Novel Capacity Planning Methods for Flexible and Reconﬁgurable

Assembly Systems

avid Gyulai

Fraunhofer Project Center for Production Management and Informatics, Institute for Computer Science and Control,

Hungarian Academy of Sciences, Kende str. 13-17, Budapest, Hungary

Department of Manufacturing Science and Technology,

Budapest University of Technology and Economics, Egry J. str. 1, Budapest, Hungary

1 STAGE OF THE RESEARCH

The importance of efﬁcient planning methods is in-

creasing with the evolution of manufacturing systems,

since ﬂexible and reconﬁgurable system structures re-

quire different planning approaches than the dedi-

cated ones. The research presented in the paper is

focused on production and capacity planning meth-

ods, which are able to cope with the dynamic changes

that occur in the reconﬁgurable and ﬂexible assembly

systems. In the preceding publications of the author,

some novel approaches were presented that support

the management of modular reconﬁgurable resources

and complex product portfolios.

A simulation-based technique was introduced in

(Gyulai et al., 2012) and (Gyulai and V

en, 2012) that

deﬁnes the boundaries and components of a modular

reconﬁgurable assembly system for companies that

face with ﬂuctuating production volumes and have

end-of-life-cycle products. In that case, frequent revi-

sion of the production system structure is required in

order to gain production space and to harmonize the

operation of the system with the order stream. The

proposed method separates the low- and high- vol-

ume products and product families dynamically, and

supports system parameter setting and ﬁne tuning of

production capacity.

As a generalization of the above described prob-

lem, the line assignment for a complex product port-

folio and the simultaneous production and capacity

planning of a modular reconﬁgurable assembly sys-

tem is presented in (Gyulai et al., 2014a) and. The

approach offers an integrated way for the assignment

of products to dedicated or reconﬁgurable resources

and for the production planning of the reconﬁgurable

ones. An essential element of the system —developed

within an industrial project— is that cost predictions

computed by multivariate linear regression on virtual

production scenarios support the solution of the line

assignment problem. The production planning level

also incorporates a sequencing module for minimiz-

ing the number of reconﬁgurations.

For the line assignment problem, a novel method

is proposed in (Gyulai et al., 2014b) that com-

bines discrete-event simulation with statistical learn-

ing models to support the strategic capacity planning

processes on a long-term horizon, based on the fore-

cast market conditions.

2 OUTLINE OF OBJECTIVES

Within the PhD research, the primary aims are to de-

ﬁne production and capacity planning methods that

efﬁciently support the production and capacity plan-

ning of the ﬂexible and the modular reconﬁgurable

assembly systems. Although several different ap-

proaches exist for similar problems, many of them

consider problem sizes with only a few products

and/or limited capabilities regarding the diversity of

product mix and degree of system ﬂexibility and scal-

ability. The target planning methods have to meet the

following requirements:

• handle several products/product families with dif-

ferent life-cycle stages and thus different yearly

volumes;

• solve the line assignment problem (that is often

referred to as capacity investment strategy) con-

sidering deterministic as well as stochastic cases;

• support the capacity and production planning of

modular reconﬁgurable assembly systems that ap-

plies changeable modules for the different assem-

bly processes;

• deﬁne reliable production planning models for

mixed-model ﬂow assembly lines, where process-

ing times and rework rates (based on the reject

rates) vary;

Gyulai D..

Novel Capacity Planning Methods for Flexible and Reconﬁgurable Assembly Systems.

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

• support the planning processes with ﬂexible meth-

ods applying self-building mathematical models;

• in order to ensure the reliability of the methods,

such optimization methods should be considered

that integrate mathematical modeling with statis-

tical learning, in order to provide reliable plans

based on real production data;

The above requirements are summarized on a con-

cept map that emphasizes the problem side of the re-

search topic as well as the considered supporting tech-

niques and technologies (Figure 1). The green boxes

highlight the concepts that are going to be investi-

gated to carry out new scientiﬁc results, or already

supported by new achievements within the current re-

search.

Figure 1: Concept map of the research topic.

3 RESEARCH PROBLEM

In the capacity management problem, different pro-

duction resources are considered that provide differ-

ent level of ﬂexibility and capacity to meet the re-

quirements given by the order stream. Dedicated

assembly systems provide a large-scale capacity for

producing one product in a high volume. Flexible as-

sembly systems are designed for producing a set of

similar products/product families with lower capac-

ity but higher ﬂexibility regarding the volume and the

product mix. Reconﬁgurable assembly systems pro-

vide better system scalability and product mix ﬂexi-

bility even in case of different product families while

keeping relatively higher throughput than the ﬂexible

lines.

