scispace - formally typeset
Search or ask a question

Showing papers by "École Polytechnique de Montréal published in 1989"


Journal ArticleDOI
TL;DR: A survey of the literature on automatic signature verification and writer identification by computer, and an overview of achievements in static and dynamic approaches to solving these problems, with a special focus on preprocessing techniques, feature extraction methods, comparison processes and performance evaluation.

981 citations


Journal ArticleDOI
TL;DR: In this article, a finite element method for the simulation of viscoelastic flow is presented, where a decoupled approach is employed for the computation of the velocity field and the components of the extra-stress tensor.
Abstract: We present a finite element method for the simulation of viscoelastic flow. A decoupled approach is employed for the computation of the velocity field and of the components of the extra-stress tensor. The high Weissenberg number problem is addressed by using together two different types of upwinding namely the streamline upwinding technique and the Lesaint-Reviart method. Numerical results are presented for the case of the 4 to 1 plane contraction.

210 citations


Journal ArticleDOI
TL;DR: In this paper, the initial biomass concentration, digestion time and pH of the hypochlorite solution were optimized to minimize degradation, and a 95% purity poly-β-hydroxybutyrate (PHB) with a weight average molecular weight (MW) of 600,000 and a polydispersity index (PI) of 4.5 was recovered from biomass initially containing PHB.
Abstract: Hypochlorite digestion of bacterial biomass from intracellular poly-β-hydroxybutyrate (PHB) has not been used on a large scale since it has been reported to severely degrade PHB. In this study, to minimize degradation, the initial biomass concentration, digestion time and pH of the hypochlorite solution were optimized. Consequently, PHB of 95% purity with a weight average molecular weight (MW) of 600,000 and a polydispersity index (PI) of 4.5 was recovered from biomass initially containing PHB with a MW of 1,200,000 and a PI of 3.

195 citations


Journal ArticleDOI
01 Jan 1989-Spine
TL;DR: The results of clinical, epidemiologic, and experimental studies support the failure mechanism predicted in the present study: rupture initiates in the fibers in the innermost layer at the posterolateral location.
Abstract: A three-dimensional nonlinear finite element model has been used to predict the strain in the disc fibers of a lumbar motion segment under various single and combined loads such as those representing symmetric and non-symmetric liftings. A progressive failure analysis also has been performed under loads representing lifting while bending to one side: assuming yield and ultimate fiber strains of 14 and 16%, respectively. Large tensile strains of about 10% in the disc fibers are predicted under the maximum loads simulating symmetric lifting. Addition of lateral bending and twisting significantly increases the maximum fiber strain to more than 20%, and hence augments the risk for disc rupture. The maximum fiber strain occurs in the innermost annulus layer at the posterolateral location. Loss of intradiscal pressure or volume has a marked diminishing effect on the magnitude of maximum fiber strain predicted under flexion loadings. Failure analysis indicates that rupture initiates in the fibers in the innermost layer at the posterolateral location. With a slight increase in the loads, rupture progresses radially to the adjacent outer layer. Further progress of rupture in the fibers toward the annulus outer periphery resulting in complete radial fissure and disc prolapse appears to require additional increase in the loads. In the presence of large intradiscal pressure, the generated partial or complete radial fissure is likely to result in annulus protrusion or disc herniation, respectively. The results of clinical, epidemiologic, and experimental studies support the failure mechanism predicted in the present study.

158 citations


Journal ArticleDOI
TL;DR: In this article, the compounding of Kraft pulp with polypropylene was stuided using a laboratory higheshear roller blender, and the effects of parameters such as surface treatment and mixing conditions were investigated.
Abstract: The compounding of Kraft pulp with polypropylene was stuided using a laboratory higheshear roller blender. Dipsersion was characterized by measuring the size and number of agglomerates in a thin compression-moldled sheet. The effects of parameters such as surface treatment and mixing conditions were investigated. It is shown that with a suitable treatment, better dispersion of fibers can be achieved.

