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Int J Flex Manuf Syst

DOI 10.1007/s10696-006-9001-5

Controlling flexible manufacturing systems based on a

dynamic selection of the appropriate operationalcriteria and scheduling policy

Boris Shnits David Sinreich

C Springer Science+Business Media, LLC 2006

Abstract This study presents the development of a multi-criteria control methodology

for flexible manufacturing systems (FMSs). The control methodology is based on a

two-tier decision making mechanism. The first tier is designed to select a dominant

decision criterion and a relevant scheduling rule set using a rule-based algorithm. In

the second tier, using a look-ahead multi-pass simulation, a scheduling rule that best

advances the selected criterion is determined. The decision making mechanism was

integrated with the shop floor control module that comprises a real-time simulationmodel at the top control level and RapidCIM methodology at the low equipment

control level.

A factorial experiment was designed to analyze and evaluate the two-tier deci-

sion making mechanism and the effects that the main design parameters have on the

systems performance. Next, the proposed control methodology was compared to a

selected group of scheduling rules/policies using DEA. The results demonstrated the

superiority of the suggested control methodology as well as its capacity to cope with

a fast changing environment.

Keywords FMS control Adaptive scheduling Simulation-based-control DEA

1 Introduction

At the beginning of the 20th century, automation played an important role in improving

productivity and quality while reducing cost. However, there was a serious drawback

to this early automationit was fixed, rigid, and tailored to each specific product.

B. Shnits () D. Sinreich

Davidson Faculty of Industrial Engineering and Management,

TechnionIsrael Institute of Technology,

Haifa 32000, Israel

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B. Shnits and D. Sinreich

Starting from the 1970s, there was a notable increase in the demand for product

variety, fast delivery, and high quality at affordable prices. To survive in fast changing

markets, many manufacturing companies had to cope with frequent model changes and

small production lots. The result was that flexibility and efficiency became essential

requirements in many manufacturing systems. Today we take it for granted that wecan purchase diverse commodities, from cars to computers, from clothing to shoes, at

affordable prices.

Instrumental to these achievements are computer integrated manufacturing (CIM)

and flexible manufacturing systems (FMSs) that offer the flexibility needed as a re-

sponse to fast changing market demands, yet maintain a high level of productivity

(Groover, 1987; Womack et al., 1990). These systems enable flexibility largely from

the use of versatile and/or redundant machines that facilitate alternative routing in

the system (Byrne and Chutima, 1997; Sabuncuoglu and Lahmar, 2003). The intro-

duction of alternative routing made it possible to better balance machine workloadsand achieve higher system robustness and productivity under dynamic conditions that

are caused by unexpected rush work orders and/or machine failures. As a result, it

is clear that the performance of an FMS is highly dependent on the selection of the

correct scheduling policy to control the system. This is not a simple task, especially

since product mix and overall system objectives change over time at a continually

increasing pace. To cope with these changes, Chandra and Talavage (1991) as well as

other researchers suggested postponing part routing and machine scheduling decisions

as much as possible. This way many more production options are kept open, and the

systems flexibility is better exploited.

Although all industrial organizations share the same main goal (profit), over time

changing internal and/or external settings may dictate different temporary objectives

for the manufacturing system, such as minimizing flow time, minimizing tardiness,

maximizing throughput, and minimizing WIP. This means that the shop floor controller

(SFC), in order to increase the systems effectiveness, has to have the capability of

dynamically addressing multiple criteria measures.

2 Literature review

FMS is a very popular research topic. Therefore, a large number of papers addressing

issues such as design, control, and analysis can be found in the literature. See review

papers such as Gupta et al. (1991), Rachamadugu and Stecke (1994), Balogun and

Popplewell (1999), and Chan et al. (2002). A major concern for some of these papers is

improving the effectiveness of FMS operations through the use of dynamic scheduling

and control methodologies. The following literature review focuses on different aspects

of this topic.

Most studies addressing this topic use adaptive or reactive scheduling that enables

an FMS to cope with randomness and variability by determining at every decision

point an appropriate scheduling policy or rule, based on the current state of the shop

floor. Different methods have been used to select dynamically the most appropriate

scheduling policy. Most of these methods are based on heuristics and use dispatching

rules.

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Controlling flexible manufacturing systems based on a dynamic selection

Wu and Wysk (1989), Ishii and Talavage (1991, 1994), and Jeong and Kim (1998)

used simulation to forecast and evaluate the performance of different dispatching rules

in order to select the best rule for the next period. Sun and Yih (1996), Soon and De

Souza (1997), and Arzi and Iaroslavitz (1999) used neural networks as a forecast-

ing mechanism. Shaw et al. (1992) and Piramuthu et al. (1994) exploited inductivelearning to determine the preferable scheduling policies for different shop floor states.

Mesghouni et al. (1999), Qi et al. (2000), Rossi and Dini (2000), and Chryssolouris and

Subramaniam (2001) solved the dynamic scheduling problem in FMS using genetic

algorithms. Yu et al. (1999) and Subramaniam et al. (2000) employed fuzzy logic and

Trentesaux et al. (2000) used intelligent agents to select the appropriate scheduling

rule. Other studies used hybrid schemes such as neural networks and inductive learn-

ing (Kim et al., 1998), fuzzy logic and a genetic algorithm (Fanti et al., 1998), fuzzy

logic and simulation (Kazerooni et al., 1997), and finally a combination of learning,

intelligent agents, and simulation (Aydin and Oztemel, 2000).It is obvious that in order to exploit in full the capabilities of an FMS, its control

system has to be able to cope successfully with changes in the status of the shop floor

such as machine failure and/or maintenance, and changes in the operational objectives

of the system. Nevertheless, many studies (see Piramuthu et al., 1994; Mesghouni

et al., 1999; Aydin and Oztemel, 2000; Rossi and Dini, 2000; Subramaniam et al.,

2000) used a single criteria/objective. This means that all the decisions related to

system operations are based entirely on a single pre-defined criterion.

