مقاله ها
نویسنده : hong sen yan-xiao dong zhang-min jiang
بازدید : 134

abstract
this paper explores the hierarchical production planning (hpp) problem of flexible automated workshops
(faws) each of which has a number of flexible manufacturing systems (fmss). the objective is to decompose
medium-term production plans (assigned to an faw by erp/mrp ii) into short-term production plans (to be
uted by fmss in the faw) so as to minimize cost on the condition that demands have just been met. herein
the hpp problem is formulated by a linear programming model with the overload penalty different from the
underload penalty and with demand constraints. since the scale of the model for a general workshop is too large to
be solved in the simplex method on a personal computer within acceptable time karmarkar’s algorithm and an
interaction/prediction algorithm respectively are used to solve the model the former for the large scale problems
and the latter for the very large scale. with the help of the above-mentioned algorithms and hpp examples
karmarkar’s algorithm and the interaction/prediction algorithm are compared and analyzed the results of which
show that the proposed approaches are quite effective and suitable for both ‘push’ and ‘pull’ production.
q 2004 elsevier ltd. all rights reserved.
keywords: flexible automated workshops; flexible manufacturing systems; hierarchical production planning; karmarkar’s
algorithm; interaction/prediction approach

1. introduction
the problem of production planning for a flexible automated workshop (faw) consisting of
flexible manufacturing systems (fmss or cells) is important and worth studying. in a manufacturing
ting production planning is essential to achieve efficient resource allocation over time in
meeting demands for finished products. since the scope of pp problems generally prohibits a
monolithic modeling approach a hierarchical production planning (hpp) approach has been widelyadvocated in the pp literature (davis & thompson 1993). to model pp problems the existing
hierarchical approaches usually employ the following concepts: (1) product disaggregation (bitran
haas & hax 1981; bitran & hax 1977; davis & thompson 1993; graves 1982; hax & meal
1975; newson 1975; saad 1988; simpson 1999; simpson & erenguc 1998; yeh tarng & chen
1988) (2) temporal decomposition (karmarkar 1988; malakooti 1989; nguyen & dupont 1993;
qiu & burch 1997; tsubone 1988) (3) process decomposition (villa 1989) and (4) eventfrequency decomposition (akella 1989; gershwin 1988; kimemia & gershwin 1983). however
those approaches are not quite suitable for the decomposition of medium-term production plans
(assigned to an faw by erp/mrp ii short for enterprise resource planning/manufacturing resource
planning) into short-term production plans (to be uted by fmss in the faw). to be specific
the product disaggregation only considers the structures of products instead of the organizational
structure of a manufacturing department. although the process decomposition considers the
organizational structure of the manufacturing department it only covers the manufacturing system
consisting of a forward chain of workshops. as the relationships among fmss in an faw are not
always serial or even very complicated the process decomposition is inapplicable to the
decomposition of medium-term production plans for faws. and the temporal and event-frequency
decomposition do not consider the organizational structure of the manufacturing department as
such either.
for this end yan (1997) and yan and jiang (1998) proposed two new approaches to the optimal
decomposition of production plans for faws with respect to delay interaction or not. by building up
linear quadratic models of pp problems and using interaction/prediction their proposed approaches
optimally decompose medium-term production plans (assigned to an faw by mrp ii/cims short for
computer integrated manufacturing system) into short-term production plans (to be uted by fmss in
the faw) at a high speed. these approaches combining the principles of both a temporal decomposition
and a process decomposition with the organizational structure of the faw are capable of solving verylarge-scale hpp problems. however their overload and underload penalty are the same. in practice the
wages for overtime are several times those for the usual hours and the underload only leads to the
decrease in the utilization of resources (such as men and equipment) so the overload penalty should be
much greater than the underload. besides only the manufacturers that can agilely respond to and
completely satisfy users’ demands can win a victory in the keen competition for markets while the
overproduction will lead to the increase in finished-product inventory and production cost. no doubt it is
desirable to just meet product demands without overproduction or underproduction. thus a linear
programming (lp) model with the overload penalty different from the underload penalty and with
demand constraints should be built up for decomposing medium-term production plans (assigned to an
faw by erp/mrp ii) into short-term production plans (to be uted by fmss in the faw). because
the model for a general workshop is of thousands upon thousands of constraints and variables it is
difficult to be solved by the simplex method on a personal computer within acceptable time. for this end
we propose that karmarkar’s algorithm and an interaction/prediction approach based on karmarkar’s
algorithm respectively should be applied to solving the model the former for the large scale problems
and the latter for the very large scale. the above-mentioned lp problem is also an hpp problem because
the karmarkar’s algorithm and interaction/prediction approach based on karmarkar’s algorithm for
solving it are in fact the methods to combine the principles of both a temporal decomposition and a
process one in hpp with the organizational structure of the faw.


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