الفهرس 
LITERATURE REVIEWOnly 14 pages are availabe for public view
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Abstract
Capacity planning of multi-item products in make to order industries represents
one of the major problems that faces the management. Many efforts have been
devoted to schedule several jobs on several machines. Some of these efforts
were successful in obtaining schedules which yield near optimal make spans.
However most of the efforts were devoted to solve the problems of single item
products without any consideration to constraints imposed by the limited
production capacity.
The objective of the present work is to device a heuristic algorithm capable of
handling capacitated scheduling problems of multi-item products on several
production facilities.
The following are the different techniques used and developed in that concern:
1. SELECTED SINGLE ITEM JOBS SCHEDULING ALGORITHMS:
Ignall & Schrage algorithm which is based on branch and bound technique and
the CDS algorithm which is based on Johnson’s algorithm, are known to posses
the highest efficiency in solving single item scheduling problems compared to
other available algorithms. For that reason, they were chosen for investigation
for further development and comparison purposes with the heuristic algorithms
to be developed in the present work. They were applied on several case studies
to study the effect of different factors which may affect the efficiency of the
algorithms. Computer programs were developed for these algorithms to solve
the flow shop single item jobs scheduling problems.
2. DEVELOPED ALGORITHMS FOR SINGLE ITEM JOBS SCHEDULING:
The aim of the developed algorithms in the present work is to obtain better
results compared to that of other researchers algorithms. Two algorithms, based
on the Branch and Bound concept, were developed to schedule a number of
single item jobs on several machines. The algorithms depends on composing an
initial sequence and then obtain other possible sequences by applying the
branching concept. By applying the sequence generation rule, a number of branches sprout and end with the job processing sequences. Further branching
can be made at any node in the generated sequences tree. The different
generated sequences at any node are determined by placing any of the
unscheduled jobs to succeed the last scheduled job in the node sequence. The
make span is then calculated for each sequence at each node. The node at which
the sequence of jobs gives the minimum make span is chosen for further
branching. Selection of nodes and subsequent branching is continued until no
improvement in the total make span is achieved and therefore, a solution is
obtained.
The developed algorithms differs only in the way of arranging the initial
sequence. In the first algorithm (TWC) the initial sequence is made by arranging
the jobs in descending order according to their total work content. The second
algorithm (DISH) depends on considering the sequence resulted from Ignall and
Schrage algorithm as an initial sequence. The DISH algorithm IS an
improvement to the schedule resulted from Ignall and Schrage algorithm.
3. DEVELOPED HEURISTIC ALGORITHM TO SOLVE CAPACITATED
SCHEDULING PROBLEMS OF MULTI-ITEM PRODUCTS:
The aforementioned developed algorithms were extended to solve capacitated
scheduling problems of multi-item products. Also, Ignall and Schrage
algorithm was extended to solve the same type of problem. The solution
algorithm was made using matrices arrangements throughout the whole
procedure were matrix algebra was applied to reach the solution. The algorithm
was made to satisfy the precedence constraints by following the Gozinto
representation and product explosion model following Vazsonyi model. The
capacitated schedule was made by following a bidding concept to decide upon
the jobs in sequence among the candidated jobs.
Several examples had been proposed to test the sensitivity and compare between
the results obtained from each. The examples were randomly generated
covering the factors affecting the problem as number of products, number of
machines, number of levels in multi item products. Also, some of the examples
were specially designed to experience odd cases.
For single jobs scheduling, the results obtained from applying the developed
heuristic algorithms were found to be superior in comparison with the results of
other researchers even for small size problems. The present algorithms yielded
the optimal solutions in most of small size cases where other algorithms failed.
Optimal solutions were determined by applying complete enumeration of
different sequences for a maximum of seven products .