Set Of Feasible Schedules Research Articles

Flexible decision support tool for dynamic single machine scheduling problems

ABSTRACT This paper addresses dynamic single machine scheduling problems. It proposes a flexible decision support tool based on a non-preemptive version of the previously-established overlapping load adjustment approach. The proposed tool adopts a two-phase proactive-reactive tactic where the first phase only characterizes the set of feasible schedules. In the second reactive phase, however, actual short-term scheduling takes place through a user-induced dynamic-event module, which progressively builds the schedule as the horizon rolls forward while ensuring the feasibility of the obtained schedule at all times. The performance of the tool is assessed using 500 randomly generated test instances of various sizes. The obtained results illustrate the flexibility of the tool as measured by the high number of potential schedule alternatives. Furthermore, the results highlight the tool’s capability of yielding a large number of high-quality schedules with respect to three performance measures.

Dancing links for optimal timetabling

Military Operations Research Society. All rights reserved. Algorithms for timetabling solutions typically involve sequential allocation of students to courses and resources as the algorithm unfolds. Most current solutions, to this end, commonly use some form of stochastic optimization. In this paper, we propose a novel paradigm for optimal timetabling that comprises two distinct phases. First, we enumerate all feasible course schedules, along with their costs, using a modified implementation of Knuth’s Dancing Links technique for the exact cover problem. To our knowledge, the only prior use of this implementation has been to solve games such as Sudoku and N-Queens. Once the list of all solutions that satisfy prerequisite and time-clash constraints is generated, the second phase applies a standard deterministic optimization to allocate students to these feasible schedules. This method has been applied to a real complex timetabling problem in the Royal Australian Navy helicopter aircrew training program. The results are compared, in terms of computational time, to an exhaustive best practice backtracking algorithm for generating a complete set of feasible schedules, as well as to a pure integer linear programming solution for generating schedules and allocating students to schedules.

An Algorithm for Generating a Dispersed Population of Feasible Schedules for Flexible Job Shop Problems

Abstract The flexible job shop problems (FJSP) are an important class of scheduling problems and they have a significant practical value. Unfortunately it is not easy to solve job shop problems and in particular FJSPs because they are NP-hard problems. In this paper we propose a method for generating a set of feasible schedules for a given FJSP.

Real-time scheduling using regularity criteria and a geometrical approach

In this paper, we focus on the use of discrete geometry for the sake of real-time modelling and analysis. We consider multiprocessor context and task sets with offsets, constrained deadlines and critical resources. We want to take regularity criteria into account during the scheduling process. We, thus, determine the geometrical characterisation of PFair schedules and present the construction steps of a geometric PFair model. Several uses of this model are then presented: we can select (partially) PFair schedules. We have also defined a PFairness comparison criterion and we use it to choose among a set of feasible schedules the most PFair ones.

A constraint programming-based solution approach for medical resident scheduling problems

Persistent calls come from within the graduate medical education community and from external sources for regulating the resident duty hours in order to meet the obligations about the quality of resident education, the well-being of residents themselves, and the quality of patient care services. The report of the Accreditation Council for Graduate Medical Education (ACGME) proposes common program requirements for resident hours. In this paper, we first develop a mixed-integer programming model for scheduling residents’ duty hours considering the on-call night, day-off, rest period, and total work-hour ACGME regulations as well as the demand coverage requirements of the residency program. Subsequently, we propose a column generation model that consists of a master problem and an auxiliary problem. The master problem finds a configuration of individual schedules that minimizes the sum of deviations from the desired service levels for the day and night periods. The formulation of this problem is possible by representing the feasible schedules using column variables, whereas the auxiliary problem finds the whole set of feasible schedules using constraint programming. The proposed approach has been tested on a series of problems using real data obtained from a hospital. The results indicate that high-quality schedules can be obtained within a few seconds.

Characterisation by decomposition in scheduling

In this paper, the authors pose the principles of a temporal decomposition method for the single machine scheduling problem. A set of feasible schedules is characterised by means of constraint-based analysis rules. These rules permit the determination of the feasible locations of each activity in a sequence, represented by the rank interval. The temporal properties pointed out serve to support the decision-making in large-scale problems and generate an interesting solution more rapidly.

Cooperative system design in scheduling

In semi-automated workshops producing small or medium runs, the human factor plays a preeminent role in the decision making process. A computerized management is sought nonetheless, considering the great number of items to maintain. In this context, classical scheduling tools using optimization techniques are not flexible enough to provide a feasible plan. Cooperative scheduling, which means a collaboration between a human operator and a system, constitutes a promising alternative for managing production. In this paper, the authors present a methodology to implement cooperative scheduling. It is based on the converging of a top-down approach to functional design and a bottom-up approach to the cognitive design of human-computer interaction. The top-down approach relies on a constraint-based analysis that aims at providing a set of feasible schedules for decision making. The bottom-up approach consists of a knowledge acquisition phase, essentially using brainwriting techniques. An industrial application in an aircraft company has been investigated. The emphasis is on the processing-order release function in a flanging shop which resulted, through constraint logic programming, in a mock-up of a cooperative system.

A decomposition approach for the single—machine scheduling problem

ABSTRACT This paper presents a temporal decomposition approach for the one—machine scheduling problem, with ready times, due dates and fixed processing times. We aim at characterizing feasible schedules of the problem and deriving benefit from the temporal properties pointed out, in order to generate a solution which minimizes the maximum lateness. The set of feasible schedules is characterized by means of constraint—based analysis rules. They permit the determination of the feasible locations of each task in a sequence, represented by the rank interval. A solving heuristic procedure is described; it decomposes the set of tasks according to their rank intervals and applicates upon each subproblem a priority rule. Computational results are reported, so that the characterization method as well as the solving procedure can be evaluated.

A decision-making process for the real time control of a production unit†

Abstract The scheduling of jobs on machines in a job-shop is considered using a multilevel decision-making structure. The levels are coordinated by considering as constraints on one level the decision made on the preceding level. For job-shop scheduling a tool is proposed to enable one to find and to analyse the set of feasible schedules in the light of the decision taken on the previous level. The information obtained as to the earliest starting and latest finishing times for performing the operations, as well as the logical sequence constraints acts as decision aids for the scheduling of the operations. The decision is made by choosing, from amongst the actions which are possible in the light of the overall objective, an action which takes into account secondary elements and considerations particular to the job-shop.