157 citations


Journal ArticleDOI
TL;DR: The wear behavior of hip prostheses alumina components was studied on 20 retrieved implants removed for socket loosening, finding that normal wear is a running-in process leading to an average wear rate of 0.025 micron/year as compared to 100 microns/year on metallic heads.
Abstract: The wear behavior of hip prostheses alumina components was studied on 20 retrieved implants removed for socket loosening. The observed wear takes two forms: a running-in of the mating surfaces and a gross disruption of the surfaces. The running-in is very shallow, in the order of 0.2 micron after 8 years of implantation. This is observed on the load-bearing areas of the components. Gross wear is not material-related but had always been associated to a high contact pressure between the edge of the socket and the femoral head. Such a high contact pressure occurs after the socket had loosened and then tilted or if it was initially positioned too vertically. The long-term success of alumina-alumina THP components depends essentially upon biomechanical considerations and upon the quality of the material. The area of contact between the head and the socket should be large enough to minimize the contact stresses. This can only be achieved by a good positioning of the socket and by a close tolerance fit of the alumina components; any deviation from sphericity should also be avoided. The normal wear behavior of alumina is a running-in process leading to an average wear rate of 0.025 micron/year as compared to 100 microns/year for UHMWPE on metallic heads.

147 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of surface pretreatment of cellulosic fibers and the processing time and temperature on the mechanical properties of the cellulose-containing polypropylene was investigated.
Abstract: A systematic study of the effect of surface pretreatment of cellulosic fibers and the processing time and temperature on the mechanical properties of the cellulose-containing polypropylene was undertaken. Using non-treated fibers, the elastic modulus increased gradually with the cellulose content, typically doubling its value at 30 phr fiber content. Treatment of fibers with coupling agent improves significantly the interfacial adhesion and therefore the mechanical properties of composite. Scanning electron micrographs reveal that the shear stress is sufficiently high to break and delaminate the cellulosic fibers. Addition of maleic anhydride modified polypropylene also improves the properties of resulting composites.

133 citations


Journal ArticleDOI
TL;DR: In this article, an analytical method to determine the transient performance of grounding grids is presented, based on the ground resistance and self and mutual inductance of each element of the grid.
Abstract: Understanding the behaviour of grounding systems to transient currents is important to establish the efficacy of protection offered by these systems to personnel and to the electrical installations against lightning. In this paper, an analytical method to determine the transient performance of grounding grids is presented. The validity of the proposed methodology has been verified by extensive field test results. Most published studies have been aimed at improving the knowledge of transient behaviour of ground electrodes of various forms. Some researchers have proposed methods to determine the impulse impedance of grounding grids also, by considering square grounding grids and by assuming the grid to be an equivalent circular plate. In actual practice however, the station grounding grids can have complex configurations. In this paper, a generalised model of grounding grid is considered for analysis under transient conditions. The two factors of importance in such an analysis are 1) the ground resistance (or conductance) and 2) self and mutual inductances of each element of the grid. In the proposed model, the distributed nature of ground conductance of each element has been lumped and represented as a nominal-pi. In this way, the leakage current is better represented than by considering the grid as an equivalent circular plate. In addition, the model proposes formation of susceptance matrix for the grid in a similar manner as the bus-admittance matrix for the load flow solution.

116 citations


Journal ArticleDOI
TL;DR: This paper shows by means of simple examples that problems can arise even for the simpler Stokes equations, and shows that care must be exercised in the choice of the pressure approximation for coupled flow problems.
Abstract: SUMMARY It is generally accepted that mixed and penalty finite element methods can routinely solve the incompressible Navier-Stokes equations. This paper shows by means of simple examples that problems can arise even for the simpler Stokes equations. The causes of the problem fall in either of two categories: round-off and ill conditioning, or a poor choice of pressure discretization. Nonsensical solutions can be obtained. Computation of the discrete divergence of the flow field is a simple and powerful tool to diagnose such conditions. In the first part of the paper several simple techniques for minimizing the effect of round-off are reviewed. In the second part it is shown that, for coupled flow problems, care must be exercised in the choice of the pressure approximation. A unified treatment of various observations by different workers is presented. This should prove useful for general users of the finite element method.

