Software modelling of manufacturing systems: A case for an object-oriented programming approach

With the recognition of the importance of Computer Integrated Systems (CIM) in improving manufacturing productivity, there is a pressing need for good software modelling approaches to support efficient design and control of manufacturing systems. Software design concepts based on Object-Oriented Programming (OOP) are emerging as powerful techniques for developing large scale software systems. This paper presents important features of object-oriented computing and the relevance of such an approach in modelling and developing software for manufacturing systems.     

Sets and indices in linear programming modelling and their integration with relational data models

LP models are usually constructed using index sets and data tables which are closely related to the attributes and relations of relational database (RDB) systems. We extend the syntax of MPL, an existing LP modelling language, in order to connect it to a given RDB system. This approach reuses existing modelling and database software, provides a rich modelling environment and achieves model and data independence. This integrated software enables Mathematical Programming to be widely used as a decision support tool by unlocking the data residing in corporate databases.     

Constructing integer programming models by the predicate calculus

A modelling language for Integer Programming (IP) based on the Predicate Calculus is described. This is particularly suitable for building models with logical conditions. Using this language a model is specified in terms of predicates. This is then converted automatically by a series of transformation rules into a normal form from which an IP model can be created. There is also some discussion of alternative IP formulations which can be incorporated into the system as options. Further practical considerations are discussed briefly concerning implementation language and incorporation into practical Mathematical Programming Systems.     

Flexible Graph Connectivity

Mathematical Programming - We introduce and study the problem Flexible Graph Connectivity, which in contrast to many classical connectivity problems features a non-uniform failure model. We...     

Soft Constraint Logic Programming and Generalized Shortest Path Problems

In this paper we study the relationship between Constraint Programming (CP) and Shortest Path (SP) problems. In particular, we show that classical, multicriteria, partially ordered, and modality-based SP problems can be naturally modeled and solved within the Soft Constraint Logic Programming (SCLP) framework, where logic programming is coupled with soft constraints. In this way we provide this large class of SP problems with a high-level and declarative linguistic support whose semantics takes care of both finding the cost of the shortest path(s) and also of actually finding the path(s). On the other hand, some efficient algorithms for certain classes of SP problems can be exploited to provide some classes of SCLP programs with an efficient way to compute their semantics.     

Modelling for a dynamic inventory-production control system

The modelling of an inventory control production scheduling system is discussed. The model uses a Dynamic Programming formulation, incorporating the characteristics of the system, so that it can be used interactively by busy managers. This was achieved by a modified Wagner-Whitin algorithm and an interactive safety stock method. The microcomputer implementation of this model was tested, showing practically useful features, and resulted in substantial cost savings and increased customer service.     

Integrating Operations Research in Constraint Programming

This paper presents Constraint Programming as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear programming to be combined with propagation and novel and varied search techniques which can be easily expressed in CP. The paper describes how CP can be used to exploit linear programming within different kinds of hybrid algorithm. In particular it can enhance techniques such as Lagrangian relaxation, Benders decomposition and column generation.     

A Goal Programming model of the reference point method

Real-life decision problems are usually so complex they cannot be modeled with a single objective function, thus creating a need for clear and efficient techniques of handling multiple criteria to support the decision process. The most commonly used technique is Goal Programming. It is clear and appealing, but in the case of multiobjective optimization problems strongly criticized due to its noncompliance with the efficiency (Pareto-optimality) principle. On the other hand, the reference point method, although using similar control parameters as Goal Programming, always generates efficient solutions. In this paper, we show how the reference point method can be modeled within the Goal Programming methodology. It allows us to simplify implementations of the reference point method as well as shows how Goal Programming with relaxation of some traditional assumptions can be extended to a multiobjective optimization technique meeting the efficiency principle.     

Genetic Algorithm based technique for solving Chance Constrained Problems

Management and measurement of risk is an important issue in almost all areas that require decisions to be made under uncertain information. Chance Constrained Programming (CCP) have been used for modelling and analysis of risks in a number of application domains. However, the resulting mathematical problems are non-trivial to represent using algebraic modelling languages and pose significant computational challenges due to their non-linear, non-convex, and the stochastic nature. We develop and implement C++ classes to represent such CCP problems. We propose a framework consisting of Genetic Algorithm and Monte Carlo Simulation in order to process the problems. The non-linear and non-convex nature of the CCP problems are processed using Genetic Algorithm, whereas the stochastic nature is addressed through Simulation. The computational investigations have shown that the framework can efficiently represent and obtain good solutions for seven test problems.     

Application of general semi-infinite programming to lapidary cutting problems

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interior-point method developed by Stein [O. Stein, Bi-level Strategies in Semi-infinite Programming, Kluwer Academic Publishers, Boston, 2003]. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on real-world data are also presented.     

Integrating the use of linear and dynamic programming methods for dairy cow diet formulation

Despite many refinements that have been made to the basic Linear Programming model used to find economically optimal diets for dairy cows, the sequential nature of the physical and physiological changes that a cow goes through during lactation have not been incorporated into the modelling process satisfactorily. This paper demonstrates how it can be achieved by integrating the use of both Linear and Dynamic Programming methods to optimise the economic performance of a dairy cow over its entire lactation. Linear Programming generates solutions for each potential liveweight change occurring during each of eleven four week periods over the lactation, then the use of DP allows both the selection of the optimal sequence of liveweight changes during the lactation and the specification of rations associated with this optimal path.     