A different approach was presented by Wu and Wysk (1989), Ishii and Talavage

(1991), Cho and Wysk (1993), Soon and De Souza (1997) and Arzi and Iaroslavitz

(1999). In these studies different criteria measures were used; however the user had to

select these manually for each scheduling period. Although this approach offers some

sort of flexibility in using different criteria measures, the entire process relies on the

users ability and proficiency. The user is required to evaluate the system state at every

decision point and determine the most appropriate criterion for the next scheduling

period. Frequent intervention places an unreasonable mental workload on the user

who needs to derive and analyze the relevant data and decide in real time what the

best course of action for the next scheduling period will be. (This is probably why

none of these studies actually tried to change the criteria measures during the systems

operation.) On the other hand, if the scheduling period is extended to accommodate

the users mental load limitations, the system may lose its ability to respond in a timely

manner to all internal and/or external changes imposed on it.

Due to these limitations, several studies, such as Chryssolouris et al. (1991),

Kazerooni et al. (1997), Bistline et al. (1998), and Fanti et al. (1998) suggested com-

bining the different criteria measures into one, using some kind of weighing scheme.

The weighing scheme has to represent the relative importance of the criteria mea-

sures in achieving the objectives set forth by the organization. Although this approach

promotes the use of different criteria measures, the weighing scheme is fixed and

constant, and therefore, cannot accommodate changes in the organizations prioritiesin response to changing shop or market conditions.

In order to meet the need to improve manufacturing system efficiency under differ-

ent conditions, Yu et al. (1999) developed a mechanism that automatically changes the

systems objectives based on the dynamics of the shop floor. Nevertheless, Yu et al.s

mechanism allows predetermination of only one dispatching rule for each objective,

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and does not incorporate a mechanism to evaluate the effectiveness of this rule under

current shop conditions.

In contrast to previous studies, the current paper suggests a mechanism that se-

lects the shops dominant operational criterion based on shop floor status, production

requirements, and system priorities. The chosen criterion is only one factor amongother relevant factors used to determine the best scheduling policy for the next period.

The dominant criterion and scheduling rule selection process is done on-line, without

interrupting the systems operation and without user intervention.

The rest of the paper is organized as follows: Section 3 describes the proposed two-

tier control scheme. The implementation of the control methodology is presented in

Section 4. Next, the performance evaluation of the proposed methodology is described

in Section 5. Finally, our conclusion and closing remarks are presented in Section 6.

3 The two-tier control methodology

The proposed control methodology expands the adaptive scheduling approach pre-

sented in the literature by enabling changes not only in the scheduling rules but also

in the objective criteria that govern the systems operations and affect the selection of

the appropriate scheduling rule.

3.1 Motivation

This research deals with a production system that operates in a highly dynamic environ-

ment, characterized by random arrivals of work orders, random machine breakdowns,

changes in due dates, and other disturbances. The literature argues that for these types

of environments, an adaptive scheduling approach seems to be more effective than

other scheduling methods. However, the shop floor control systems presented in ear-

lier studies are only partially adaptable to these dynamic changes. This study makes the

case that in a dynamic environment, it is important not only to select a good scheduling

rule, but also to determine an appropriate decision criterion upon which the perfor-

mance of each scheduling rule is measured. To better understand this relationship let

us consider the following example: Let us assume that at a certain point in time all the

work orders on the shop floor have due dates far into the future. In such a case, it could

make sense to select a criterion measure that aims to reduce the work orders flow

time, thereby freeing up machine time to better cope with future unexpected events.

This means that the scheduling rules will be selected based on how they can advance

the objective of minimizing flow time. However, if several urgent work orders arrive

with close due dates and high penalties for tardiness, it makes sense to change the

operational criterion measure to that of minimizing tardiness. This also means that the

scheduling rules will now be evaluated to see how they can advance the objective of

minimizing tardiness.This study focuses on developing and analyzing a multi-criteria adaptive scheduling

methodology for controlling an FMS. In order to cope with the dynamic and multi-

criteria environment in which an FMS operates, the proposed scheduling and control

scheme uses a two-tier control scheme. The suggested control mechanism is self-

adaptable to changing operational objectives and shop floor status. The dominant

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criteria and the best scheduling policy are selected automatically at every decision

point (when it is necessary to make a scheduling decision). The main assumption

is that such a control methodology should improve overall system performance and

efficiency. This concept was first introduced in Shnits et al. (2004) as a possible solution

to the increase in the FMS environments variability and volatility. While Shnits et al.(2004) was only a conceptual and feasibility study, the current study forms in detail

the two-tier decision-making control mechanism and analyses its performance.

3.2 Description of the two-tier control scheme

In contrast to the adaptive control methodologies suggested in previous studies that

were based on dynamic selection of scheduling rules while determining the operational

criterion by a user, the proposed control mechanism selects first the shops dominant

operational criterion and only then the scheduling rule that best advances this criterionis chosen. The dominant criterion and scheduling rule selection process is performed

automatically without interrupting the manufacturing systems operation and without

any user intervention.

The different decision criteria can be classified as either customer-oriented or

system-oriented. The former includes criteria such as minimization of tardiness, late-

ness, number of tardy jobs etc., while the latter includes criteria such as throughput

maximization or flow time minimization. As it turns out, there are rules that better pro-

mote one decision criterion while other rules operate better with another criterion. The

suggested scheduling and control scheme, illustrated in Fig. 1, comprises a two-tier

decision making hierarchy.

Tier 1 is used to determine a dominant decision criterion based on the following:

r Production order requirements include part type information, quantities, arrival

times, due dates, and bonuses/penalties.r Actual shop floor status includes workload evaluation variables such as the number

of parts in the system, the actual system workload; work order urgency variables

such as average time to due date, critical ratio, average slack of parts in queue;

resource availability variables such as number of operating machines, time since the

last failure; and system utilization variables.r Manufacturing system priorities define the organizations operation policy by

determining target WIP levels, accepted tardiness, and customer relative importance.

