This paper investigates the practical engineering problem of traffic sensors placement on stretched highways with ramps. Since it is virtually impossible to install bulky traffic sensors on each highway segment, it is...
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This paper investigates the practical engineering problem of traffic sensors placement on stretched highways with ramps. Since it is virtually impossible to install bulky traffic sensors on each highway segment, it is crucial to find placements that result in optimized network-wide, traffic observability. Consequently, this results in accurate traffic density estimates on segments where sensors are not installed. The substantial contribution of this paper is the utilization of control-theoretic observability analysis--jointly with integerprogramming--to determine traffic sensor locations based on the nonlinear dynamics and parameters of traffic networks. In particular, the celebrated asymmetric cell transmission model is used to guide the placement strategy jointly with observability analysis of nonlinear dynamic systems through Gramians. Thorough numerical case studies are presented to corroborate the proposed theoretical methods and various computational research questions are posed and addressed. The presented approach can also be extended to other models of traffic dynamics.
In this paper, we propose an exact solution approach to solve a joint product line selection and pricing problem with a fixed cost factor. We adopt the multinomial logit model to estimate the sales of each marketed pr...
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In this paper, we propose an exact solution approach to solve a joint product line selection and pricing problem with a fixed cost factor. We adopt the multinomial logit model to estimate the sales of each marketed product, and suppose that the introduction of each product to the market incurs some constant fixed costs. Utilizing an implicit function form of the optimal price, we transform the original problem into the one with the decision variables for the product introduction only. The efficiency of the proposed transformation approach is demonstrated through simulations. We further discuss its applicability to generalized problems.
We consider a convex, or nonlinear. separable minimization problem with constraints that are 44 dual to the minimum cost network flow problem. We show how to reduce this problem to a polynomial number of minimum s.t-c...
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We consider a convex, or nonlinear. separable minimization problem with constraints that are 44 dual to the minimum cost network flow problem. We show how to reduce this problem to a polynomial number of minimum s.t-cut problems. The solution of the reduced problem utilizes the technique for solving integer programs on monotone inequalities in three variables, and a so-called proximity-scaling technique that reduces a convex problem to its linear objective counterpart. The problem is solved in this case in a logarithmic number 14 of calls. O(log U). to a minimum cut procedure, where U is the range of the variables. For a convex problem on n variables the minimum cut is solved on a graph with O(n(2)) nodes. Among the consequences of this result is a new cut-based scaling algorithm for the minimum cost network flow problem. When the objective function is an arbitrary nonlinear function we demonstrate that this constrained problem is solved in pseudopolynomial time by applying a minimum cut procedure to a graph on O(nU) nodes.
In this paper we investigate certain aspects of infeasibility in convexinteger programs, where the constraint functions are defined either as a composition of a convex increasing function with a convexinteger valued...
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In this paper we investigate certain aspects of infeasibility in convexinteger programs, where the constraint functions are defined either as a composition of a convex increasing function with a convexinteger valued function of n variables or the sum of similar functions. In particular we are concerned with the problem of an upper bound for the minimal cardinality of the irreducible infeasible subset of constraints defining the model. We prove that for the considered class of functions, every infeasible system of inequality constraints in the convexinteger program contains an inconsistent subsystem of cardinality not greater than 2 (n) , this way generalizing the well known theorem of Scarf and Bell for linear systems. The latter result allows us to demonstrate that if the considered convexinteger problem is bounded below, then there exists a subset of at most 2 (n) -1 constraints in the system, such that the minimum of the objective function subject to the inequalities in the reduced subsystem, equals to the minimum of the objective function over the entire system of constraints.
This work considers the resolution of the system of fuzzy integer inequalities. It is Shown that a system of fuzzy integer inequalities with concave membership functions can be reduced to a regular convexinteger prog...
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This work considers the resolution of the system of fuzzy integer inequalities. It is Shown that a system of fuzzy integer inequalities with concave membership functions can be reduced to a regular convex integer programming problem. A modified solution algorithm of the p -th power Lagrangian method is introduced to deal with the resulting convex integer programming problem as a sequence of linearly constrained convex integer programming problems. Some computational results are included.
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