115 citations


Journal ArticleDOI
TL;DR: In this paper, the mechanical and rheological properties of blends of a thermotropic liquid crystalline polyester with a polycarbonate have been investigated by performing solid state relaxation measurements and the relaxation modulus was also found to increase by the addition of LCP.
Abstract: Mechanical and rheological properties of blends of a thermotropic liquid crystalline polyester with a polycarbonate have been investigated. The blends are fibrillar in character and exhibit great hardness and toughness due to high degree of molecular orientation which develops during the melt blending and processing steps. Increases of the Young modulus by 100 percent are observed for blends containing only 10 percent of liquid crystalline polymer, LCP. Time-dependent behavior of the blends was investigated by performing solid state relaxation measurements and the relaxation modulus was also found to increase by the addition of LCP. The effect is relatively small in the glassy zone of viscoelastic response, but increases through the transition and viscous flow regions. The melt viscosity of the polycarbonate is slightly shear thinning whereas that of the unblended LCP increases rapidly with decreasing shear rate at low shear rate. This suggests the presence of yield stresses as confirmed by measurements on the Rheometics RSR in the stress sweep mode. The melt viscosity of the blends was found to be similar to that of the unblended polycarbonate, but more shear-thinning and less viscous. Preliminary results of scanning electron microscopy (SEM) and differential scanning calorimetry (DSC) are also presented.

102 citations


Journal ArticleDOI
TL;DR: It appears that nonhomogeneous fibre reinforced composite model of the disc annulus is more realistic resulting in a more accurate computation of stresses in the annulus fibrosus.

Journal ArticleDOI
TL;DR: In this paper, the strength properties of composites made of untreated cellulose fibers and linear low density polyethylene were investigated as a function of processing parameters, and it was shown that the strength increases with processing time and temperature.
Abstract: The strength properties of composites made of untreated cellulose fibers and linear low density polyethylene were investigated as a function of processing parameters. Studies have shown that the strength properties of composites increase with processing time and temperature. The increase in strength is accompanied by the appearance of new infrared absorption bands at 1718 and 1735 cm−1. A linear relationship between the absorbance and yield strength of composites indicates that oxidation, possibly directly at interfaces, takes place and enhances adhesion between the cellulose and polyethylene.

01 May 1989
TL;DR: In this paper, a two-phase algorithm is proposed for global optimization problems for a Lipschitz function implicitly defined on an interval [a, b] and a sufficient condition for the globally optimal points to be in one-to-one correspondance with the obtained intervals is given.
Abstract: We consider the following global optimization problems for a Lipschitz functionf implicitly defined on an interval [a, b] Problem P′: find a globallye-optimal value off and a corresponding point; Problem Q″: find a set of disjoint subintervals of [a, b] containing only points with a globallye-optimal value and the union of which contains all globally optimal points A two-phase algorithm is proposed for Problem P′ In phase I, this algorithm obtains rapidly a solution which is often globallye-optimal Moreover, a sufficient condition onf for this to be the case is given In phase II, the algorithm proves thee-optimality of the solution obtained in phase I or finds a sequence of points of increasing value containing one with a globallye-optimal value The new algorithm is empirically compared (on twenty problems from the literature) with a best possible algorithm (for which the optimal value is assumed to be known), with a passive algorithm and with the algorithms of Evtushenko, Galperin, Shen and Zhu, Piyavskii, Timonov and Schoen For smalle, the new algorithm requires only a few percent more function evaluations than the best possible one An extended version of Piyavskii's algorithm is proposed for problem Q″ A sufficient condition onf is given for the globally optimal points to be in one-to-one correspondance with the obtained intervals This result is achieved for all twenty test problems

Journal ArticleDOI
TL;DR: Although Sb 2 O 4, a mixed Sb III Sb V oxide, is well known to posses a two-component Mossbauer Sb spectrum, it is shown to exhibit one-component Sb d-orbital photoemission peaks as discussed by the authors.

01 Apr 1989
TL;DR: The problems of using an approximation for the Lipschitz constant are addressed, reducing as much as possible the expected length of the region of indeterminacy which contains all globally optimal points and avoiding remaining subintervals without points with a globallyε-optimal value.
Abstract: We consider the following global optimization problems for a univariate Lipschitz functionf defined on an interval [a, b]: Problem P: find a globally optimal value off and a corresponding point; Problem Pź: find a globallyź-optimal value off and a corresponding point; Problem Q: localize all globally optimal points; Problem Qź: find a set of disjoint subintervals of small length whose union contains all globally optimal points; Problem Qź: find a set of disjoint subintervals containing only points with a globallyź-optimal value and whose union contains all globally optimal points. We present necessary conditions onf for finite convergence in Problem P and Problem Q, recall the concepts necessary for a worst-case and an empirical study of algorithms (i.e., those ofpassive and ofbest possible algorithms), summarize and discuss algorithms of Evtushenko, Piyavskii-Shubert, Timonov, Schoen, Galperin, Shen and Zhu, presenting them in a simplified and uniform way, in a high-level computer language. We address in particular the problems of using an approximation for the Lipschitz constant, reducing as much as possible the expected length of the region of indeterminacy which contains all globally optimal points and avoiding remaining subintervals without points with a globallyź-optimal value. New algorithms for Problems Pź and Qź and an extensive computational comparison of algorithms are presented in a companion paper.