Based on the chosen decision criterion, a predefined relevant rule set (from a

database of scheduling/dispatching rules) is chosen, together with an appropriate per-

formance measure that is subsequently used to evaluate these rules. Based on the

performance measure determined in tier 1, as well as the current shop floor state

and production order requirements, in tier 2 a scheduling rule (from a set of relevant

scheduling/dispatching rules established in tier 1), which best advances this measure,is chosen using a forecasting mechanism based on a look-ahead multi-pass simulation

module. Once the best scheduling rule is selected, the shop floor control system of the

FMS uses it to dispatch work orders during the next scheduling period.

The activation of the decision making process described above is done using a

triggering module. Following are some possible trigger activation modes:

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Forecasting theBest Scheduling

Policy

Decision

Criterions

Feedback

Tier 1

Real Time Shop

Floor Control

System

Actual FMS

Equipment

Scheduling

Work OrdersEquipmentStatus

Scheduling

Rules

Dominant

Decision

Criterion

Selection of

Dominant

Decision Criterion

and Relevant

Scheduling rulesRelevant

Scheduling

Rules

Production Order RequirementsSystem Priorities

Production Order

Requirements

Trigger forActivation

Decision Making

Mechanism

Trigger

Tier 2

Report

SelectedScheduling

Policy

Shop Floor

Status

Production Order Requirements

Fig. 1 The two-tier control scheme

r Selecting the dominant decision criterion and an appropriate scheduling rule for a

predefined scheduling period.r Reviewing the current decision criterion and scheduling rule at every change in

the shop floor status, e.g., each time a resource becomes available, or every time a

resource fails.r Reviewing the current decision criterion and scheduling rule each time the differ-

ences between the actual shop floor parameters and the expected parameters as

predicted by the last simulation forecast exceed some predetermined threshold.

4 The implementation of the two-tier control methodology

The suggested methodology implementation is largely based on the Arena 7.0 simula-

tion tool. This simulation language was selected from among others due to its ability

to operate in conjunction with a real time (RT) package, which is used as the real

time shop floor control software. Moreover, VBA (visual basic for applications) is

an integral part of Arena 7.0. This enables convenient access to databases, and easy

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automation of Arena models. All information regarding the manufacturing system

(type of machines, the different part types including their possible routings, and the

redundancy among the machines) as well as the shop floor status at every decision

point is kept in an MS Access database. The flow of data between the Arena models

and the database is done through VBA using ActiveX Data Objects (ADO) technology.

4.1 FMS characteristics

We assume that the FMS is composed of several programmable multifunctional ma-

chining centers with large tool magazines and automatic tool changing capabilities.

In order to reduce machine waiting/idle time, each machining center is equipped with

a two position automatic palletizer that acts as an input/output buffer. In addition,

the system has a central buffer (AS/RS) that stores parts between process operations

and a material handling system that transfers parts between the central buffer and themachining centers. The FMS is capable of manufacturing a large, but finite, variety of

part types. Each part type needs to go through several operations in a predetermined

order that is based on some technological constraints. Each of these operations can be

performed by several machines subject to the availability of the appropriate tooling.

However, the processing time of an operation may differ from machine to machine.

Following are additional operation characteristics:

r

Production orders of the different part types arrive randomly or according to someproduction requirement list.

r Handling and transferring of parts in the FMS are done in single units (on single

unit-load pallets).r Each work order in the FMS occupies at any given point in time a single resource (a

machine, a material handling device, an input/output buffer, a central storage buffer

location).r Each machining center can operate on only one work order at a time.r There is no pre-emption.r

Tooling change times and load/unload time are included in part type processingtime.

r Processing time for each part type operation on each machining center is known and

fixed.r Work order due dates are known and fixed.r Machines can break down at random.r Transportation time between the central buffer and the machining centers is constant

for all part types.r Material handling devices are available whenever required.

4.2 Implementation mechanism

The implementation mechanism, illustrated in Fig. 2, consists of several separate mod-

ules operating in cooperation: the shop floor management block, the block responsible

for running the equipment, and the decision making block.

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Shop Floor

Controller

Arena RT

Shop Floor Management

Continuous OperationSystem Status

& Forecast

Database

MS Access

The Best

Dispatching Rule

Current System

Status

On-LineData

Collection

Decision

Criterion and

RelevantDispatching

Rules

Determining

Mechanism

Rule-Based

Algorithm

Forecasting

Mechanism

Arena

Fast Mode

Decision Making

Activation at each

decision point

Decision

CriterionDispatching

Rules Set

Production

Requirements

MS Excel

Nearest

Requirements

Forecast

FMSEquipment

Equipment Operation

Equipment

Controllers

RapidCIM(MPSGs)

Commands

Reaction to messages

Messages

Parts Arrival

Trigger

Mechanism Real SFStatus

Forecast

DM Activation

Fig. 2 The implementation of the suggested two-tier control methodology

4.2.1 The shop floor management module

The shop floor management module that serves as the FMS controller was imple-

mented using the Arena RT simulation tool. This module is responsible for sending

messages containing instructions on the required activities to the lower level equip-

ment controllers. This module also receives the execution completed messages back

from the equipment controllers and keeps track of the current equipment status. The

Arena simulation model is developed in a manner that supports alternative routings

and enables, if necessary, the dynamic exchange of scheduling policies (according to

instructions sent from the decision making mechanism that will be explained later),

without interrupting the systems operation.

During operation, the shop floor control module keeps track of parts moving from

the WIP central buffer to the different machining centers and back. This information is

collected in a database and appropriate tables in the database are updated accordingly

to reflect the current state of the shop floor.

4.2.2 The equipment operation module

The equipment controllers in the proposed scheme are C++ applications that are

designated to receive messages from the shop floor control module, interpret these

messages, send operation commands to the appropriate equipment unit, and transfer the

completion messages back to the shop floor control module. The equipment controllers

were implemented using the RapidCIM methodology (Wysk et al., 1992). However,

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the suggested control scheme does not use the shop-level task executer, known as

the big executer (BigE) because of its rigidity (it was created for specific production

data and certain control logic), which affects the systems ability to utilize alternative

routing and produce a variety of part types.

