Minimum Size Constraints Research Articles

A Bayesian methodology for simultaneously detecting and estimating regime change points and variable selection in multiple regression models for marketing research

We present a Bayesian change point multiple regression methodology which simultaneously estimates the location of change points/regimes, the corresponding subset of independent variables per regime, as well as the associated regimes’ regression parameters. Unlike existing switching multiple regression models, our method does not require the presence of all independent variables in each regime to detect change points. This allows us to relax the minimum size constraint on each regime as fewer observations are needed to estimate the unknown regression coefficients. Thus our method provides a means to search for small regimes where only a few independent variables are significant. Note that accuracy of change points can drastically affect the identified models within each regime. As the number of change points in the data is typically unknown, we have provided a probability based model selection heuristic to determine its value. Both synthetic and real data sets are utilized to demonstrate that our procedure can yield better fitted models over aggregate OLS regression models and traditional MLE based regime switching models. Furthermore, an actual prescription drug data application involving a promotion response model is used to gainfully illustrate the methodology.

Fuzzy multiobjective optimization of truss-structures using genetic algorithm

In this paper, a method for solving fuzzy multiobjective optimization of space truss with a genetic algorithm is proposed. This method enables a flexible method for optimal system design by applying fuzzy objectives and fuzzy constraints. The displacement, tensile stress, fuzzy sets, membership functions and minimum size constraints are considered in formulation of the design problem. An algorithm was developed by using MATLAB programming. The algorithm is illustrated on 56-bar space truss system design problem and the results are discussed.

Coordinating Sales and Raw Material Discounts in a Global Supply Chain

In this paper, the supplier of a key component to a global manufacturer offers a one‐time price discount; we study the firm's optimal response to the discount under two different strategies. In the first strategy, the firm does not pass along the discount to its customers (sales subsidiaries); the firm simply coordinates purchasing and production among the different factories to take advantage of this one‐time price discount. In the second strategy, the firm offers price discounts for its most profitable products in different sales subsidiaries to increase their demand. We carried out experiments for the two strategies based on a mathematical programming model, built around Toshiba's global notebook supply chain. Model constraints include, among others, material constraints, bill‐of‐materials, capacity and transportation constraints, minimum lot size constraints, and a constraint on minimum fill rate (service level constraint). Unlike most models of this type in the literature, which define variables in terms of single arc flows, we employ path variables, which allow for direct identification and manipulation of profitable and non‐profitable products.

A Mixed-Integer Formulation of the Minimum Patch Size Problem

Abstract Forest harvest scheduling models have addressed wildlife habitat concerns in a variety of ways. One way is through minimum patch size constraints specifying that a certain amount of the forest must consist of patches meeting both minimum size and minimum age requirements. Patch size requirements may be necessary because a forest with only small patches of mature habitat may not be able to support populations of some wildlife species. Maximum harvest opening size constraints, which are often imposed for legal or policy reasons, tend to divide forest habitat into small patches. Minimum patch size constraints may be able to help mitigate the negative impact of maximum harvest opening size restrictions. Patch size requirements have been considered elsewhere, but a mixed-integer linear programming (MILP) formulation has never been presented. This article presents such a formulation, which allows minimum patch size problems to be solved using the branch and bound algorithm available through commercial solver packages. An example problem is formulated, solved, and discussed. For. Sci. 49(4):608–618.

The effect of decimalization on the components of the bid-ask spread

Previous empirical studies that decompose the bid-ask spread were done when securities traded in discrete price points equal to one-sixteenth or one-eighth of a dollar. These studies concluded that inventory and adverse-selection costs were economically insignificant compared to order-processing costs. Natural questions arise as to: (i) whether price discreteness allowed market makers to enjoy excess rents, thus reducing the significance of the inventory and adverse selection costs; (ii) whether discreteness decreased the traders' incentives to gather information; or (iii) whether methodologies previously employed mis-estimated the inventory and the adverse-selection costs. We show that the recent conversion to decimal pricing results in significantly tighter spreads. However, the dollar value of spreads attributed to adverse selection and inventory costs do not change significantly. Almost all of the reduction occurs in the order-processing component. As a result, inventory and adverse-selection costs now account for a significantly larger proportion of the traded spreads. A plausible explanation is that the minimum tick size constraint previously in place under fractional pricing allowed market makers to enjoy spreads that were larger than their actual costs.

The Effect of Decimalization on the Components of the Bid-Ask Spread

Previous empirical studies that decompose the bid-ask spread were done when securities traded in discrete price points equal to one-sixteenth or one-eighth of a dollar. These studies concluded that inventory and adverse-selection costs were economically insignificant compared to order-processing costs. Natural questions arise as to: (i) whether price discreteness allowed market makers to enjoy excess rents, thus reducing the significance of the inventory and adverse selection costs; (ii) whether discreteness decreased the traders' incentives to gather information; or (iii) whether methodologies previously employed mis-estimated the inventory and the adverse-selection costs. We show that the recent conversion to decimal pricing results in significantly tighter spreads. However, the dollar value of spreads attributed to adverse selection and inventory costs do not change significantly. Almost all of the reduction occurs in the order-processing component. As a result, inventory and adverse-selection costs now account for a significantly larger proportion of the traded spreads. A plausible explanation is that the minimum tick size constraint previously in place under fractional pricing allowed market makers to enjoy spreads that were larger than their actual costs.

