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On Scheduling Cycle Shops: Classification, Complexity And Approximation
"... . This paper considers problems of finding nonperiodic and periodic schedules in a cycle shop which is a special case of a job shop but an extension of a flow shop. The cycle shop means the machine environment where all jobs have to pass the machines over the same route like in a flow shop but so ..."
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. This paper considers problems of finding nonperiodic and periodic schedules in a cycle shop which is a special case of a job shop but an extension of a flow shop. The cycle shop means the machine environment where all jobs have to pass the machines over the same route like in a flow shop but some of the machines in the route can be met more than once. We propose a classification of cycle shops and show that recently studied reentrant flow shops, robotic flow shops, loop reentrant flowshops and V shops are special cases of cycle shops. Problems solvable in polynomial time, pseudopolynomial time, NPhard problems and performance guarantee approximations are presented. Related earlier results are surveyed. 1.
Precedence constraint posting for cyclic scheduling problems
 In CPAIOR
"... Abstract. Resource constrained cyclic scheduling problems consist in planning the execution over limited resources of a set of activities, to be indefinitely repeated. In such a context, the iteration period (i.e. the difference between the completion time of consecutive iterations) naturally repla ..."
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Abstract. Resource constrained cyclic scheduling problems consist in planning the execution over limited resources of a set of activities, to be indefinitely repeated. In such a context, the iteration period (i.e. the difference between the completion time of consecutive iterations) naturally replaces the makespan as a quality measure; exploiting interiteration overlapping is the primary method to obtain high quality schedules. Classical approaches for cyclic scheduling rely on the fact that, by fixing the iteration period, the problem admits an integer linear model. The optimal solution is then usually obtained iteratively, via linear or binary search on the possible iteration period values. In this paper we follow an alternative approach and provide a port of the key Precedence Constraint Posting ideas in a cyclic scheduling context; the value of the iteration period is not apriori fixed, but results from conflict resolution decisions. A heuristic search method based on Iterative Flattening is used as a practical demonstrator; this was tested over instances from an industrial problem obtaining encouraging results.
Subproblems in Identical Jobs Cyclic Scheduling: Properties, Complexity and Solution Approaches
 Cornell University
, 1993
"... This paper considers an identicaljobs, reentrant flow, cyclic scheduling problem in repetitive manufacturing environments. An integer programming formulation is developed with system performance measured using a weighted linear combination of cycle length and flow time. The variables in this for ..."
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This paper considers an identicaljobs, reentrant flow, cyclic scheduling problem in repetitive manufacturing environments. An integer programming formulation is developed with system performance measured using a weighted linear combination of cycle length and flow time. The variables in this formulation decompose into two sets: a combinatorial set, called the "cyclic precedence structure," that characterizes all precedence relations between operations in a cyclic schedule, and a set of continuous production timing variables. Given the entire precedence structure, we efficiently solve the resulting production timing subproblem by determining the optimal cycle length and operation start times. We show that under certain conditions, a single cyclic schedule with the specified precedence structure simultaneously minimizes both flow time and cycle length. The related cycle offset subproblem of mapping operations to cycles to minimize flow time while achieving a target throughput, given ...
Highmultiplicity cyclic job shop scheduling
 OPERATIONS RESEARCH LETTERS
, 2008
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Periodic Schedules For Linear Precedence Constraints
"... We consider the computation of periodic cyclic schedules for linear precedence constraints graph: a linear precedence constraint is defined between two tasks and induces an infinite set of usual precedence constraints between their executions such the the difference of iterations is a linear functio ..."
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We consider the computation of periodic cyclic schedules for linear precedence constraints graph: a linear precedence constraint is defined between two tasks and induces an infinite set of usual precedence constraints between their executions such the the difference of iterations is a linear function.The objective function is the minimization of the maximal period of a task. Firstly, we recall that this problem can be modelled using linear programming. Then, we develop a polynomial algorithm to solve it for unitary graphs, which is a particular class of linear precedence graph.We also show that a periodic schedule may not exists for this special case. In the general case, we compute a decomposition of the graph into unitary components and we suppose that a periodic schedule exists for each of them. We compute lower bounds on the periods and we show that an optimal periodic schedule may not achieve them. Then, we introduce the notion of quasiperiodic schedule, and we prove that this new class of schedule always reach these bounds.
Contents lists available at ScienceDirect Artificial Intelligence
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A Study of Sequencing Heuristics for Periodic Production Environments.
"... This paper considers the identical jobs, single enditem cyclic scheduling problem (CSP) of determining good schedules for repetitive production systems with a flexible manufacturing capability. The goal is to optimize system throughput and work in process inventory by determining the efficient trad ..."
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This paper considers the identical jobs, single enditem cyclic scheduling problem (CSP) of determining good schedules for repetitive production systems with a flexible manufacturing capability. The goal is to optimize system throughput and work in process inventory by determining the efficient tradeoff frontier between cycle length and flow times. We present a new, tighter integer programming formulation of CSP corresponding to a network flow problem with some nonnetwork capacity constraints. Since CSP is computationally intractable, we consider several heuristic approaches some of which use subproblems which we have considered in previous research. The five heuristics we examine fall into two generic categories: Myopic methods for schedule generation / improvement (the Graves et al method and a new push / pull heuristic) and truncated exponential search strategies (beam search / truncated branch and bound, simulated annealing algorithms and a new gambling procedure). Our computatio...