Journal ArticleDOI
TL;DR: In this article, an analysis of the uranium-zirconium alloy system has been performed and a phase diagram was calculated, and the results are compared with the available thermodynamic data and accepted phase diagrams and general agreement was found.

Journal ArticleDOI
TL;DR: The possibility of using the nutritionally versatile bacterium Pseudomonas cepacia to produce poly-β-hydroxyalkanoic acid was evaluated and it was shown that growth of P. cEPacia became nitrogen limited when the molar carbon-to-nitrogen ratio of the medium fed into the fermentor was above 15.5%.
Abstract: The possibility of using the nutritionally versatile bacterium Pseudomonas cepacia to produce poly-β-hydroxyalkanoic acid was evaluated. Chemostat culture showed that growth of P. cepacia became nitrogen limited when the molar carbon-to-nitrogen ratio of the medium fed into the fermentor was above 15. When grown under nitrogen limitation in batch culture with fructose as the sole source of carbon, P. cepacia accumulated poly-β-hydroxybutyric acid (PHB) in excess of 50% of the dry weight of its biomass. In batch culture, almost no PHB was produced until the onset of nitrogen limitation. After this point, PHB was produced at a linear rate of 0.12 g liter−1 h−1 (from a constant value of 1.6 g of cellular protein liter−1). PHB produced by P. cepacia had a weight-average molecular weight of 5.37 × 105 g mol−1 and a polydispersivity index of 3.9. Poly(β-hydroxybutyric acid-β-hydroxyvaleric acid) copolymer was produced with a poly-β-hydroxybutyric acid-poly-β-hydroxyvaleric acid ratio of up to 30% by weight when propionic acid was added to the medium.

Journal ArticleDOI
TL;DR: Several sets of values are available for the shape factor of the cylindrical injection zone used to perform a field permeability test as mentioned in this paper, and they differ from Hvorslev's factor by up to 100%.
Abstract: Several sets of values are available for the shape factor of the cylindrical injection zone used to perform a field permeability test. Depending on the selected value, the resulting difference for hydraulic conductivity may reach 40% for long intake zones, and more than 100% for short intake zones. The commonly used shape factor is that given by Hvorslev (1951). Seven other factors derived from numerical models are now available: they differ from Hvorslev's factor by up to 100%. Three possible reasons for the differences are examined. Reference is made to Laplace's equation and related mathematical results derived before 1945. Shape factor values obtained by numerical methods are shown to be more or less accurate solutions of particular cases when impervious or recharging boundaries exist close to the injection zone. Their influence upon the shape factor value can be calculated analytically, as shown in a detailed example. Analytical shape factor equations are given for a cylindrical injection zone with either a pervious or an impervious bottom. Based on the method of image wells, two other equations are established to correct the shape factors if draining (constant head) or impervious layers are known to be located close to the injection zone. These equations should be used for field permeability tests in boreholes or piezometers.

01 Jan 1989
TL;DR: The extent to which such global optimization problems can be solved exactly using analytical methods is studied, and a series of tests, similar to those of combinatorial optimization, organized in a branch-and-bound framework are proposed.
Abstract: Global optimization problems with a few variables and constraints arise in numerous applications but are seldom solved exactly. Most often only a local optimum is found, or if a global optimum is detected no proof is provided that it is one. We study here the extent to which such global optimization problems can be solved exactly using analytical methods. To this effect, we propose a series of tests, similar to those of combinatorial optimization, organized in a branch-and-bound framework. The first complete solution of two difficult test problems illustrates the efficiency of the resulting algorithm. Computational experience with the programbagop, which uses the computer algebra systemmacsyma, is reported on. Many test problems from the compendiums of Hock and Schittkowski and others sources have been solved.

