Modeling of control loop in production sheduling and inventory level control process.
Gjeldum, Nikola ; Tufekcic, Dzemo ; Veza, Ivica 等
Abstract: Performance of manufacturing organization depends on
production scheduling which is an essential part of the management of
production systems. Effective scheduling can lead to performance those
results in meeting the company's customer service goals, and
reducing work-in-process inventories (Wiers, 1997). Objectives of
production control can be graphically represented over time in diagrams:
inventory, lead time, utilization, input orders and output of production
process. In this paper, the fact that the input and output amount of
work coming from released orders of one product are not equal in every
period, requires a technique to balance input against output
continuously, and to establish a control loop.
Key words: scheduling, control loop, inventory, optimization.
1. INTRODUCTION
The input and output amount of work coming from released orders are
not equal in every period, so any shop floor control system has to look
for a technique to balance input against output continuously, and to
establish a control loop (Wiendahl, 1994). The scheduling is carried out
by an employee, a computer program, or a combination of both and acts as
a controller, fixing the planed status and thus leading in the control
line to the actual production process. The process is monitored by
feedback records of the inventory level so as to minimize influence of
disruptive factor that is inconstant released orders. The aim of this
paper is to define adequate mathematical model which is used to
determine the influence of input parameters, release orders quantity and
forecast on inventory level. The closed-loop scheduling and control
cycle responsible for a continuous flow of manufacturing process and
inventory level maintenance is one of internal parts of production
scheduling and control process.
2. PRODUCTION PROCESS SIMULATION MODEL
To schedule production of one product, wood casement with standard
dimensions and shape, which consists of three production processes, the
simulation model has been made. The material flow in production process,
information flow, and all process data necessary for building a
simulation model is shown on Fig. 1.
[FIGURE 1 OMITTED]
The examined model, created using ProModel software tool, has all
necessary properties of production process. The total lead time L/T for
the product is 2.6 working days. The inventory level in the warehouse of
finished products is set to value which is suitable for fulfilling the
costumer orders for at least 7 days, according to the current orders
quantity. The additional constraint is limit of inventory level on one
hundred products in case that orders for 7 days are smaller then that
inventory level quantity of one hundred finished products. The input and
output curves of the work center within a period generally do not follow
a straight line, and vary quite strongly at times, and leads to
producing an unsteady inventory level. Because of that, simulation of
the model was examined and optimized for the orders entered into
simulation with external file generated by random number generator with
addition of noises in generation like difference of order level for
different periods of year. Orders used in simulation for optimizing the
production plan are shown on Fig. 2. for one year period.
Input parameters used to establish a closed loop production control
have been evaluated at the end of the scheduled week, at Wednesday morning. The production demand according to the weekly plan quantity Q
can be expressed by a linear equation:
Q = [x.sub.0] + [a.sub.1] [x.sub.1] + [a.sub.2] + [x.sub.2] +
[a.sub.3][x.sub.3](1)
The value [x.sub.0] is evaluated at the end of scheduled week, and
gives a production plan according to the produced quantity in the last
week of simulation. This is the main member of equation and gives a
constant production plan in case those other parameters in equation are
equal to zero.
The first parameter [x.sub.1] is the difference between quantity in
orders from last simulated week and the week before. The evaluated
number is then multiplied with the factor of signification [a.sub.1].
The value of this product, gives the partial influence on the production
demand for next week of simulation on the way that it increases or
decreases the production demand compared to last week of simulation.
The second parameter [x.sub.2] is difference between current
inventory level in the final product warehouse and calculated inventory
level according to the last evaluated daily order quantity multiplied by
7 days, or constraint of one hundred finished products.
[FIGURE 2 OMITTED]
The third parameter [x.sub.3] is the difference between the current
production demand and forecast for next three months gathered by the
costumer. Demand forecasting is frequently different from the actual
production plan (Nishioka, 2003). Those three months forecast is based
on the expected orders in next three months period according to the
external file order list, but modified with normal distribution factor
which make those data different then future orders quantity.
