Application of Mathematical Programming to the Plywood Design and Manufacturing Problem

Plywood manufacture includes two fundamental stages. The first is to peel or separate logs into veneer sheets of different thicknesses. The second is to assemble veneer sheets into finished plywood products. At the first stage a decision must be made as to the number of different veneer thicknesses to be peeled and what these thicknesses should be. At the second stage, choices must be made as to how these veneers will be assembled into final products to meet certain constraints while minimizing wood loss. These decisions present a fundamental management dilemma. Costs of peeling, drying, storage, handling, etc. can be reduced by decreasing the number of veneer thicknesses peeled. However, a reduced set of thickness options may make it infeasible to produce the variety of products demanded by the market or increase wood loss by requiring less efficient selection of thicknesses for assembly. In this paper the joint problem of veneer choice and plywood construction is formulated as a nonlinear integer programming problem. A relatively simple optimal solution procedure is developed that exploits special problem structure. This procedure is examined on data from a British Columbia plywood mill. Restricted to the existing set of veneer thicknesses and plywood designs used by that mill, the procedure generated a solution that reduced wood loss by 79 percent, thereby increasing net revenue by 6.86 percent. Additional experiments were performed that examined the consequences of changing the number of veneer thicknesses used. Extensions are discussed that permit the consideration of more than one wood species.

Functional programming systems revisited

Functional Programming (FP) systems are modified and extended to form Nondeterministic Functional Programming (NFP) systems in which nondeterministic programs can be specified and both deterministic and nondeterministic programs can be verified essentially within the system. It is shown that the algebra of NFP programs has simpler laws in comparison with the algebra of FP programs. "Regular" forms are introduced to put forward a disciplined way of reasoning about programs. Finally, an alternative definition of "linear" forms is proposed for reasoning about recursively defined programs. This definition, when used to test the linearity of forms, results in simpler verification conditions than those generated by the original definition of linear forms.

A dynamic programming model for optimising feeding and slaughter decisions regarding fattening pigs

Costs of purchasing new piglets and of feeding them until slaughter are the main variable expenditures in pig fattening. They both depend on slaughter intensity, the nature of feeding patterns and the technological constraints of pig fattening, such as genotype. Therefore, it is of interest to examine the effect of production technology and changes in input and output prices on feeding and slaughter decisions. This study examines the problem by using a dynamic programming model that links genetic characteristics of a pig to feeding decisions and the timing of slaughter and takes into account how these jointly affect the quality-adjusted value of a carcass. The model simulates the growth mechanism of a pig under optional feeding and slaughter patterns and then solves the optimal feeding and slaughter decisions recursively. The state of nature and the genotype of a pig are known in the analysis. The main contribution of this study is the dynamic approach that explicitly takes into account carcass quality while simultaneously optimising feeding and slaughter decisions. The method maximises the internal rate of return to the capacity unit. Hence, the results can have vital impact on competitiveness of pig production, which is known to be quite capital-intensive. The results suggest that producer can significantly benefit from improvements in the pig's genotype, because they improve efficiency of pig production. The annual benefits from obtaining pigs of improved genotype can be more than €20 per capacity unit. The annual net benefits of animal breeding to pig farms can also be considerable. Animals of improved genotype can reach optimal slaughter maturity quicker and produce leaner meat than animals of poor genotype. In order to fully utilise the benefits of animal breeding, the producer must adjust feeding and slaughter patterns on the basis of genotype. The results suggest that the producer can benefit from flexible feeding technology. The flexible feeding technology segregates pigs into groups according to their weight, carcass leanness, genotype and sex and thereafter optimises feeding and slaughter decisions separately for these groups. Typically, such a technology provides incentives to feed piglets with protein-rich feed such that the genetic potential to produce leaner meat is fully utilised. When the pig approaches slaughter maturity, the share of protein-rich feed in the diet gradually decreases and the amount of energy-rich feed increases. Generally, the optimal slaughter weight is within the weight range that pays the highest price per kilogram of pig meat. The optimal feeding pattern and the optimal timing of slaughter depend on price ratios. Particularly, an increase in the price of pig meat provides incentives to increase the growth rates up to the pig's biological maximum by increasing the amount of energy in the feed. Price changes and changes in slaughter premium can also have large income effects. Key words: barley, carcass composition, dynamic programming, feeding, genotypes, lean, pig fattening, precision agriculture, productivity, slaughter weight, soybeans

Existence theorem for a generalized Hammerstein type equation

An existence theorem is obtained for a generalized Hammerstein type equation

A phase space approach to generalized Hamilton–Jacobi theory

Generalizations of H–J theory have been discussed before in the literature. The present approach differs from others in that it employs geometrical ideas on phase space and classical transformation theory to derive the basic equations. The relation between constants of motion and symmetries of the generalized H–J equations is then clarified. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Solution of a generalized Korteweg—de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived. ©1974 American Institute of Physics.