Journal ArticleDOI
TL;DR: In this paper, Lamb's operational interpretation of quantum mechanics is used for measuring a translational state operator (whether pure or mixed) via its Wigner function, which closely parallel methods that might be used in classical mechanics to determine a true phase space probability distribution.
Abstract: In quantum mechanics, the state of an individual particle (or system) is unobservable, i.e., it cannot be determined experimentally, even in principle. However, the notion of “measuring a state” is meaningful if it refers to anensemble of similarly prepared particles, i.e., the question may be addressed: Is it possible to determine experimentally the state operator (density matrix) into which a given preparation procedure puts particles. After reviewing the previous work on this problem, we give simple procedures, in the line of Lamb's operational interpretation of quantum mechanics, for measuring a translational state operator (whether pure or mixed), via its Wigner function. These procedures closely parallel methods that might be used in classical mechanics to determine a true phase space probability distribution; thus, the Wigner function simulates such a distribution not only formally, but operationally also.

Journal ArticleDOI
TL;DR: Based on correlations between rib arc length and other measurements of rib size, there was evidence of general rib hypertrophy on the long rib side of patients having length asymmetries.

Journal ArticleDOI
TL;DR: In this paper, the pore size distribution of nonwoven heat-bonded geotextiles is analyzed using a geometrical probability approach and an expression of pore sizes distribution of these filters is derived from basic manufacturing parameters.
Abstract: The structure of nonwoven heat-bonded geotextiles is analyzed using a geometrical probability approach. An expression of the pore size distribution of these filters is derived from basic manufacturing parameters. Two experimental techniques used to evaluate fabric opening size—dry sieving of glass beads and hydrodynamic sieving of soils—are investigated and the results compared to the calculated opening size obtained using the pore size distribution equation. Excellent agreement has been found between the calculated opening size and the filtration opening size measured with the hydro dynamic sieving technique.

Journal ArticleDOI
TL;DR: In this paper, the authors theoretically studied the heat transfer through an automated venetian blind window system and found that the predicted auxiliary load can be reduced by up to 36 percent and 47 percent for winter and summer, respectively.
Abstract: The heat transfer through an automated venetian blind window system is theoretically studied. The assumptions for the solution of the problem were: Heat transfer is unidimensional, heat exchanges are at steady-state for the whole system, thermal exchange by convection over the blind is negligible, materials used are diffuse-gray surfaces, and radiative exchanges with the room walls are considered as if all the surfaces are blackbodies at indoor air temperature. The solution of the governing equations (system of nonlinear equations) is carried out by using an iterative numerical method. Summarized results are presented and compared to the case of a regular window in a typical Canadian climate during winter and summer seasons and with different louver angles. It is found that by using an automated blind system, the predicted auxiliary load can be reduced by up to 36 percent and 47 percent for winter and summer, respectively.

Journal ArticleDOI
TL;DR: A method of partitioning an urban region into zones so as to minimize the total number of vehicles used or the total distance traveled by all the vehicles is developed.
Abstract: We studied the following organization for the letter and parcel pick-up and delivery problem in an urban environment: the working day is divided in time periods during which each vehicle starts from a sorting center, travels to a precise area of the region, picks up and delivers letters and parcels, and then returns to the depot to have the collected material sorted out for delivery during the following period. The intent of this approach is to have each zone serviced by one vehicle only to facilitate the work of the dispatcher and the routing of each vehicle. We have developed a method of partitioning an urban region into zones so as to minimize the total number of vehicles used or the total distance traveled by all the vehicles. The first part of the method determines the zones and the average number of points to visit. Then, a first refinement of the method takes into account the daily variability of the demand in each zone, and a second refinement examines the advantage of allowing some overlapping of zones for the purpose of having an overloaded vehicle relieved by one from an adjacent zone.