In order to clarify the research topic, the bound-

aries of the problem in question are deﬁned around the

assembly segment of individual plants, without focus-

ing on the corresponding supply chain processes. The

considered capacity management problem is split up

into two main sub-problems according to the focus,

nature and time horizon of the decisions involved.

Figure 2: Illustration of the capacity management problem.

3.1 Line Assignment

The line assignment problem is aimed at minimiz-

ing the production costs by the optimal assignment

of the products to the dedicated/ﬂexible or reconﬁg-

urable resources. The time horizon of the decision is

some months, and the objective function includes the

costs that are relevant on the strategic level. The to-

tal production cost is composed of the investment, the

operation, and the personnel costs. When searching

for the optimal allocation, the actual customer orders

as well as the forecast volumes are considered on the

predeﬁned time horizon. The line assignment prob-

lem can be seen as subdividing the set of products, P,

into products assembled on the dedicated lines, D, on

the reconﬁgurable lines, R, and products outsourced,

OS. In the relevant literature, the line-assignment

problem is often referred to as capacity investment

strategy whose objective is to determine the optimal

capital investment in types of production capacities

with distinct ﬂexibility.

For products p ∈ D or p ∈ OS, the production costs

can be assigned directly to individual products, and

denoted by a parameter C

. In case p is assembled on

a product-speciﬁc dedicated line, the production cost

can be computed as the sum of the investment cost

(zero if a dedicated line for p already exists), a high

ﬁxed cost, and a volume dependent operation cost.

Analogously, for an outsourced product p, C

is com-

posed of a small ﬁxed cost and a relatively high unit

cost.

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In contrast, the cost related to the reconﬁgurable

lines depends on the actual product mix and the pro-

duction plan adopted, and cannot be directly divided

among individual products. With a given optimiza-

tion model for production planning, this cost can be

described as a general, non-linear function of the pro-

duction volumes, resource requirements, and further

parameters of the products assembled on the recon-

ﬁgurable lines. Therefore, the overall production cost

incurred in the reconﬁgurable system is captured by a

function C

, and it incorporates the investment costs

and the operation costs related to those lines. A key

challenge in the line assignment problem is comput-

ing, as well as predicting this cost for an arbitrary set

of products R.

3.2 Production and Capacity Planning

On a lower level of the decision hierarchy, the produc-

tion and capacity planning problems of the ﬂexible

and reconﬁgurable assembly systems are considered,

namely to minimize the production costs on a certain

discretized time horizon by optimal lot-sizing and ca-

pacity allocation policy. In order to ﬁnd the optimal

production lot-sizes and capacity assignment, novel

mixed-integer programming approaches are required

that capture the dynamic underlying processes that

occur in ﬂexible and reconﬁgurable assembly sys-

tems.

On the one hand, many different lot-sizing ap-

proaches exist that focus on dedicated and ﬂexible

assembly systems, but their applicability on modular

systems is limited due to the different nature of the

underlying processes. On the other hand, the existing

methods are usually based on some assumptions as

for example the deterministic process times, capac-

ity requirements or production costs. Therefore, the

research is focused on the implementation of novel

methods that face such challenges like the variance of

the production data and dynamic nature of the pro-

cesses.

The general objective of the mid-term plans is the

maximization of the proﬁt or minimization of the cost

corresponding to the execution of the calculated plan.

These objective functions are usually composed by

different factors. On the one hand, production-related

costs like the deviation costs of the order fulﬁllment

(represented by tardiness or delivery performance),

operation costs of the machines and control of the

human operators strongly depend on the calculated

plan. On the other hand, the optimal number of the

resources and the cost of the manpower are capacity

related factors that affects highly not only the costs

but the system’s performance as well.

4 STATE OF THE ART

Strategic capacity planning has broad literature, how-

ever, the line assignment or capacity investment strat-

egy considering reconﬁgurable resources is a rela-

tively novel ﬁeld in production research.

Ceryan and Koren introduce an approach that for-

malize capacity planning as an optimization problem

based on the ﬂexibility premium and determines the

optimal resource portfolio for a ﬁxed planning hori-

zon (Ceryan and Koren, 2009). Niroomand et. al pro-

pose a method based on mixed integer programming

that determines the cost-optimal capacity set based on

the lifecycle of a product discretized in time. The

method efﬁciently considers the reconﬁgurations oc-

curring in a reconﬁgurable system that applies plat-

forms and changeable modules (Niroomand et al.,

2012).

Based on the dynamically changing nature of the

order stream, the capacity and system conﬁguration

planning process is often formulated as a Marko-

vian Decision Problem that can be solved by dy-

namic programming or learning algorithms (Asl and

Ulsoy, 2003)(Colledani and Tolio, 2005)(Deif and El-

Maraghy, 2006). These methods consider capacity

planning and management as a sequence of decisions

on a longer horizon, and their objective is to ﬁnd an

optimal policy to minimize the costs on the long run.