On the bottleneck linear programming problem

In this paper, the results on primal methods for Bottleneck Linear Programming (BLP) problem are briefly surveyed, the primal method is presented and the degenerate case related to Bottleneck Transportation Problem (BTP) is explicitly considered. The algorithm is based on the idea of using auxiliary coefficients as is done by Garfinkel and Rao [6]. The modification presented for the BTP rectifies the defect in Hammer's method in the case of degenerate basic feasible solution. Illustrative numerical examples are also given.

Regularized numerical integration of multibody dynamics with the generalized alpha method*

This paper discusses the consistent regularization property of the generalized α method when applied as an integrator to an initial value high index and singular differential-algebraic equation model of a multibody system. The regularization comes from within the discretization itself and the discretization remains consistent over the range of values the regularization parameter may take. The regularization involves increase of the smallest singular values of the ill-conditioned Jacobian of the discretization and is different from Baumgarte and similar techniques which tend to be inconsistent for poor choice of regularization parameter. This regularization also helps where pre-conditioning the Jacobian by scaling is of limited effect, for example, when the scleronomic constraints contain multiple closed loops or singular configuration or when high index path constraints are present. The feed-forward control in Kane's equation models is additionally considered in the numerical examples to illustrate the effect of regularization. The discretization presented in this work is adopted to the first order DAE system (unlike the original method which is intended for second order systems) for its A-stability and same order of accuracy for positions and velocities.

Programming rumen bacterial communities in newborn Merino lambs

Establishment of the rumen microbiome can be affected by both early-life dietary measures and rumen microbial inoculation. This study used a 2 × 3 factorial design to evaluate the effects of inclusion of dietary fat type and the effects of rumen inoculum from different sources on ruminal bacterial communities present in early stages of the lambs’ life. Two different diets were fed ad libitum to 36 pregnant ewes (and their lambs) from 1 month pre-lambing until weaning. Diets consisted of chaffed lucerne and cereal hay and 4% molasses, with either 4% distilled coconut oil (CO) provided as a source of rumen-active fat or 4% Megalac® provided as a source of rumen-protected fat (PF). One of three inoculums was introduced orally to all lambs, being either (1) rumen fluid from donor ewes fed the PF diet; (2) rumen fluid from donor ewes fed CO; or (3) a control treatment of MilliQ-water. After weaning at 3 months of age, each of the six lamb treatment groups were grazed in spatially separated paddocks. Rumen bacterial populations of ewes and lambs were characterised using 454 amplicon pyrosequencing of the V3/V4 regions of the 16S rRNA gene. Species richness and biodiversity of the bacterial communities were found to be affected by the diet in ewes and lambs and by inoculation treatment of the lambs. Principal coordinate analysis and analysis of similarity (ANOSIM) showed between diet differences in bacterial community groups existed in ewes and differential bacterial clusters occurred in lambs due to both diet and neonatal inoculation. Diet and rumen inoculation acted together to clearly differentiate the bacterial communities through to weaning, however the microbiome effects of these initial early life interventions diminished with time so that rumen bacterial communities showed greater similarity 2 months after weaning. These results demonstrate that ruminal bacterial communities of newborn lambs can be altered by modifying the diet of their mothers. Moreover, the rumen microbiome of lambs can be changed by diet while they are suckling or by inoculating their rumen, and resulting changes in the rumen bacterial microbiome can persist beyond weaning.

Solution of a generalized Korteweg-de Vries equation

The solitary-wavelike solution of the generalized Korteweg-de Vries equation with mixed nonlinearity is obtained. Two asymptotic cases of the solution have been discussed and solitary wave solutions have been derived.

On a generalized dynamic model of bi-state social interaction processes

A non-linear model, construed as a generalized version of the models put forth earlier for the study of bi-state social interaction processes, is proposed in this study. The feasibility of deriving the dynamics of such processes is demonstrated by establishing equivalence between the non-linear model and a higher order linear model.

Symmetries and constraints in generalized Hamiltonian dynamics

A general analysis of symmetries and constraints for singular Lagrangian systems is given. It is shown that symmetry transformations can be expressed as canonical transformations in phase space, even for such systems. The relation of symmetries to generators, constraints, commutators, and Dirac brackets is clarified.

An operational-level multi-stage mine production timetabling model for optimally synchronising drilling, blasting and excavating operations

This paper proposes a new multi-stage mine production timetabling (MMPT) model to optimise open-pit mine production operations including drilling, blasting and excavating under real-time mining constraints. The MMPT problem is formulated as a mixed integer programming model and can be optimally solved for small-size MMPT instances by IBM ILOG-CPLEX. Due to NP-hardness, an improved shifting-bottleneck-procedure algorithm based on the extended disjunctive graph is developed to solve large-size MMPT instances in an effective and efficient way. Extensive computational experiments are presented to validate the proposed algorithm that is able to efficiently obtain the near-optimal operational timetable of mining equipment units. The advantages are indicated by sensitivity analysis under various real-life scenarios. The proposed MMPT methodology is promising to be implemented as a tool for mining industry because it is straightforwardly modelled as a standard scheduling model, efficiently solved by the heuristic algorithm, and flexibly expanded by adopting additional industrial constraints.