4.2.3 The decision making mechanism

The decision making mechanism, activated at every decision point, comprises two

modules according to the proposed two-tier control scheme. The first module is im-

plemented using a rule-based algorithm and its task is to determine the preferable

decision criterion and relevant scheduling rules. This algorithm receives the current

system state (shop floor status and nearest production requirements) from the database

and returns the chosen dominant decision criterion.

The literature reveals (see Shnits et al., 2004) that the two most frequently usedcriteria are mean flow time (system oriented) and mean tardiness (customer oriented).

These two criteria were also chosen to serve, in the current study, as the FMS per-

formance evaluation measures. As a result, a rule-based algorithm was developed to

choose at any decision point one of these two criteria. Following is the notation and

suggested rules.

Notation:

j Part index 1, . . . , J

t Current time

Pj Average remaining processing time for a part j

DDj Due date for part j

M Number of repaired machines

C Ij Critical index for part j , where C Ij = Pj/(DDj t)

TCj Tardiness cost per time unit for part j

K1, K2, K3 System coefficients, where K1 0, K2 0, K3 0

C1,C2 Threshold levels for the tardiness costs

Rules:

If

j Pj

M> K1

j

(D Djt)J

and

j T Cj

J> C1, then

Choose Mean Tardiness as the dominant decision criterion

Else

If j : C Ij > K2 or1

C Ij< K3, then

If T Cj > C2, then

Choose Mean Tardiness as the dominant decision criterion

Else

Choose Mean Flow Time as the dominant decision criterionEnd If

Else

Choose Mean Flow Time as the dominant decision criterion

End If

End If

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The expression

j Pj/M denotes the average required time to complete the parts

that are processed in the system at that point in time. This expression is compared

to the average time to the due date

j (D Dj t)/J of these parts. If the for-

mer is greater than the latter, the system may have a problem meeting all of the

parts due dates. In such a case, it seems logical to determine processing priori-ties that minimize the parts mean tardiness. On the other hand, if it turns out that

there is enough time to complete parts in the system without violating the agreed

upon due dates, it makes more sense to try and minimize the parts mean flow

time.

It should be noted that even if, on average, there is no time pressure in the sys-

tem (first condition), there may be some urgent parts that are in danger of missing

their due dates or have missed them already. These cases can be detected through

the use of the critical index C Ij (second condition). If there are such parts in

the system, the mean tardiness criterion is chosen over the mean flow time cri-terion. The algorithm also makes it possible to take into consideration the aver-

age tardiness cost as well as the tardiness cost for each part separately, using C1and C2.

The coefficients K1, K2, and K3 reflect the system priorities by defining the rela-

tive importance of the considered criteria. Coefficient K1 refers to the overall system

status, while the coefficients K2 and K3 refer to parts individually. In case mini-

mizing tardiness is more important than minimizing flow time, K1 and K2 need to

be set relatively low. On the other hand, if minimizing flow time is more impor-

tant, K1

and K2

need to be set relatively high. In a system that considers minimiz-

ing tardiness as an organizational goal, the coefficients K2 and K3 should be set as

K2 > 0 and K3 = 0, so parts in danger of becoming late can be taken care of ahead of

time.

Preliminary test runs revealed that when K2 K1, the effect of the first condition

among the rules becomes negligible. However, when K2 K1, the effect of the

second condition (with K2) among the rules becomes negligible. In order to have

both conditions effective, K2 needs to be set slightly higher than K1. Based on this

insight it was decided to consider K1 (the main coefficient of the algorithm) as an

independent variable and to set K2 equal to K1 + 0.3 (the preferred gap between these

two coefficients as determined though the preliminary tests) in all of the following

experiments.

The second module of the decision making mechanism is the forecasting module

that is used for selecting the best scheduling rule from the relevant (according to the

dominant criteria measure) scheduling rule set. The forecasting module is developed

using the Arena 7 simulation tool and is similar to the model that serves as the shop

floor controller. A scheduling rule is chosen after the simulation model evaluates (look-

ahead) all relevant scheduling rules in the given rule set. Each evaluation run begins

with the current shop floor status that is supplied by the system status database. The

forecasting mechanism also takes into account the estimated production requirements,i.e., the new parts that are expected to arrive at the shop during the evaluation run. Once

the best scheduling rule is determined, it is passed on to the shop floor management

module via a communications network. This rule will govern the shop floor controllers

operation until a new decision will be required.

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The evaluation of the different scheduling rules is performed according to a perfor-

mance measure that is related to the dominant decision criterion that was determined

by the top tier of the decision making mechanism. Following is the notation and the

two performance measures FCfor the mean flow time decision criterion and TCfor

the mean tardiness decision criterion:

Notation:

TW The duration of the look-ahead time-window

D Dj Due date for part j (in terms of the time-frame of the time-window)

ATj Arrival time of part j to the system (in terms of the time-frame of the time-

window)

C Tj Completion time of part j (in terms of the time-frame of the time-window)Pj Average remaining processing time for part j

FC=

J

j=1

(min(C Tj , T W) ATj + Pj ), (1)

T C=

J

j=1

max(0,min(C Tj , T W) D Dj + Pj ). (2)

The expression min(C Tj , T W) + Pj estimates the completion time of part j . For

parts that are completed during the simulation look-ahead run, Pj = 0and C Tj < T W;

hence, this expression is set to C Tj . However, for parts that do not complete their

process at the end of the look-ahead simulation run, Pj > 0 and T W < C Tj ; hence,

completion time is estimated as T W+ Pj .

The scheduling rules implemented in this study (listed in Table 1) include some

of the most popular scheduling rules that appeared in the literature (see, e.g., Gupta

et al., 1989; Montazeri and Wassenhove, 1990; Sabuncuoglu and Hommertzheim,

1993; Kutanoglu and Sabuncuoglu, 1999; Shnits et al., 2004). It is importantto notice that these rules were selected without loss of generality and other

scheduling rules or algorithms can be included in the scheduling/dispatching rule

set.