Hon and Xu propose a simulation-based method to

optimize the system structure of a reconﬁgurable sys-

tem based on the different stages of the products’ life-

cycle (Hon and Xu, 2007).

The production planning problems of the ﬂexi-

ble ﬂow assembly lines are usually aimed at min-

imizing the costs inﬂuenced by the due dates, in-

ventories and capacity requirements (Boysen et al.,

2009a) and (Boysen et al., 2009b). In case of manu-

ally operated assembly lines, the most crucial point in

planning is the workload planning and capacity con-

trol of the human operators. In (Giard and Jeunet,

2010), the authors present a mixed-integer program-

ming (MIP) approach to simultaneously solve the pro-

duction planning and workload smoothing problem in

case of mixed-model assembly lines.

5 METHODOLOGY

In order to satisfy the requirements given by dynamic

and changeable processes in the ﬂexible and recon-

ﬁgurable systems, such planning methods are pro-

posed that cope with the underlying production pro-

cesses and capable of adopting to the changes and

disturbances. As depicted by Figure 1., the research

NovelCapacityPlanningMethodsforFlexibleandReconﬁgurableAssemblySystems

is focused on implementing novel capacity manage-

ment/production planning methods for assembly sys-

tems and ﬂexible solutions that support them from

technical side (simulation, mathematical models etc.).

5.1 Novel Capacity Management

Approaches

5.1.1 Deterministic and Stochastic Models for

the Line Assignment Problem

In order to determine the cost-optimal line assign-

ment, deterministic as well as stochastic optimization

problems can be deﬁned. In the deterministic case,

the following assumptions are made. Order volumes

and forecasts are available for the given time horizon.

It is assumed that the capacity of a single line is suf-

ﬁcient to assemble the product in the desired volume,

and therefore, the option of dividing the order volume

between different production modes can be ignored.

The price of the machines and the costs of the hu-

man operators are constant over time. As previously

stated in section 3.1, the greatest challenge in solving

the line assignment is the nonlinear nature of the cost-

function corresponding to the reconﬁgurable lines. To

tackle this, a regression-based approach is introduced

in (Gyulai et al., 2014a), where the multivariate pre-

diction function is integrated in the mathematical op-

timization model.

In the stochastic line assignment problem, the or-

der volumes and forecasts are given by probability

distribution functions. The price of the machines and

the costs of the human operators may also change

over time. Therefore, the stochastic line assignment

problem can represented by a Markovian Decision

Process (MDP), whose objective is to ﬁnd the cost-

optimal policy to assign the products to the different

types of production lines beside the sufﬁcient amount

of capacities. By deﬁning a proper function that gives

the production costs in each time step (state), the

stochastic line assignment problem can be solved by

reinforcement learning methods.

5.1.2 Flexible Mid-term Planning Methods

Within the ﬁrst stage of the research, a novel produc-

tion planning method was proposed, that solves the

integrated conﬁguration and scheduling of the system.

As described in Section 3.2, the production planning

models for the different assembly system types need

to consider diverse factors to provide the optimal so-

lution. Since there is no tight link among the system

types from modeling perspective (e.g. a product is

assembled in two different systems, or common ma-

terial provision constraints), the mid-term planning

problem can be decomposed into sub-models for the

different systems.

The following model provides and optimal so-

lution for the simultaneous production and capacity

planning in a modular reconﬁgurable system. The

problem is solved on a discrete time horizon with time

units corresponding to individual shifts. The planning

problem is formulated as a MIP as follows.

Parameters and sets:

J = {1. . . l} set of machine types

P = {1. . . m} set of products

T = {1 . . . n} set of shifts

purchase price of machine j

operation cost of machine j

per shift

h cost of an operator per shift

processing time of product p

changeover time for product p

the required number from ma-

chine j by product p

Decision variables:

= {1 . . . l} required quantity of ma-

chine j

t p

the number of lines produc-

ing p in shift t

min

∑

j=1

+ h

∑

t=1

∑

p=1

t p

∑

t=1

∑

p=1

∑

j=1

t p

subject to

≥

∑

p=1

t p

+ s

) ∀ j, t

∑

p=1

t p

∀p

≥ 0 x

t p

∈ {0, 1} s

t p

≥ 0

Considering the production planning problem of

the ﬂexible assembly lines, the goal is to minimize

the total production cost mostly inﬂuenced by the ca-

pacity usage, inventories and tardiness. This gen-

eral problem is often referred to as master schedul-

ing, and decides on the type and amount of products

to be produced in the planning horizon and assigns

them to planning periods (e.g. shifts) (Boysen et al.,

2009a). Although several efﬁcient approaches exist

to determine the optimal mid-term production plan,

many of them disregard the underlying processes that

often leads to infeasible plans due to unplanned ca-

pacity shortages. These problems are often caused by

the varying processing times and failures and reworks,

that can be considered in novel planning models that

integrate statistical models in order to apply reliable

historical data.

