By Dr. Stéphane Dauzère-Péres, Jean-Bernard Lasserre (auth.)
Production administration is a huge box enthusiastic about all of the facets concerning creation, from the very backside judgements on the laptop point, to the top-level strategic decisicns. during this e-book, we're excited by construction making plans and scheduling elements. conventional construction making plans methodologies are in accordance with a now largely ac cepted hierarchical decom?osition into numerous making plans determination degrees. the better within the hierarchy, the extra mixture are the types and the extra very important are the selections. during this ebook, we simply reflect on the final determination degrees within the hierarchy, particularly, the mid-term (or tacticaQ making plans point and the momentary (or operationaQ scheduling point. within the literature and in perform, the choices are taken in series and in a top-down procedure from the top point within the hierarchy to the ground point. the selections taken at a few point within the hierarchy are limited through these already taken at top degrees and in flip, needs to translate into possible ambitions for the subsequent reduce degrees within the hierarchy. it's a logic comment to claim that the total hierarchical determination method is coherent if the interactions among varied degrees within the hierarchy are taken into consideration in order that a call taken at a few point within the hierarchy interprets right into a possible aim for the subsequent determination point within the hierarchy. besides the fact that, and surpris ingly adequate, this important consistency factor is never investigated and few effects come in the literature.
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Additional resources for An Integrated Approach in Production Planning and Scheduling
A is the set of pairs of operations subject to precedence constraints in the routing. Ek is the set of pairs of operations to be processed on machine k. prjk is the per unit (of product i) processing time of operation Ojjk and P:jk is the total duration. Tjjk is the set-up time on machine k of operation Ojjk. tjjk is the starting time of operation Oijk. The problem can be formulated as follows: V( Oij'k' , Ojjk) E A VOjjk E N V( Ojljlk, Ojjk) E Ek, k E M Any feasible solution of (0) is a schedule.
While J c exists, r u" = Cma",. 37 A Modified Shifting Bottleneck Procedure 1. If J p is the end of an artificial critical path, consider two new problems, one in which Jc is required to be processed before J p by setting: (1) Pcp:= Pc; and another one in which Jc is required to be processed after all jobs of I by setting: (2) Pte := Pk, 'v'Jk E I. If J p is the end of a real critical path, consider two new problems, one in which J c is required to be processed before all jobs of I by setting: qc := max(qc, Pr + qp); (3) E JreI and another in which Jc has to be processed after all jobs of I by setting: rc:= max(rc, minr~ JreI + E Pr).
In the remaining of this section, we describe Carlier's algorithm, extensively used in the Shifting Bottleneck (SB) procedure. Then, an algorithm is proposed to take into account the new precedence constraints induced by the SB procedure. The problem is to minimize the makespan of jobs that must be processed on a single machine. J* denotes the set of these jobs. For each job J i , Pi, ri, ti, and qi denote the processing time, release date, start time, and delivery time respectively. ", - ti ~ qi + Pi t·• - t·J> - p'J or t·J - t·.
An Integrated Approach in Production Planning and Scheduling by Dr. Stéphane Dauzère-Péres, Jean-Bernard Lasserre (auth.)