5 Performance evaluation of the proposed control scheme

The performance of the proposed dynamic scheduling and control mechanism was

evaluated in two steps. The first step (described in Section 5.2) focused on testingthe effects the different environmental and control variables have on the system per-

formance. In the second step (described in Section 5.3), the efficiency of the pro-

posed control methodology was evaluated by comparing it to some known individual

scheduling rules/policies and methods.

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Table 1 Scheduling/dispatching rules in use

Scheduling/dispatching rules in use

Rank Rule Description

1 FCFS First come first serve

2 LRPT Least remaining processing time

3 EDD Earliest due date

4 STPT Shortest total processing time

5 FASFS First arrive to system first serve

6 SLACK Minimum slack (difference between due date and current possible

completion time)

7 CR Critical ratio (ratio of remaining processing time and time to due date)

8 LRA Largest relative advantage (a part selected for processing on a specific

machine is the one that has an advantage in processing on this machine

relative to the other machines)9 SIO Shortest imminent operation

10 ATC Apparent tardiness cost (exponential function based measure taking into

account expected waiting time, slack and processing time of each part)

5.1 The test environment

The performance of the suggested two-tier control scheme was evaluated using a

test environment that is similar in size and scope to environments used in other

previous studies on dynamic scheduling such as Ishii and Talavage (1991, 1994),

Chandra and Talavage (1991), Kazerooni et al. (1997), Arzi and Iaroslavitz (1999),

Subramaniam et al. (2000), and Chryssolouris and Subramaniam (2001). The ex-

perimental environment in this study consists of six work-centers that can fail from

time to time and must be repaired. Machine failure and repair time were assumed

to follow an exponential distribution. The mean time between failures (MTBF) and

mean time to repair (MTTR) in minutes, for each work-center, were randomly

chosen from the uniform distributions U[1000, 3000] and U[100, 200] minutes,

respectively.

Parts are assumed to arrive to the shop according to a Poisson arrival process. Two

mean interarrival time (1/k) values for each part type k were determined. The first

was to achieve 86% machine utilization. This utilization in practical terms is on the

high end of what is considered manageable. The second interarrival time was chosen

to achieve a 73% machine utilization. As opposed to the previous workload, 73% is

at the lower end of what is considered acceptable in practical terms.

The system produces simultaneously ten different part types. Each of the part types

requires several operations and each of the operations can be performed on several

machines. The number of operations for each part type was randomly chosen using

the uniform distribution U[1, 7]. The average processing time of operation i for a partof type k, Oi k minutes, was randomly chosen from the uniform distribution U[5, 35].

The redundancy capabilities of the system were described through the number of

work-centers that are capable of processing each of the operations. This number was

randomly chosen for each operation from the uniform distribution U[1, 6]. Next, based

on this number, the actual work-centers were randomly selected. The actual processing

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Table 2 Summary of the parameters characterizing the test environment

System Parameter Distribution

Number of machines in the system 6

Machine MTBF (minutes) Uniform [1000, 3000]Machine MTTR (minutes) Uniform [100, 200]

Number of part types 10

Number of operations each part of each type Uniform [1, 7]

is required to go through

Redundancy levelthe number of machines Uniform [1, 6]

that can perform an operation

Average processing time Oi k for each operation Uniform [5, 35]

i of each part type k (minutes)

Operation processing time on redundant machines Omi k (minutes) Oi k (1 + Uniform[0.15, 0.15])

Production demandthe required quantity of each part type Uniform [25, 75]

Average machine utilization (AMU) 73%, 86%Due date tightness (DDT) 200, 300

time on each of these work-centers Omi k was generated using the following equation:

Omi k = Oi k (1 + U[0.15, 0.15]).

The number of parts of each part type was also randomly chosen from the uniform

distribution U[25, 75] parts. The due date for every part was calculated as the sum-

mation of the parts arrival time, the average parts processing time and a random

variable chosen from the uniform distribution U[0, DDT], where DDT was defined

as the parameter that expresses the due date tightness. Two different levels for the

parameter DDTwere chosen, 200 minutes and 300 minutes. Table 2 summarizes the

parameters and their distributions that characterize the test environment.

A finite time horizon was used in this study. As such, the simulation run time was

defined as the time needed to complete processing all the parts defined. The actual

time varied between 8700 minutes and 10400 minutes based on the production data

generated and the parameter values selected. The warm-up period in all simulationruns was set at 3000 minutes. The simulation test environment was built based on

principles of discrete-event simulation modeling (Law and Kelton, 2000).

The activation of the decision making process is done right before a resource

becomes available and only if more than one part is currently waiting for this resource.

In addition, the elapsed time between two consecutive decisions has to be greater than

some threshold value (currently set to 2 minutes).

5.2 Analyzing the main parameters of the decision making mechanism

The decision making mechanism described in Section 4.2.3 is a principal component of

the proposed control scheme. The parameters of the decision making mechanism have

a significant impact on the system performance. Therefore, the aim of this experiment

is to analyze the effects these parameters have on the systems performance and to

determine the parameters preferable values.

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Table 3 The different levels of

the tested factors Factor Levels

K1 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

TW 20 50 80

AMU 73 86

DDT 200 300

5.2.1 Experiment design

A production data set for this experiment was randomly generated using the distribu-

tions described in Table 2. Based on preliminary tests, two control parameters were

found to be significant and were chosen to participate in the experiment: the look-

ahead time-window (TW) and the coefficient K1 of the rule-based algorithm. The

coefficient K2 was set to K1 + 0.3 and K3 was set to 0 (see Section 4.2.3). In order

to better analyze the effects that above mentioned control parameters have on the

systems performance, it was essential to define several shop floor states. Two param-

eters were chosen to characterize these states. The first defines the average machine

workload/utilization (AMU) and the second defines the due date tightness (DDT). All

together four experimental variables were used; their possible values are listed in Ta-

ble 3. Based on these values, a factorial experiment was designed to test the effects

that these variables have on the systems performance as measured by the mean flow

time FT and mean tardiness TR. It should be noted that the tardiness cost was not

taken into consideration in this experiment.

