Marek Mika

Project scheduling with finite or infinite number of activity processing modes - A survey

This paper surveys single-project, single-objective, deterministic project scheduling problems in which activities can be processed using a finite or infinite (and uncountable) number of modes concerning resources of various categories and types. The survey is based on a unified framework of a project scheduling model including resources, activities, objectives, and schedules. Most important models and solution approaches across the class of problems are characterized, and directions for future research are pointed out.

Simulated Annealing for Multi-Mode Resource-Constrained Project Scheduling

In this paper the resource-constrained project scheduling problem with multiple execution modes for each activity and the makespan as the minimization criterion is considered. A simulated annealing approach to solve this problem is presented. The feasible solution representation is based on a precedence feasible list of activities and a mode assignment. A comprehensive computational experiment is described, performed on a set of standard test problems constructed by the ProGen project generator. The results are analyzed and discussed and some final remarks are included.

Tabu search for multi-mode resource-constrained project scheduling with schedule-dependent setup times

Abstract In this paper, a multi-mode resource-constrained project scheduling problem with schedule-dependent setup times is considered. A schedule-dependent setup time is defined as a setup time dependent on the assignment of resources to activities over time, when resources are, e.g., placed in different locations. In such a case, the time necessary to prepare the required resource for processing an activity depends not only on the sequence of activities but, more generally, on the locations in which successive activities are executed. Activities are non-preemptable, resources are renewable, and the objective is to minimize the project duration. A local search metaheuristic—tabu search is proposed to solve this strongly NP-hard problem, and it is compared with the multi-start iterative improvement method as well as with random sampling. A computational experiment is described, performed on a set of instances based on standard test problems constructed by the ProGen project generator. The algorithms are computationally compared, the results are analyzed and discussed, and some conclusions are given.

Local search metaheuristics for discrete–continuous scheduling problems

Problems of scheduling nonpreemptable jobs which require simultaneously a machine from a set of parallel, identical machines and a continuous, renewable resource are considered. For each job there are known: its processing speed as a continuous, concave function of a continuous resource allotted at a time and its processing demand. The optimization criterion is the schedule length. The problem can be decomposed into two interrelated subproblems: (i) to sequence jobs on machines, and (ii) to find an optimal (continuous) resource allocation among jobs already sequenced. Problem (ii) can be formulated as a convex programming problem with linear constraints and solved using proper solvers. Thus, the problem remains to generate a set of all feasible sequences of jobs on machines (this guarantees finding an optimal schedule in the general case). However, the cardinality of this set grows exponentially with the number of jobs. Thus, we propose to use heuristic search methods defined on the space of feasible sequences. Three metaheuristics: tabu search (TS), simulated annealing (SA) and genetic algorithm (GA) have been implemented and compared computationally with a random sampling technique. The computational experiment has been carried out on an SGI PowerChallenge XL computer with 12 RISC R8000 processors. Some directions for further research have been pointed out.

A metaheuristic approach to scheduling workflow jobs on a Grid

In this chapter we consider the problem of scheduling workflow jobs on a Grid. This problem consists in assigning Grid resources to tasks of a workflow job across multiple administrative domains in such a way that minimizes the execution time of a particular set of tasks. The considered problem is formulated as a multi-mode resource-constrained project scheduling problem with schedule-dependent setup times, which is an extension of the classical resource-constrained project scheduling problem to minimize the makespan (RCPSP). We present a binary linear programming (0-1 LP) formulation of the problem, and propose a local search metaheuristic approach to solve the considered problem.

Solving the discrete-continuous project scheduling problem via its discretization

Abstract. In this paper a discrete-continuous project scheduling problem is considered. In this problem activities simultaneously require discrete and continuous resources. The processing rate of each activity depends on the amount of the continuous resource allotted to this activity at a time. All the resources are renewable ones. The activities are nonpreemtable and the objective is to minimize the makespan. Discretization of this problem leading to a classical (i.e. discrete) project scheduling problem in the multi-mode version is presented. A simulated annealing (SA) approach to solving this problem is described and tested computationally in two versions: with and without finding an optimal continuous resource allocation for the final schedule. In the former case a nonlinear solver is used for solving a corresponding convex programming problem. The results are compared with the results obtained using SA for the discrete-continuous project scheduling problem where the nonlinear solver is used for exact solving the continuous part in each iteration. The results of a computational experiment are analyzed and some conclusions are included.

Modelling Setup Times in Project Scheduling

In this chapter project scheduling problems with setup times are considered. Some practical applications justifying considering setups separately from activities are described. An extensive classification of setup times adapted from machine scheduling is proposed, including activity vs. class setup, separable vs. inseparable setup, as well as sequence-independent and sequence-dependent setup times. A new category of setup times - schedule-dependent ones - is discussed. The main part of the paper shows how to model setup times in the presence of particular project components, such as: precedence constraints, resource availability constraints, multiple resource units requests, multiple resources, etc. Some possible extensions of the presented models are given.

Discrete-continuous scheduling to minimize the makespan for power processing rates of jobs

Abstract A class of discrete-continuous scheduling problems is considered when each nonpreemptable, independent job simultaneously requires for its processing a machine from a set of m identical, parallel machines and an amount, arbitrary within interval [0,1], of a continuously divisible, renewable resource available in amount 1. Job processing rates are described by power functions of the resource amount allotted at a time. Some properties of optimal schedules are proved which allow to find such schedules analytically in some cases and to construct efficient heuristics in the general case. Results of a computational experiment are described.

Overview and State of the Art

In this chapter we present a state-of-the-art in the area of multi-mode project scheduling problems. These problems are characterized by the fact that each activity of a project can be executed in one of several modes, representing a relation between the resource requirements of the activity and its duration. In the overview we present the models and solution approaches that have been proposed in the literature across the class of multi-mode project scheduling problems up to now. Firstly we deal with the basic multi-mode resource-constrained project scheduling problems with the objective to minimize the project duration. We present the mixed-integer linear programming formulations of the problem, describe the exact approaches, the existing methods for lower bounds calculation, as well as heuristic approaches to solve the problem. Secondly, we also discuss special cases and extensions of the basic problem. Finally, we analyze multi-mode problems with other objectives, distinguishing between financial and resource-based objectives.

An Almost Optimal Heuristic for Preemptive C max Scheduling of Dependent Tasks on Parallel Identical Machines

We consider the problem of scheduling preemptable, dependent tasks on parallel, identical machines to minimize the makespan. The computational complexity of this problem remains open if the number of machines is fixed and larger than 2. The aim of this paper is to compare two heuristic algorithms on a basis of a computational experiment. The solutions generated by the heuristics are compared with optimal solutions obtained by a branch-and-bound algorithm. Computational results show that the heuristic based on node ordering finds optimal schedules for 99.9% of instances with the maximum relative deviation from optimum of 4.8%.