3. OPIMIZATION PROCESS
Optimization of the model has been executed by changing input
factors and monitoring a result of an objective function. The objective
function is the inventory level in the final product warehouse.
According to the lean production principles, excessive production and
high inventory level are the biggest waste in production process (Rother
& Shook 2003). Inventory level higher then it is necessary for
fulfilling the costumer demands, leads to a additional costs in
warehouse. To decrease overall costs, the inventory has to be maintained
at the lowest possible level, but high enough to realize all customer
orders in next period.
Simulation has been executed with a goal to minimize number of
product days in the final product warehouse, by changing factors of
significations a1, a2 and a3. These factors, together with examined
parameters, make changes in production week plan quantity. Optimal
factors of significations are given in Table 1.
The optimal mathematical model for the next week plan for the shop
floor can be expressed by equation:
Q = [x.sub.0] + 0.13[x.sub.1] + 0.08[x.sub.2] + 1.4[x.sub.3] (2)
During simulation ProModel software constantly monitors content of
finished product warehouse. The content is daily evaluated from the
simulation and added to accumulated value in previous period. The value
of total inventory shows how many finished product days are stored in
the warehouse.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
On the Fig. 3. is shown inventory level in the finished product
warehouse over one year simulated period. The inventory level is
unsteady, due to a very big variation in orders quantity. In case of
examined production process, customer demands increases up to five times
different value in period within one month. The optimal mathematical
model handled this situation with rapidly increasing of production
demand on shop floor. After normalizing the order quantity on the
average level, the model needs additional period for stabilization of
inventory level. On Fig. 4. is shown the weekly production plan
generated by optimal mathematical model.
Optimal mathematical model generated by optimization of production
process gives an optimal reaction of production on shop floor on varying
released orders quantity. Examination of mathematical model with
additional different orders lists generated by random number generator
gives also the optimal results with optimal mathematical model control.
The future research will be in the direction of implementation of
this or similar simple mathematical models into simulation with two or
more different products processed on the group of work centers on the
same shop floor. In manufacturing systems with a wide variety of
products, processes, and production levels, production schedules can
enable better coordination to increase productivity and minimize
operating costs (Herrmann, 2006).
4. CONCLUSION
The aim of this paper was to define adequate mathematical model
which is used to determine the influence of input parameters, release
order quantity and forecast on inventory level in the finished product
warehouse. Conclusion can be made that the mathematical model, which is
used in control loop, has to be optimized to give best response on
actual released orders quantities. If mathematical model has the members
of equation which gives a faster, or slower response then optimal, the
production plan for next week will be or insufficient, or excessive for
fulfilling the costumer demands. For given input parameters from
simulation model in the mathematical model for production plan, any
other factors of signification values will give the larger total
inventory value which makes that mathematical model for control not good
as optimal one. For the production processes with different lead times
the speed of response on changes in order quantity, and inventory level,
will be different, and the mathematical model can be optimized by the
simulation for that particular process. This approach in production
scheduling can be used for encouragement of production control personnel
in defining the production plans for the shop floor.
5. REFERENCES
Herrmann, W. (2006). Impr oving Production Scheduling: Integrating
Organizational, Decision-Making, and Problem-Solving Perspectives,
Available from: http://www.isr.umd.edu/Labs/CIM/projects/ierc2006/IERC-2006.pdf Accessed: 2007-06-14
Nishioka, Y. (2003). Collaborative Agents for Production Planning and Scheduling, Available from: http://www.pslx.org/en/doc/TR-001.pdf
Accessed: 2007-06-12
Rother, M. & Shook, J. (2003). Learning to See, The lean
enterprise institute, ISBN 0-9667843-0-8, Brookline
Wiendahl, H. (1994). Load-Oriented Manufacturing Control,
Springer-Verlag, ISBN 0-387-19764-8, Berlin Heidelberg
Wiers, C. (1997). Human-Computer Interaction in Production
Scheduling, Technische Universiteit Eindhoven, ISBN 90-386-0355-X,
Eindhoven
Table 1. Optimal factors of signification.
[a.sub.1] [a.sub.2] [a.sub.3] Total inventory [product day]
0.13 0.08 1.4 37887