Automated model construction: A logic based approach

Attempts to integrate Artificial Intelligence (AI) techniques into Decision Support Systems (DSS) have received much attention in recent years. Significant among these has been the application of knowledge-based techniques to support various phases of the modeling process. This paper describes a logic based approach to mechanically construct Linear Programming (LP) models from qualitative problem specifications and illustrates it in the context of production, distribution and inventory planning problems. Specifically, we describe the features of a first-order logic based formal language called PM which is at the heart of an implemented knowledge-based tool for model construction. Problems specified in PM define a logic model which is then used to generate problem-specific inferences, and as input to a set of logic programming procedures that perform model construction.     

A review of Goal Programming and its applications

This paper presents a review of the current literature on the branch of multi-criteria decision modelling known as Goal Programming (GP). The result of our indepth investigations of the two main GP methods, lexicographic and weighted GP together with their distinct application areas is reported. Some guidelines to the scope of GP as an application tool are given and methods of determining which problem areas are best suited to the different GP approaches are proposed. The correlation between the method of assigning weights and priorities and the standard of the results is also ascertained.     

Modelling and decision support in physiology and medicine: a methodological framework with lllustration

This paper presents a methodological framework for modelling that has found wide application in the complex domains of physiology and medicine. The processes of model validation are centrally embedded within this framework. The parallelism between modelling per se and the development of model-based decision support systems is then considered, showing that it is possible to devise a unified methodological framework which encompasses the requirements both of model validation and decision support system evaluation. The applicability of the framework is demonstrated in the validation of a mathematical model of blood glucose dynamics; and in the development and evaluation of decision support systems such as those which are aimed at addressing the problem of advising the insulin-dependent diabetic patient on the adjustment of insulin dosage     

On the complexity of finding a local minimizer of a quadratic function over a polytope

Mathematical Programming - We show that unless P=NP, there cannot be a polynomial-time algorithm that finds a point within Euclidean distance $$c^n$$ (for any constant $$c \ge 0$$ ) of a local...     

Solving Vehicle Routing Problems Using Constraint Programming and Metaheuristics

Constraint Programming typically uses the technique of depth-first branch and bound as the method of solving optimization problems. Although this method can give the optimal solution, for large problems, the time needed to find the optimal can be prohibitive. This paper introduces a method for using local search techniques within a Constraint Programming framework, and applies this technique to vehicle routing problems. We introduce a Constraint Programming model for vehicle routing, and a system for integrating Constraint Programming and local search techniques. We then describe how the method can be accelerated by handling core constraints using fast local checks, while other more complex constraints are left to the constraint propagation system. We have coupled our local search method with a meta-heuristic to avoid the search being trapped in local minima. Several meta-heuristics are investigated ranging from a simple Tabu Search method to Guided Local Search. An empirical study over benchmark problems shows the relative merits of these techniques. Investigations indicate that the specific long-term memory technique used by Guided Local Search can be used as a diversification method for Tabu Search, resulting in significant benefit. Several new best solutions on the Solomon problems are found in relatively few iterations of our algorithm.     

Arguments constructed within the mathematical modelling cycle

Socio-cultural theories in mathematics education field recently emphasize the importance of the collective argumentation within small-group work. Since mathematical modelling tasks require a process in which students search for a solution for real life problems through small-group work, the arguments in this process become an issue of concern. This study examines the arguments constructed within the mathematical modelling cycle by considering the participants’ modelling processes. In this context, four primary pre-service mathematics teachers worked on a modelling task and their arguments were explained through the components of Toulmin’s argumentation schema. Findings revealed that the data and the claims of most of the arguments corresponded to the starting and ending points of the modelling transition in which the current arguments constructed. The existence of the arguments corresponded through warrant-claim originated from inquiring the assumptions in the modelling cycle. In addition, the participants made assumptions as warrants to support their arguments and as rebuttals to show the degree of certainty of claims in intra-group challenging situations. Both the warrants and the backings depended on modelling context as well as mathematics context.     

Box-total dual integrality,box-integrality,and equimodular matrices

Mathematical Programming - Box-totally dual integral (box-TDI) polyhedra are polyhedra described by systems which yield strong min-max relations. We characterize them in several ways, involving the...     

Scalable subspace methods for derivative-free nonlinear least-squares optimization

Mathematical Programming - We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a...     

Interactive Sequential Goal Programming

This paper introduces a new solution method based on Goal Programming for Multiple Objective Decision Making (MODM) problems. The method, called Interactive Sequential Goal Programming (ISGP), combines and extends the attractive features of both Goal Programming and interactive solution approaches for MODM problems. ISGP is applicable to both linear and non-linear problems. It uses existing single objective optimization techniques and, hence, available computer codes utilizing these techniques can be adapted for use in ISGP. The non-dominance of the "best-compromise" solution is assured. The information required from the decision maker in each iteration is simple. The proposed method is illustrated by solving a nutrition problem.