Journal ArticleDOI
TL;DR: In this article, the hydraulic anisotropy ratios of homogeneous clays, rocks and granular soils appear to be very similar in the bedding plane of sedimentary rocks.
Abstract: Many values of the ratio kmax/kmin are available for clays and rocks which can be cut for tests in different directions. In comparison, few reliable results are available for non-cohesive materials. The hydraulic anisotropy ratios of homogeneous clays, rocks and granular soils appear to be very similar. In particular, kmax/kmin seems to be lower than 4, which confirms that this ratio has an upper limit related to the shape of particles, their arrangement, or the directional tortuosity within the pore space. In the bedding plane of sedimentary rocks, the ratio kb.max/kb.min is usually lower than 1.5, thus these rocks are nearly isotropic in their bedding plane. In granular soils, the kh/kv, contrary to common opinion, is not always higher than 1. Experimental values for sands and gravels are in the 0.75 to 4.1 range. The influence of densification on hydraulic anisotropy is found to be similar for a sand and a clay, and probably for any soil having settled in still water and influenced subsequently only by gravity. The hydraulic anisotropy of sandstone is found to be in continuity with that of sand, and it increases with densification.

Patent
25 Sep 1989
TL;DR: In this article, a method and an apparatus for impregnating one side of a porous board, such as gypsum boards, with a precise amount of compatible phase change material is presented.
Abstract: A method and an apparatus for impregnating one side of a porous board, such as gypsum boards, with a precise amount of compatible phase change material. A predetermined amount of the phase change material is applied at a predetermined uniform rate to the one surface of the board so that a predetermined amount of the phase change is impregnated. The rate of application is lower than the absorption rate of phase change material. Also, the temperature of the board must be above the melting point of the phase change material during the impregnation. The process and apparatus may be either a continuous, a semi-continuous or a batch operation, and the resulting product is intended as a building construction material.

Journal ArticleDOI
TL;DR: In this article, a technique has been developed to provide a close estimate of the equilibrium composition in multiphase multicomponent systems and both the standard Gibbs energies of species and mass constraints are considered in this computation.
Abstract: A technique has been developed to provide a close estimate of the equilibrium composition in multiphase multicomponent systems. Both the standard Gibbs energies of species and mass constraints are considered in this computation. The estimates accelerate the rate of convergence of more general Gibbs energy minimization methods and are useful in predicting stoichiometric reactions. Special situations where the output may be taken as the final solution are discussed. These include the computation of multielement stability diagrams involving stoichiometric phases.

Journal ArticleDOI
TL;DR: It is shown that the confinement of electrons in quantum wires of width W, modeled with a parabolic potential of frequency \ensuremath{\Omega), leads to a shift of the magnetophonon resonance peaks to smaller magnetic fields.
Abstract: It is shown that the confinement of electrons in quantum wires of width W (\ensuremath{\sim}0.1 \ensuremath{\mu}m) much larger than the magnetic length ${l}_{B}$ and much smaller than the mean free path ${l}_{e}$ (${l}_{B}$\ensuremath{\ll}W\ensuremath{\ll}${l}_{e}$), modeled with a parabolic potential of frequency \ensuremath{\Omega}, leads to a shift of the magnetophonon resonance peaks to smaller magnetic fields. The usual resonance condition ${\ensuremath{\omega}}_{\mathrm{LO}=\mathrm{P}{\ensuremath{\omega}}_{c}}$, where P is an integer and ${\ensuremath{\omega}}_{\mathrm{LO}}$ and ${\ensuremath{\omega}}_{c}$ are the optical-phonon frequency and cyclotron frequency, respectively, becomes ${\ensuremath{\omega}}_{\mathrm{LO}=\mathrm{P}\mathrm{\ensuremath{\omega}}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}$, with \ensuremath{\omega}\ifmmode \tilde{}\else \~{}\fi{} equal to (${\ensuremath{\omega}}_{c}^{2}$+${\ensuremath{\Omega}}^{2}$${)}^{1/2}$. The magnetoconductivity ${\ensuremath{\sigma}}_{\mathrm{xx}}$ decreases when the confinement becomes stronger (when the width decreases). Level broadening and finite-thickness corrections are taken into account.

Journal ArticleDOI
TL;DR: A survey of results relating the supertwistor correspondence on {ital N}-extended super-Minkowski space {ital M}{sup 4/4{ital N}} to supersymmetric Yang-Mills (SSYM) theroy can be found in this paper.

01 Jan 1989
TL;DR: This paper shows how the subtour elimination constraints developed by Miller, Tucker and Zemlin for the traveling salesman problem can be improved and extended to various types of vehicle routing problems.
Abstract: This paper shows how the subtour elimination constraints developed by Miller, Tucker and Zemlin for the traveling salesman problem can be improved and extended to various types of vehicle routing problems (A)