5.2.2 Experiment results

The effects that the four experimental variables have on the system performance as

described by the measures FT and TR are summarized in Tables 4 and 5, respectively.

The bold font indicates statistically significant effects.

Table 4 Analysis of variance of the variable effects on FT

Source DF Sum of squares F Ratio Prob > F

AMU 1 22736.323 17131.1


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Table 5 Analysis of variance of the variable effects on TR

Source DF Sum of squares F Ratio Prob > F

AMU 1 467.14876 5307.479


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4

4.5

5

5.5

6

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

K1

TR

Fig. 4 The effect K1 has on TR

137

138

139

140

141

20 50 80

TW

FT

Fig. 5 The effect TWhas on FT

4.8

5

5.2

5.4

20 50 80

TW

TR

Fig. 6 The effect TWhas on TR

Tables 4 and 5 indicate that some of the interactions between the control variables

(TW and K1) and the shop state variables (AMU and DDT) also have a significantimpact on the systems performance as manifested through the measures FT and TR.

These interactions are illustrated in Figs. 711.

Figures 7 and 8 show that for tight due dates (DDT= 200), reducing the look-ahead

time window TWimproves system performance as exhibited by both measures FTand

TR. For spacious due dates (DDT= 300), better system performance is achieved with

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137

138

139

140

141

TW =20 TW=50 TW =80

TW

FT

DDT=

200

DDT=

300

Fig. 7 DDT*T W interaction

effect on FT

3

4

5

6

7

20 50 80

TW

TR

DDT=

200

DDT=

300

Fig. 8 DDT*TWinteraction

effect on TR

120

130

140

150

160

20 50 80

TW

FT

AMU=86%

AMU=73%

Fig. 9 AMU*T W interaction

effect on F T

a mid-range look-ahead time window. This means, that when due dates are tight,

myopic decisions seem to work better. However, when due dates are more spacious,

considering future events has a potential to improve the decision making process.

It is obvious that as the systems workload increases, the decision-making process

is invoked more often. Therefore, its efficiency becomes a more crucial issue. Thisrelationship is illustrated in Figs. 9 and 10, which show that as the workload in the

shop (machine utilization) increases the impact that the look-ahead time window has

on both performance measures FTand TR is more significant.

The analysis also reveals that when due dates are tight, the selection algorithm of

the dominant decision criterion has a smaller impact (via its control variable K1) on

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2

4

6

8

20 50 80

TW

TR

AMU=86%

AMU=73%

Fig. 10 AMU*T W interaction

effect on TR

3

4

5

6

7

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

K1

TR

DDT=200

DDT=300

Linear

(DDT=300)

Linear

(DDT=200)

Fig. 11 DDT*K1 interaction

effect on TR

4

4.5

5

5.5

6

6.5

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

K1

TR

TW=20

TW=50

TW=80

Linear

(TW=20)

Linear

(TW=50)

Linear

(TW=80)

Fig. 12 TW*K1 interaction

effect on FT

the systems performance. This is mainly because the remaining time slack for the

different parts is too small and does not leave much room for maneuvering. Figure

11 shows that when due dates are more spacious, reducing K1 has a more significant

effect on improving the performance measure TR.Table 5 lists the interaction between the control variables TWandK1 as statistically

significant. The effect that this interaction has on the performance measure TR is

illustrated in Fig. 12. The figure shows that as K1 is set lower in conjunction with

larger look-ahead time windows, lower tardiness values can be achieved. However,

when K1 is set large, small and mid-range look-ahead time windows are preferred since

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those have been shown to reduce TR. The explanation for this effect is related to the role

K1 has in the decision criteria selection algorithm. Setting K1 small means giving a

higher priority to minimizing tardiness and keeping parts due dates over minimizing

flow time. In such a case, increasing the look-ahead time window promotes early

detection of situations where time pressure may hamper the systems ability to meetthe parts due dates. Early detection improves the controllers ability to handle this

incidence. On the other hand, setting K1 large means reducing the priority of tardiness

as a performance measure. In this case it is less important to have an early detection

capability of time pressure situations; therefore, a look-ahead time window can be

reduced.

Table 5 also indicates that the interactions AMU*DDT*TW and AMU*DDT*K1have a significant effect on TR. Each one of these interactions is composed of the system

state variableAMUand the interactionsDDT*TWandDDT*K1 that were presented and

explained earlier (see Figs. 8 and 11). The analysis of the interactionsAMU*DDT*TWand AMU*DDT*K1 reveals that the effects of the interactions DDT*TWand DDT*K1are more significant as machine utilization is higher (AMU= 86%). This result is

consistent with the conclusion reached from analyzing Figs. 9 and 10, i.e., as the

systems workload increases, the effects of the different control variables and their

interactions become more significant because it becomes more important to implement

an efficient decision-making process.

The effects that the shop state variables AMU and DDT have on the systems

performance were also analyzed. This analysis reveals as expected, that when the

systems workload increases, mean flow time and mean tardiness increase as well.

In addition, tight due dates in conjunction with a higher system workload cause a

significant increase in the mean tardiness. On the other hand, when machine utilization

is relatively low, tardiness is almost not affected by the tight due dates.

5.3 Comparison of the proposed methodology to common scheduling policies

The main characteristics of the proposed control scheme are its two-tier decision-

making mechanism and its dynamic selection of criteria and scheduling rules. There-

fore, the following evaluation analysis focuses on these two characteristics.

The first objective is to assess the capability of the proposed methodology to cope

with a dynamic production environment. To do that, the performance of a system

using the suggested control methodology was compared to the performance of the same

system using the individual scheduling policies/rules described in Table 1. The second

objective is to assess the significance of determining a dominant criteria measure before

evaluating the different scheduling policies/rule. To do that, the performance of the

proposed two-tier decision-making mechanism was compared to the performance of

an adaptive control scheme used a single, fixed, operational decision criterion.

