"MODELING HYBRID PRODUCTION SYSTEMS.
A POSSIBLE CHARACTERIZATION."
Authors:
Rafael RUIZ USANO
Adolfo CRESPO MARQUEZ
Dpto. de Organizacién Industrial y Gestién de Empresas
Escuela Superior de Ingenieros Industriales
UNIVERSIDAD DE SEVILLA
41012 - SEVILLA (SPAIN)
ABSTRACT
The paper describes the process of modeling, under the
system dynamics point of view, a production planning problem
which is managed using a hybrid "push/pull" approach.
The results obtained from the hybrid model are compared, for
several production scenarios,..to. those. obtained for push and
"pull" schemes separately. Computational results are presented
and discussed under financial and non-financial perspectives.
INTRODUCTION
Some advisable configurations for hybrid control schemes in
production were suggested by Karmarkar (Karmarkar U.S., 86, page
26). The possibility of building a hybrid system considering the
utilization of a kanban approach for those stages in the factory
which have short and predictable lead times, and a "push" (MRP)
approach for the ones with a long and variable lead time, is one’
of the ideas that Karmarkar proposes to develop.
This paper, departing. from a.three. stages kanban system
model already validated (O’Callaghan R., 86), introduces the new
contro] schemes which lead .to,. the hybrid "push/pull"
configuration, evaluating. and measuring the performance of the
new model for scenarios in which it should be more efficient.
SYSTEM DYNAMICS '93. 419
THE INITIAL PULL MODEL
The kanban system original model is basically the one
described by O'Callaghan, shown in figure 1.
Figure 1. ©The kanban system. model.
In that model, “for-every-stage of the process, production
is ordered by means of the remaining kanbans (production orders)
at the end of every kanban cycle, such as:
Production Rate (PR) =Production Orders (PO) /kanban eyele (IT)
Moreover, in every stage, the production orders can ‘be
calculated as follows:
POi =.NKi * UCi--' Ti - WIPi
where:
NKi : Number of kanbans for the stage number i.
UCci : Units per container (or per kanban)
Ii : ‘Inventory placed at the end of the stage.
WIPi: Work in process in the stage.
420 SYSTEM DYNAMICS '93
The number of kanbans is calculated every time a planning
period starts and according to the production plan selected for
that period of time.
NKi = (PP/UCi) (LTi+ITi) (1+SSi)
where:
PP :Production plan for the particular planning period.
LTi:Lead time of the stage number i.
ITi:Kanban cycle for the stage number i.
SSi:Safety period considered for the stage i.
The production plan in the original model is estimated
taking into account both the orders backlog, and the demand
forecast.
PP = X * F + (1-X) * DSR
Where:
X : Weight factor.
Demand forecast .*
: Desired shipment rate = BKL/NDD
BKL: Orders backlog
NDD: Normal delivery delay
The only one exogenous’ variable in the model is the market
demand. The production plan,. as determined by the number of
kanbans, introduces the effects of variations in the market
demand for every step of production. These effects are updated
every planning period.
The kanban system, by itself, can be considered as a mixture
of push and pull. effects. The process control is predominatelly
"pull", but a "push" effect is occasionally introduced into the
system, adding or substracting kanbans every time a new
production plan is calculated.
+ The dynamo ecuation for this forecast would be one such
as: F.K=SMOOTH(D.K,TD) where TD is the time considered for the
forecast.
SYSTEM DYNAMICS '93 421
THE INITIAL PUSH MODEL
The fundamentals of the push pattern used for building the
hybrid control scheme are described by Crespo & Ruiz-Usano
(Crespo A. & Ruiz-Usano R., 92). The model’s most important
feature is the method of calculation used to achieve the net
requirements of every stage of production (i.e. production
rates), which causes a "push" effect in the system according to
variations in demand. That means that there is a short delay in
the transmission of. the market evolution: to» the production
stages.
Gross requirements of the last stage = PP
NRi = GRi + (SSi - Ii)/TAT
GRi = NR
Where:
NRi Net requirements of the stage number i.
GRi Gross m " = .
TAI : Fime to adjust the inventory.
PP : Production plan.
This idea follows the basic structure shown by Morecroft
(Morecroft J., 83) for an MRP system dynamics model.
tL = fn bes gh
PR2_5 i) —_$.NRI_}GrRnM > *
a a
PORI¢ ~~ PR1_s IRM_i +5, NRRM.
i hae ae
AMAR *___RMOR,
DEMAND > PP Mt
Figure 2. The "push". MRP system model.