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5.2 Novel Planning Techniques

5.2.1 Statistical Learning Methods Integrated in

Optimization Models

In such models, the constraints and/or the objective

function can rely on statistical learning models that

are built upon real historical data, and able to pre-

dict accurately the parameters like the idle times, ca-

pacity requirements. In a preceding publication of

the author, a novel decision support method was pre-

sented that integrates the mid-term capacity planning

results (section 5.1.2) in a deterministic line assign-

ment model by applying prediction models (Figure

3) (Gyulai et al., 2014a). Integration is established

via feedback from production planning to line assign-

ment, in the form of multivariate regression for esti-

mating the cost function.

Figure 3: Workﬂow of the capacity management method.

5.2.2 Self-building Mathematical Models

To extend the scope of the previously described meth-

ods, and increase their ﬂexibility regarding the fre-

quent modiﬁcations in the system structure, a rule-

based, self-building mathematical modeling frame-

work is required. Such self-building approaches are

commonly applied in simulation modeling and pro-

vide the tight coupling between the physical structure

of the production system and the corresponding simu-

lation model, applying low-level control data or high

level production data (Pfeiffer et al., 2012), (Popovics

et al., 2012).

In order to deﬁne the mathematical planning

model of ﬂexible and reconﬁgurable systems, the

boundaries of the modeling set as well as the data

structure have to be well-deﬁned. The aim of self-

building modeling in this case is to set up a meta-

modeling framework that is capable of providing fea-

sible mid-term production plans for mixed-model as-

sembly lines and modular reconﬁgurable assembly

systems. The robustness of the plans would be based

on real production data collected from the manu-

facturing execution system (e.g. processing times)

and the closed-loop evaluation procedure provided

by discrete-event simulation. Although there is a

lack of such available solution in the literature, some

existing approaches offer high-level ruled-based and

meta-modeling techniques for production planning

(Bousonville et al., 2005), (Iijima, 1996).

6 EXPECTED OUTCOME

In case of the line assignment problem, the goal is

to provide the optimal solution for the deterministic

and the stochastic case as well. In the determinis-

tic problem, the objective is to provide the optimal

solution by minimizing the total production costs in

a particular time considering the orders-on-hand and

the forecast volumes. In an ideal case, the line as-

signment can be iterated over time in a rolling hori-

zon framework which ensures the cost-optimal as-

signment among lines as market conditions vary.

Regarding the stochastic line assignment problem

that considers the volatility of the market conditions

more efﬁciently, the ideal solution would be the op-

timal, long term capacity management policy that

determine when and how to relocate products from

reconﬁgurable lines to dedicated ones (or outsource

them), and vica versa. On the one hand, such pol-

icy would rely on the product life-cycle that gives an

estimation about the production volumes for the up-

coming periods with a certain level of conﬁdence. On

the other hand, ﬂuctuating order streams and chang-

ing parameters (e.g. the price of the resources) can

be forecast by applying probability density functions

as well. By this way, the problem can be formulated

as a Markovian decision process, that can be solved

by reinforcement learning or stochastic optimization

techniques.

On the mid-term horizon, two main outcomes are

expected. For the modular, reconﬁgurable systems,

the mid-term plan should provide the lot-sizes, the re-

quired amount of human workforce and the number

of reconﬁgurable resources in discrete time (shifts).

The plan must be optimal by minimizing a function

that is composed of the cost of reconﬁgurations, hu-

man labor and the investment and operational cost of

the resources.

As for the mixed model assembly lines, the lot-

sizing models should provide plans that are similar to

the previous case, however, these plans have to con-

sider the on-line production data like the rework rates

and ﬂuctuating processing times. Furthermore, the

NovelCapacityPlanningMethodsforFlexibleandReconﬁgurableAssemblySystems

optimal number of the operators working at the line

and the optimal capacity control of the human work-

force are also need to be considered, since their im-

pact on the production planning factors like process-

ing times and WIP are critical.

The implementation of the methods and tech-

niques in a framework (as depicted in Figure 1) would

result in a comprehensive production planning and

capacity management solution that provide reliable

long- and mid-term solutions for companies apply-

ing identical assembly system structures. The core

of the planning system would be the common pro-

duction database that could be fed either by the pro-

duction planners or the MES system. The database

would form the basis for the integrated optimization

models as well as for the self-building mathematical

models that can provide feasible solution for the line

assignment problem and the mid-term capacity and

production planning problems.

ACKNOWLEDGEMENTS

Research has been partially supported by the Hun-

gary, Grants No. ED 13-2-2013-0002 and VKSZ 12-

1-2013-0038.

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