A Constraint-Based Declarative Programming Framework for Scheduling and Resource Allocation Problems

Scheduling and resource allocation problems are widespread in many areas of today’s technology and management. Their different forms and structures appear in production, logistics, software engineering, computer networks, project and human resources management, services, etc. The literature (problem classification, scheduling and resource allocation models, solutions) is vast and exhaustive. In practice, however, classical scheduling problems with fixed structures and standard constraints (precedence, disjoint, etc.) are rare. Practical scheduling problems include also logical and nonlinear constraints, and they use nonstandard criteria of schedule evaluations. Indeed, in many cases, decision makers are interested in the feasibility and/or optimality of a given schedule for specified conditions formulated as general and/or specific questions. Thus, there is a need to develop a programming framework that will facilitate the modeling and solving of a variety of diverse scheduling problems. The framework should be able to (a) model any types of constraints, (b) ask questions/criteria relating to the schedule execution mode and (c) be highly effective in finding solutions (schedule development). This paper proposes such a constraint-based declarative programming framework for modeling and solving scheduling problems which satisfies the assumptions above. It was built with the Constraint Logic Programming (CLP) environment and supported with Mathematical Programming (MP). The functionality and effectiveness of this framework are presented with the use of an illustrative example for the resource-constrained scheduling problem with additional resources.

AN EXACT SOLUTION FOR THE RESOURCE-CONSTRAINED CONSTRUCTION SCHEDULING PROBLEM

Reduced time and, by the same token, the cost of the project is a crucial factor in contemporary construction. This article presents a method for the exact optimisation of a resource-constrained scheduling problem. Based on the Critical Path Method, graph theory and linear programming, an algorithm was developed and the FROPT program was written in Matlab to minimise the execution time of the task. By using the newly-created program, sample networks were calculated and the results were compared with results obtained by using the MS Project scheduling program (using approximation algorithm). The execution time obtained by using FROPT were on average 10% shorter than those obtained using MS Project. In selected cases the improvement in execution time reached 25%. A deterministic approach to the problem may shorten planned project times and bring financial benefits. Due to the exponential complexity of the algorithm, it is most useful in solving small or highly coherent networks. The algorithm and program may result in benefits not offered by commercial software for planners of building projects.