: This paper proposes an extension of the constraint-based approach to job-shop scheduling, that accounts for the flexibility of temporal constraints and the uncertainty of operation durations. The set of solutions to a problem is viewed as a fuzzy set whose membership function reflects preference. This membership function is obtained by an egalitarist aggregation of local constraint-satisfaction levels. Uncertainty is qualitatively described is terms of possibility distributions. The paper formulates a simple mathematical model of jobshop scheduling under preference and uncertainty, relating it to the formal framework of constraint-satisfaction problems in Artificial Intelligence. A combinatorial search method that solves the problem is outlined, including fuzzy extensions of well-known look-ahead schemes. 1. Introduction There are traditionally three kinds of approaches to jobshop scheduling problems: priority rules, combinatorial optimization and constraint analysis. The first kind ...

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FLEXIBILITY IN A KNOWLEDGE-BASED SYSTEM FOR SOLVING DYNAMIC RESOURCE-CONSTRAINED SCHEDULING PROBLEMS SEPTEMBER 1994 DAVID WALDAU HILDUM B.A., BRANDEIS UNIVERSITY M.S., Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Daniel D. Corkill The resource-constrained scheduling problem (RCSP) involves the assignment of a limited set of resources to a collection of tasks, with the intent of satisfying some particular qualitative objective, under a variety of technological and temporal constraints. Real-world environments, however, introduce a variety of complications to the standard RCSP. The dynamic resourceconstrained scheduling problem describes a class of real-world RCSPs that exist within the context of dynamic and unpredictable environments, where the details of the problem are often incomplete, and subject to change over time, without notice. Previous approaches to solving resource-constrained scheduling problems failed to focus on the dynamic nature of real-worl...

Abstractions are generally thought to reduce the complexity of problem solving. In this report, we present two abstraction techniques and one partitioning heuristic to solve resource allocation problems. The clustering heuristic decomposes the resource allocation problem into easy and difficult components interacting through abstracted pools of resources. The hierarchy of resource pools allows the user to intervene in conflict resolution at the most appropriate level of abstraction. The temporal abstraction techniques simplify the decoupled components. They also aid the user in assessing the tightness of the problem and the types of missing resources. We propose an algorithm that interleaves these processes. The main advantages of our approach are limiting the need for backtracking, providing an interactive framework for conflict resolution, and offering a comprehensive view of resource contention.

This paper describes our continuing work on enabling a tutor to evaluate algebraic solutions to word problems in physics. Current tutoring systems require students to explicitly define each variable that is used in the algebraic equations. We have developed a constraint propagation based heuristic algorithm that finds the possible dimensions and physics concepts for each variable. In earlier work we developed techniques that worked for a small set of problems and evaluated them on a small number of students. The work described here covers an extension to and evaluation of a much larger class of problems and a larger number of students. The results show that our technique uniquely determines the dimensions of all the variables in 89 % of the sets of equations. By asking the student for dimension information about one variable, an additional 3 % of the sets can be determined. Thus a physics tutoring system can use this technique to reason about a student’s answers even when the scaffolding and context are removed.

One of the key components of an Intelligent Tutoring System (ITS) is the mechanism for reasoning about the student’s input. The impact of this component extends far beyond the presentation of the lesson material to the success of the system itself. It affects how precisely the system can pinpoint student errors and thus the subsequent help that the system provides. This paper describes an example of a class of physics problems whose answers are most naturally represented as systems of algebraic equations. Analyzing such input requires not only an understanding of algebra but also knowledge of physics concepts. This paper describes a technique for determining the dimensional consistency of algebraic equations in physics using constraint propagation. Unlike other methods, it does not depend on the user defining the dimensions of each variable. Instead, it uses a knowledge base of well known physics variables combined with constraint propagation to determine both the dimensions of values (variables and constants) and also the dimensional consistency of an equation. The technique has been successfully tested on answers obtained from a class of college level introductory physics students.

. In this paper a heuristic approach for the project job-shop scheduling problem is presented. The goal of project scheduling is to determine a schedule of possibly parallel operations related to a set of jobs, competing for a restricted set of available resources, while optimizing a pre-defined performance criterion. The scheduling of a job-shop type production system is generally an NP-complete problem, so the computation time grows exponentially with the problem dimension. However, for most real world problems a pragmatic approach is usually followed: finding a reasonable solution in an acceptable amount of time. For this reason, the main goal of the present research encompasses the efficient achievement of feasible solutions, satisfying technological constraints, resource capacity restrictions, and due dates regarding each job. The proposed approach is based on a constraint management system allowing two types of solutions for project scheduling problems: quasi-optimal albeit time ...

In this paper a heuristic approach for the project job-shop scheduling problem is presented. The scheduling of a job-shop type production system is generally an NP-complete problem, so the computable time grows exponentially with the problem dimension. However, for most real world problems a pragmatic approach is usually followed: finding a reasonable solution in an acceptable amount of time. For this reason, the main goal of the present research encompasses the efficient achievement of feasible solutions, satisfying technological restrictions, resource capacity constraints, and due dates regarding each job. The proposed approach is based on two complementary scheduling perspectives: operation and relation (between operations). The schedule is constructed according to the essential characteristics that impose a precedence relation between operations, although the scheduling effort is oriented towards the operation that seems to be in the most critical condition at each stage. The syste...