A pseudo‐fully stressed design approach for optimum design of steel frames

AbstractAn iterative approach based on the fully‐stressed design concept employing scaling to find an efficient search path to the optimum design is developed for statically indeterminate elastic frames subjected to behavioural constraints on member stresses and nodal displacements, and side constraints on member sizes. In this approach the fully stressed solution, which recognizes only the stress constraints, is scaled to the boundary of the feasible design region by employing the other constraints on the structure. The inactive constraints in an iteration are identified by the Kuhn‐Tucker conditions. The computed stresses of the inactive constraints, for the time being, are considered to be the allowable values in order to develop a pseudo‐fully stressed solution with a new set of allowable stresses. Convergence takes places when the normalized change in the value of the objective function between the scaled and unsealed pseudo‐fully stressed designs is less than a specified tolerance. The method employs the established relationships between sectional area, section modulus and moment of inertia of W‐shapes to express the objective and constraint functions in terms of one design variable for each member. The efficiency and accuracy of the method in optimization of structural steel frames is demonstrated by sample problems designed for stress, displacement and minimum size constraints. The algorithm is verified against published results.

Optimum design of multistorey structures with shear walls

Multistorey structures are a necessity particularly in city centres where land values are high. They provide economical solution for such cases and play an important role in modern urban design. In a way, they represent a monumental perspective of structural engineering technology. In this study an algorithm is presented for the optimum design of multistorey reinforced concrete structures with shear walls. The method considers displacement, ultimate axial load and bending moment and minimum size constraints. Member depths are treated as design variables. The values of design variables are evaluated from recursive relationships in every design cycle depending on the dominance of design constraints. The first relationship was obtained for the displacement limitations using optimality criteria approach. The second was an iterative algorithm developed for the case of dominant ultimate axial and bending moment constraints. The third is minimum size restrictions. The largest among three was adopted as the new value of design variable in the next optimum design cycle. This procedure is repeated until convergence is obtained. The steps of design algorithm is given and number of design examples are considered to demonstrate its practicability and effectiveness.

Optimum Design of Pin‐Jointed Steel Structures With Practical Applications

An efficient optimum design algorithm is presented for the pin‐jointed steel structures subjected to multiple load cases. The displacement, stress, buckling, and minimum size constraints are considered in the formulation of the design problem. Optimality criteria approach is employed for handing the displacement restrictions. The stress and buckling limitations are reduced to lower bounds on design variables and treated as similar to those of minimum size constraints. This is achieved by first expressing the allowable critical stresses as specified by the design codes as nonlinear equations, and then solving them to obtain the critical values of design variables. This leads to a straightforward and easy‐to‐program algorithm that is particularly suitable for microcomputers. The numerical examples solved, on the other hand, clearly show the practical applicability and efficiency of the method, even in the case of large structures.

Optimum design of nonlinear space trusses

The structural optimization algorithms developed in recent years mainly consider the elastic behaviour of structures. The reserve of resisting loads in nonlinear regions is totally ignored. The optimum design algorithm presented in this study takes into account the response of the structure beyond the elastic limit. This is achieved by coupling a nonlinear analysis technique with an optimality criteria approach. The first is used to provide the nonlinear behaviour of the structure as the design variables are changed. The latter is employed to obtain a recursive relationship to be utilized to update these design variables. The design algorithm includes the displacement limitations. Consideration of the post buckling and post yielding behaviour of the truss members makes the necessity of stress and buckling constraints irrelevant. Minimum size constraints are imposed on the design variables. A number of design examples are presented to demonstrate the application of the method.

Cusp-stabilized mirror-based neutron source

An optimally sized Fusion Engineering Test Facility should produce 10–20 MW of power at 2 MW/m2 steady-state wall loading. Because mirror cells do not scale with size, one can choose the fusion power and wall loading free from minimum size constraints. A cusp stabilized axisymmetric mirror is seen to be ideally suited for this purpose due to excellent access, a simple coil set, and good MHD properties. We present parameters for a proof of principle experiment as well as for a neutron source facility.

Fracture toughness of polycarbonate structural foams

This paper describes some preliminary studies of the crack-induced fracture of structural foams molded from LexanR resin. Single edge-notch (SEN), double-cantilever beam (DCB), and compact tension specimens of various sizes were evaluated independently. A rapid rise in the nominal crack tip stress with decreasing sample size in the SEN and compact tension specimens was found to introduce significant errors in the strain-energy release rate (G) values calculated from data on small samples. Minimum sample size constraints were established from plots of G against σnom/σF. The concept of plane strain failure in these materials appears to be complicated by significant microscopic crazing and shear yielding in the thin bubble walls resulting in G values which are somewhat higher than those reported for the solid resin. This localized deformation, which is not readily discerned from the shape of the load/elongation curves or the macroscopic appearance of the fracture surfaces, results in an overestimation in the inherent flaw size for these materials.