5.3.1 Using DEA for evaluating an efficiency of the proposed methodology

Since the proposed control methodology was developed to deal with an environment

in which the systems operational objectives change over time, it is imperative to use

a multi-criteria analysis technique for its evaluation. Carlyle et al. (2003) list sev-

eral multi-criteria analysis methods and measures. However, one of the most popular

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techniques (not mentioned in the above study) is a data envelopment analysis (DEA)

approach (Charnes et al., 1978). DEA was used in a large number of studies and ap-

plied in a wide variety of domains. See, e.g., Roll et al., 1989; Golany et al., 1994;

Adler and Golany, 2001. Production scheduling is one such domain (Ruiz-Torres and

Lopez, 2004).DEA is a technique used for evaluating the relative efficiencies of decision-making

units (DMUs). According to the DEA approach, the relative efficiency of a DMU is

defined as a ratio of the weighted sum of outputs to the weighted sum of inputs. The

efficiency of each DMU is calculated based on the best set of weights that are selected

for each DMU.

In this study, DEA approach is used to compare the relative efficiency of the different

scheduling rules/policies, based on the two chosen performance measuresflow time

and tardiness. These measures are used as the DEA models output while the input

that signifies the systems production and resource data was set to 1: (the input usedfor all of the different scheduling policies in each comparison has to be identical).

Following is the notation and the reduced DEA model:

Notation:

Yr j The value of the performance measure r for scheduling rule/policy j (j = 0

signifies the specific scheduling policy)

r The weight of the performance measure r (the decision variable of the model)m The number of performance measures in the output vector

n The number of output vectors (scheduling policies under consideration)

E0 The efficiency of the specific scheduling policy

Max E0 =

m

r=1

rYr0

s.t.

m

r=1

rYr j 1; j = 1, . . . , n; r= 1, . . . ,m; r 0

The linear programming model, described above, has to be solved for each one of

the scheduling rules/policies that are considered. The model determines the optimal

weights r for the performance measures that maximize the weighted efficiency E0for each scheduling rule/policy subject to the constraints that the efficiency of the

scheduling rules/policies cannot exceed 1.

5.3.2 Experiment design

For a more comprehensive comparison analysis, three different sets of production data

were generated randomly (each using a different random seed) based on the distribu-

tions described in Table 2. Each of these data sets was tested under four different shop

floor states, characterized by a combination of the values of the shop state variables

AMUand DDT, as listed in Table 6.

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Table 6 Characterization of the

different shop floor states Shop floor state AMU DDT

1 73 200

2 73 300

3 86 200

4 86 300

Hence each scheduling rule/policy was tested using three different randomly gener-

ated sets of production data and four shop floor states. In other words, each scheduling

rule/policy was tested using 12 different scenarios.

The values of the experimental variables for the proposed control methodology were

set based on the results obtained from the previous experiment (described in Section

5.2). Based on the results illustrated in Figs. 58, the look-ahead time-window TW

was set to 50 for relatively loose due dates (DDT= 300) and to 20 for tighter duedates (DDT= 200). Next, based on the results illustrated in Figs. 3 and 4, the levels

of the control variable K1 were set to 0.8, 1.0, 1.2, 1.4, 1.6, and 1.8. To demonstrate

the capabilities of the proposed control methodology, the two-tier control scheme was

tested for each one of these values. The coefficients K2 and K3 were set as previously

indicated (see Section 5.2.1).

5.3.3 Experiment results

The average flow time F T and average tardiness T R over all 12 scenarios were cal-culated for each scheduling rule/policy listed in Table 1. These values were compared

to the average flow time and average tardiness achieved by the manufacturing system

operating using the proposed control methodology over all 12 scenarios for each of

the different values of the control variable K1. This comparison is denoted hereafter

as the aggregate comparison. A similar comparison was performed for each one of

the shop states separately, denoted hereafter as the separate comparison. The differ-

ence between the two comparisons is that in the latter, the average flow time F T and

average tardiness T R were calculated separately for each of the four shop floor states

over three scenarios only (three data sets).

In order to use the above-described DEA model, the average flow time and average

tardiness obtained is normalized as follows:

F TN=

Max{F T} F T

Max{F T} Min{F T} 100 (3)

T RN=

Max{T R} T R

Max{T R} Min{T R} 100 (4)

The normalized flow time F TN and normalized tardiness T RN, for the aggregatecomparison, are illustrated in Fig. 13. Figure 13 clearly shows that the results obtained

for the proposed control methodology (using the different K1 values) form an efficient

frontier. The two extreme points of this frontier represent the performance of the

adaptive control methodology operating with a single criterionflow time (FTC) or

tardiness (TRC). Figure 13 demonstrates that the proposed methodology can cope

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ATC

SLACK

EDD

CR

LRAFASFS

LRPTSIO

STPT

FCFS

FTC

TRC

45

55

65

75

85

95

50 55 60 65 70 75

FTN

TRN

Scheduling Rules

Proposed

Methodology

Single-Criteria Multi-

Pass Scheduling

Poly. (Proposed

Methodology)

Fig. 13 The performance of the proposed control methodology versus the performance of the individual

scheduling rules/policies

better with a dynamic environment compared to other scheduling rules/policies tested

in terms of flow time and tardiness.

The DEA results, shown in Table 7, confirm the overall superiority of the suggestedtwo-tier control methodology. According to the DEA, the efficiency of the proposed

scheduling mechanism is equal to 1 or very close to 1 (for all K1 values) and is higher

compared to the efficiency of the individual scheduling rules.