422 SYSTEM DYNAMICS '93.
THE HYBRID CONTROL SCHEME
In the hybrid control, the "push" approach is used to manage
the first stage of production, considered in this case the
Procurement Stage, before the assembly line. The lead time of
this stage, which is equal to the suppliers delivery time, will
be longer than the lead times considered for the stages 2 and 3
(subassembly and assembly processes) managed by the "pull" kanban
system.
According to the previous paragraph, an interface between
the pull system in assemby and the push system in procurement,
must be established.
The model presented here calculates the net requirements of
all production stages, taking into account the quantity of
inventory remaining after each stage. These calculations will
signal a requisition rate for raw materials to suppliers, but
will never indicate a value to set assembly production rates. In
fact, subassembly and assembly production rates may be calculated
following the normal kanban procedure.”
MRP DECISION
KANBAN DECISION
Figure 3. The Hybrid approach.
SYSTEM DYNAMICS '93 423
THE SCENARIOS
All
LT1 = 2 Days.
LT2 = .5 Days.
LT3 = .5 Days.
CAPACITY CONSTRAI|
Demand increase
Step of
Step of
Breakdown in one stage
sc.3. One-day
sc.4. One-day
se.5. One-day
Bottlenecks
Procurement:
Subassembly
-Assembly
NT
10% after
20% after
de
de
in
in
in
breakdown
breakdown
breakdown
120 units per
scenarios will consider that.
and. day.
and. day.
lst. stage.
and. stage.
3rd. stage.
Considering a 20 day demand increase pulse of 120
units/day:
sc.6. In the
sc.7. In the
sc.8. In the
ist. stage only 110 units per day.
2nd. stage only 110 units per day.
3rd. stage only 110 units per day.
CRITERIA FOR MODEL PERFORMANCE EVALUATION
Financial Aspects
c.1. Sales
c.2.
c.3.
Non-Finantial Aspects
c.4.
c.5.
Money in inventory (average).
Money turnover
units in inventory (average)
time in the system for one unit (average)
SYSTEM DYNAMICS '93
day in all stages.
EXPERIMENTAL RESULTS
Financ.
SCENARIO 1- sc.1. Financ. | Financ. | Non-Fi. | Non-Fi.
c.l. C.2. C.3. C.4s c.5.
Kanban Model 21870 25,091 847,1 456,56 4,3001
Hybrid Approach 21870: 28,046 787,51 412,35 -|3,8868
SCENARIO 2- sc.2.
Kanban Model 23410 29,435 762,2 431,42 3,871
Hybrid Approach 23410 31,063 717,55 410,87 3,6875
SCENARIO 3- sc.3.
Kanban Model 20000 24,865 805,07 432,66 4,3265
Hybrid Approach 20000 27,829 721,02 390,69 3,906
SCENARIO 4- sc.4.
Kanban Model 20000 | 24,452 | 820,89 | 439,29 | 4,3907
Hybrid Approach 20000 27,652 725,53 393,16 3,9297
SCENARIO 5- sc.5.
Kanban Model 20000 | 24,391 823,5 | 440,18 |-4,3991
Hybrid Approach 20000 27,764 720,38 390 5.9
SCENARIO 6- sc.6.
Kanban Model 21600 28,416 747,99 416,67 3,9845
Hybrid Approach 21600 30,588 691,5 390,62 S,/ 7293:
SCENARIO 7- sc.7.
Kanban Model 21600 | 24,069 | 881,75 484,2 | 4,6213
Hybrid Approach 21600 26,296 609,57 449,2 4,2867
SCENARIO 8- sc.8.
Kanban Model 21600 22,652 955 507,03 4,8285
Hybrid Approach 21600 25,331 852,24 456,31 4,3461
SYSTEM DYNAMICS '93 425
CONCLUSIONS
This research indicates that the utilization of system
dynamics as a methodology to study production alternatives is an
effective strategy for management téams. Problems can be’ studied
according to. the management perpectives most. adequate for
individual environmental conditions. Simulations using system
dynamics present an easy way to try different solutions to
various. problems by. means. of hybrid configurations. System
dynamics can also aid in the search for parameter: values which
contribute to the system compensation when managed with a hybrid
scheme.
BIBLIOGRAPHY
Karmarkar U.S. "Push, Pull. and Hybrid control schemes"
Quantitative Methods, working paper series.QM 86-
14, The Graduate School of Management, University
of Rochester, 86.
Morecroft J.D. OA System Perspective on MRP". Decision Science.
Vol. 14 N°.1. 1983.
Crespo A. & Ruiz Usano R. "New Production Planning Systems: A
System Dynamics Perspective". Proceedings of the
International System Dynamics Conference.
Utrecht, The Netherlands. 1992.
426 ; SYSTEM DYNAMICS '93
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