in many real applications, various attributes are usually considered in a transportation problem. The current paper, proposes an extension to this problem in the presence of multiple in-commensurate inputs and outputs for each arc. The concept of relative efficiency is defined for each possible transportation plan. Two linear programming models are proposed to determine the transportation plan with the maximum efficiency. A numerical example is used to illustrate the applicability of the approach.     

An equitable method for allocating fixed costs by using data envelopment analysis

This paper concerns the shared cost allocation problem by using Data Envelopment Analysis (DEA), which is observed in practical applications such as public services and production processes. In the management context, the cost allocation problem tries to balance the different desires of two management layers: central manager and each sector manager. The cost can be assigned in an equitable way to the various Decision Making Units (DMUs). To achieve this goal, we present a new DEA-based method for dividing a fixed cost among DMUs. In the proposed method, the fixed cost is assigned to DMUs such that the efficiency measures and the Returns to Scale classifications of all DMUs before and after assigning the fixed cost remain unchanged. Also, the gaps among the costs allocated to DMUs will be minimized. The proposed method has the flexibility to consider the management standpoints. Finally, numerical results of an elucidatory example are furnished to demonstrate the applicability and reliability of our scheme.     

Allocating fixed costs or resources and setting targets via data envelopment analysis

In many applications of data envelopment analysis (DEA), there is often a fixed cost or input resource which should be imposed on all decision making units (DMUs). Cook and Zhu [W.D. Cook, J. Zhu, Allocation of shared costs among decision making units: A DEA approach, Computers and Operations Research 32 (2005) 2171-2178] propose a practical DEA approach for such allocation problems. In this paper, we prove that when some special constraints are added, Cook and Zhu’s approach probably has no feasible solution. The research of this paper focuses on two main aspects: to obtain a new fixed costs or resources allocation approach by improving Cook and Zhu’s approach, and to set fixed targets according to the amount of fixed resources shared by individual DMUs. When such special constraints are attached, our model is proved to be able to achieve a feasible costs or resources allocation. Numerical results for an example from the literature are presented to illustrate our approach.     

An equitable solution for multicriteria bargaining games

In this paper we study bargaining models where the agents consider several criteria to evaluate the results of the negotiation process. We propose a new solution concept for multicriteria bargaining games based on the distance to a utopian minimum level vector. This solution is a particular case of the class of the generalized leximin solutions and can be characterized as the solution of a finite sequence of minimax programming problems.     

An approach to the investigation of optimal quadrature formulas for singular integrals with fixed singularity

For classes of functions given on the segment [0,1], we obtain optimal quadrature formulas for singular integrals with fixed singularity. The obtained results are extended to the case of two-dimensional integrals.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 9, pp. 1300–1304, September, 1995.     

A two-phase approach for setting targets in DEA with negative data

Conventional DEA models have been introduced to deal with non-negative data. In the real world, in some occasions, we have outputs and/or inputs, which can take negative data. In DEA literature some approaches have been presented for evaluating performance of units, which operate with negative data. In this paper, firstly, we give a brief review of these works, then we present a new additive based approach in this framework. The proposed model is designed to provide a target with non-negative value associated with negative components for each observed unit, failed by other methods. An empirical application in banking is then used to show the applicability of the proposed method and make a comparison with the other approaches in the literature.     

An order-statistics-based method for constructing multivariate distributions with fixed marginals

A new system of multivariate distributions with fixed marginal distributions is introduced via the consideration of random variates that are randomly chosen pairs of order statistics of the marginal distributions. The distributions allow arbitrary positive or negative Pearson correlations between pairs of random variates and generalise the Farlie–Gumbel–Morgenstern distribution. It is shown that the copulas of these distributions are special cases of the Bernstein copula. Generation of random numbers from the distributions is described, and formulas for the Kendall and grade (Spearman) correlations are given. Procedures for data fitting are described and illustrated with examples.     

An efficient algorithm for multi-hoist cyclic scheduling with fixed processing times

We consider no-wait production processes, where identical products are processed sequentially on n machines and transported by programmable hoists. We present an O(n⁵) algorithm that determines the minimum number of hoists required for all possible cycle-times; given the number of hoists, it also finds the minimum-time cyclic hoist-schedule.     

An approximate expression related with RSA fixed points

Let T=T(n,e,a)be the number of fixed points of RSA(n,e)that are co-prime with n=pq,and A,B be sets of prime numbers in (1,x)and(1,y) respectively.An estimation on the mean-value M(A,B,e,a)=1/(#A)(#B)∑p∈A,q∈B,(p.q)=1 logT(pq,e,a)is given.     

An algorithm for a bilevel problem with equilibrium and fixed point constraints

We prove the solution existence and propose an iterative algorithm for solving equilibrium problems over the common solutions of a monotone equilibrium problem and the fixed points of a strictly pseudocontractive mapping in Hilbert spaces. The algorithm is a combination of the proximal point and Halpern methods. Strong convergence is established.     

Bilinear modeling solution approach for fixed charge network flow problems

We present a continuous, bilinear formulation for the fixed charge network flow problem. This formulation is used to derive an exact algorithm for the fixed charge network flow problem converging in a finite number of steps. Some preliminary computational experiments are reported to show the performance of the algorithm.     

Logical-optimization approach to pursuit problems for a group of targets

Doklady Mathematics - Problems of automatic action planning and optimal control of unmanned vehicles in an adversarial environment are considered. An approach based on nonmonotonic logic in the...     

An implementable augmented Lagrange method for solving fixed point problems with coupled constraints

An augmented Lagrange function method for solving fixed point problems with coupled constraints is studied, and a theorem of its global convergence is demonstrated. The semismooth Newton method is used to solve the inner problems for obtaining approximate solutions, and numerical results are reported to verify the effectiveness of the augmented Lagrange function method for solving three examples with more than 1000 variables.     

An algorithm for finding equilibrium in the linear exchange model with fixed budgets

We propose a new method for finding equilibrium in a linear exchange model with fixed budgets. The algorithm rests on consideration of the two dual polyhedral complexes generated by an associated transportation problem of the model. The algorithm uses the thoroughly developed fragments of the method of potentials for a transportation problem, which enables us to considering only systems of linear equations with a triangular matrix at every step. The algorithm admits starting with an arbitrary initial price vector. We prove the finiteness of the algorithm.     

A new data envelopment analysis based approach for fixed cost allocation

Annals of Operations Research - In many real applications, there exist situations where some independent and decentralized entities will construct a common platform for production processes. A...     

Saddle point approach to solving problem of optimal control with fixed ends

The global resolution of constrained non-linear bi-objective optimization problems (NLBOO) aims at covering their Pareto-optimal front which is in general a one-manifold in \(\mathbb {R}^2\). Continuation methods can help in this context as they can follow a continuous component of this front once an initial point on it is provided. They constitute somehow a generalization of the classical scalarization framework which transforms the bi-objective problem into a parametric single-objective problem. Recent works have shown that they can play a key role in global algorithms dedicated to bi-objective problems, e.g. population based algorithms, where they allow discovering large portions of locally Pareto optimal vectors, which turns out to strongly support diversification. The contribution of this paper is twofold: we first provide a survey on continuation techniques in global optimization methods for NLBOO, identifying relations between several work and usual limitations, among which the ability to handle inequality constraints. We then propose a rigorous active set management strategy on top of a continuation method based on interval analysis, certified with respect to feasibility, local optimality and connectivity. This allows overcoming the latter limitation as illustrated on a representative bi-objective problem.