Table 7 Efficiency of the different scheduling policies using DEA

Efficiency

Proposed methodology K1 = 0.8 1

K1 = 1 1

K1 = 1.2 0.99512

K1 = 1.4 0.995411

K1 = 1.6 0.994344

K1 = 1.8 1

Single-criteria multi-pass scheduling Flow Time Criterion (FTC) 1

Tardiness Criterion (TRC) 0.989646

Scheduling rules FCFS 0.727013

LRPT 0.897867

EDD 0.920309

STPT 0.775118

FASFS 0.853347

SLACK 0.952912

CR 0.944172

LRA 0.940022

SIO 0.829488

ATC 0.955631

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Table 8 Efficiency of the different control policies for the different shop floor states using DEA

Efficiency

State 1 State 2 State 3 State 4

Proposed methodology K1 = 0.8 1 0.990054 0.998446 1K1 = 1 1 0.995301 1 0.997821

K1 = 1.2 0.970675 1 0.989293 0.986362

K1 = 1.4 0.96972 0.988091 0.986969 0.999154

K1 = 1.6 1 0.978381 0.984593 0.992929

K1 = 1.8 1 1 1 1

Single-criteria multi- Flow Time Criterion 1 1 1 1

pass scheduling Tardiness Criterion 1 1 0.959939 0.977331

Scheduling rules FCFS 0.5214 0.592615 0.470359 0.556963

LRPT 0.85679 0.855099 0.838447 0.765246

EDD 0.910446 0.891681 0.811733 0.890083STPT 0.668246 0.70139 0.585165 0.534077

FASFS 0.813288 0.821505 0.702578 0.712895

SLACK 0.913532 0.948549 0.885791 0.929625

CR 0.864443 0.907183 0.856493 0.940456

LRA 0.88709 0.882016 0.931812 0.866255

SIO 0.761105 0.777093 0.69382 0.636301

ATC 0.913854 0.931459 0.894204 0.93819

11.02%

-5.87%-10%

-5%

0%

5%

10%

15%

FT TR

Performance Measures

Relativeimprovementof

theproposedmethodology

N N

Fig. 14 Comparision of the

proposed methodology to an

adaptive mechanism using only

the flow time criterion

The results obtained for the separate comparison were similar to the results for the

aggregate comparison illustrated in Fig. 13 and Table 7. Table 8 lists the DEA results

for each of the four shop floor states examined.

The DEA results, listed in Table 8, show the superiority of the suggested two-

tier control methodology for each of the four shop floor states. The efficiency of the

proposed scheduling mechanism is equal to 1 or very close to 1 (for all K1 values)

and is higher compared to the efficiency of the individual scheduling rules.Figures 14 and 15 illustrate the ability of the suggested control methodology to cope

with the multi-criteria environment. These figures show the relative improvement (over

all the 12 scenarios) achieved by the proposed control methodology (average over all

K1 values) compared to an adaptive mechanism (using the same scheduling rules) that

uses only a single criterion.

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-0.31%

13.04%

-5%

0%

5%

10%

15%

FT TR

Performance Measures

Relativeimprovementof

theproposedmethodology

N N

Fig. 15 Comparision of the

proposed methodology to an

adaptive mechanism using only

the tardiness criterion

The results illustrated in Fig. 14 reveal that an adaptive mechanism that uses flowtime as a single performance criterion achieves better flow time performance compared

to the proposed multi-criteria control methodology. However, its tardiness performance

is much worse compared to that achieved by the proposed control methodology. The

results illustrated in Fig. 15 reveal that an adaptive mechanism that uses tardiness

as a single performance criterion achieves similar tardiness performance compared

to the proposed multi-criteria control methodology. However, its flow time perfor-

mance is much worse compared to that achieved by the proposed control methodol-

ogy. Moreover, it seems that even if some of the parts in the system have tight due

dates, and as a result, the declared objective of the system is the minimization of

tardiness, it can be beneficial to change the systems operational decision criterion

occasionally from tardiness minimization to flow time minimization. This, highlights

the importance of the mechanism for the dynamic selection of an appropriate decision

criterion.

It should be noted that the relative improvement achieved by the proposed control

methodology compared to the single-criteria adaptive scheduling mechanism was also

examined separately for the different shop floor states defined in Table 6. The results

obtained were similar to those shown in Figs. 14 and 15. This means that the mechanism

for the dynamic selection of an appropriate decision criterion is important for all the

tested shop floor states.

6 Conclusions and final remarks

This study presents a new multi-criteria dynamic scheduling methodology for con-

trolling FMSs. In order to cope with the unpredictable environment in which an FMS

operates, the proposed control scheme uses a two-tier decision-making mechanism.

Although the capabilities of the proposed control mechanism were extensively an-

alyzed, it should be noted that the results obtained in this study cannot be simplygeneralized, especially since these results rely on a specific test environment. Hence,

further analysis of this mechanism was needed.

The proposed control methodology was evaluated and compared to individual

scheduling rules/policies and to an adaptive single-criteria scheduling method. The

results obtained demonstrate the superiority of the suggested control methodology as

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well as its capability to cope with a fast-changing environment. The analysis clearly

shows that in a dynamic environment, it is important not only to select a good schedul-

ing rule/policy, but also to determine an appropriate decision criterion according to

which the performance of each scheduling rule/policy is measured. Specifically, it was

demonstrated that even if the declared objective of the system is the minimization oftardiness, it can be beneficial to occasionally select a criterion measure that aims to

reduce the work orders flow time, thereby freeing up machine time to better cope with

future unexpected events. The implementation of the proposed control methodology

is based on using similar simulation models for decision-making as well as for the

direct control of the actual manufacturing system.

The decision making mechanism in this study is limited to select at any decision

point one of two criteriamean flow time or mean tardiness. A possible research

extension of the proposed methodology can include support for additional decision

criteria or the capability to select some weighted combination of the dominant criteria.In addition, in the proposed methodology, the relative importance of the different sys-

tem objectives is expressed by the coefficients of the rule-based algorithm. Choosing

the right values for these coefficients is not a simple task. It might be useful to develop

some decision support system to facilitate this task. This however was outside the

scope of this paper.

Another issue is the activation of the decision-making mechanism. In this study,

the decision-making processes was activated right before a resource became available.

Hence, a possible research extension is to test different triggering modes, e.g., at fixed

time intervals or based on the gap between actual and planned performance. Additional

future research topics include testing the effects that machine redundancy have on the

performance of the proposed methodology and how efficient this methodology is for

less dynamic environments.

Acknowledgments This study has been supported, in part, by the Technion Hal and Inge Marcus Fund.

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