Order Acceptance and Scheduling in Metal Additive Manufacturing: An Optimal Foraging Approach

Abstract

Metal Additive Manufacturing (MAM), as an advanced direct digital manufacturing method with shortened lead time and increased performance, has been increasingly applied in industrial sectors, in particular those characterised by small production batches but high level of demand customization. In a manufacturing company, the first baffling problem faced is how to properly respond to the price and due date inquiries from customers, i.e.,
the problem of Order Acceptance and Scheduling (OAS). OAS problem has been proved as NP-hard problem and studied extensively by academic scholars and industrial practitioners in the past decades. However, the nature of MAM process, e.g. serial-batching scheduling and inconclusive production time, makes the OAS problem in MAM environment become more challenging.
This paper introduces the OAS problem faced by MAM companies for the first time in the literature and proposes a novel decision model inspired by Optimal Foraging Theory (OFT) for solving this problem. The proposed model combines scheduling optimization and order acceptance decision-making for the cases where the MAM machines, following various optimal foraging strategies, compete for orders by providing attractive offers to maximize the utilization of machine and optimize the payoff from an order acceptance decision as well.

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Twentieth
International
Working Seminar
on
Production Economics
PRE-PRINTS
VOLUME 1
Papers scheduled for
Tuesday, February 20, 2018
8.00 am to 21.15 pm
Edited by
Robert W. Grubbström, Hans H. Hinterhuber
and Janerik E. Lundquist
CONGRESS INNSBRUCK
INNSBRUCK
AUSTRIA
February 19-23, 2018
Linköpings Universitet – LiU-Tryck
Linköping 2018
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The Scientific Field of Production Economics
Production Economics focuses on scientific topics treating the interface between
engineering and management. All aspects of the subject in relation to manufacturing
and process industries, as well as production in general are covered. The subject is
interdisciplinary in nature, considering whole cycles of activities, such as the product
life cycle - research, design, development, test, launch, disposal - and the material
flow cycle - supply, production, distribution, recycling and remanufacturing.
The ultimate objective is to create and develop knowledge for improving industrial
practice and to strengthen the theoretical base necessary for supporting sound decision
making. It provides a forum for the exchange of ideas and the presentation of new
developments in theory and application, wherever engineering and technology meet
the managerial and economic environment in which industry operates.
Tracing economic and financial consequences in the analysis of the problem and
solution reported, belongs to the central theme.

The International Working Seminars
on Production Economics
The purpose of the International Working Seminars on Production Economics is to
provide an opportunity for research scientists and practitioners to meet, present and
develop their ideas on subjects within the field of Production Economics. A
Discussant is appointed for each paper. The intention is that models and methods
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Pre-Prints
Twentieth International Working Seminar on Production Economics, Innsbruck,
Austria, February 19-23, 2018
Contents of Volume 1
Presentations in Sessions Tuesday, February 20, 2018
Invited Keynote Speaker
Ou Tang
TEXT MINING FOR DATA COLLECTION IN PRODUCTION
ECONOMICS RESEARCH
1
Regular Sessions
Per J. Agrell, Manuel Herrera Rodriguez, Casiano Manrique
and Lourdes Trujillo
LINER SHIP FLEET DEPLOYMENT MODELS AND THE COST OF TIME:
THE CASE OF THE CHINA – USA MARITIME ROUTES
3
Erinç Albey, Z. and Melis Teksan
NONIDENTICAL PARALLEL MACHINE SCHEDULING WITH TIME-
DEPENDENT DETERIORATION OF JOBS
13
Sarah Van der Auweraer and Robert Boute
FORECASTING SPARE PART DEMAND USING SERVICE
MAINTENANCE INFORMATION
25
Mahsa Bahramkhoo, Kaveh Khalili-Damghani and Alireza Pakgohar
NEW BI-OBJECTIVE LOCATION-COVERAGE MODELS TO
DETERMINE LOCATION OF BANKS' ATMS CONSIDERING FAILURE
RATE (CASE STUDY: SAMAN BANK)
37
Christian Bohner, Stefan Minner and Frederik Wielens
FLEET RENEWAL FOR CONTAINER LINER SHIPPING – A
STOCHASTIC PROGRAMMING APPROACH
49
Emanuele Borgonovo, G.B. Hazen, V.R. Jose and E. Plischke
INFORMATION DENSITY IN LINEAR PROGRAMMING
61
Gionata Carmignani, Gloria Cervelli and Francesco Zammori
MODIFIED QFD APPROACH FOR CONTEXT ANALYSIS AND RISK
MANAGEMENT ACCORDING TO ISO STANDARDS
69
Mehmet Chakkol, Max Finne and Jonathan Canion
COLLABORATING EFFECTIVELY IN COMPLEX PROJECTS
83
Federica Ciccullo, Margherita Pero and Andrea Sianesi
SUPPLY CHAIN COORDINATION MECHANISMS DURING NEW
PRODUCT DEVELOPMENT IN THE MACHINERY INDUSTRY: A
MATTER OF CONTINGENCIES
95
Sharareh R.Dehkordi, Wenbo Cai and Layek Abdel-Malek
THE IMPACT OF ADOPTING 3D PRINTING TECHNOLOGY ON
RETAILER’S CAPACITY AND INVENTORY DECISIONS
109
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iv
Jan Niklas Dörseln, Timo Klünder and Marion Steven
PROCUREMENT 4.0 – COST EFFECTS OF DIGITALIZATION ON
PROCUREMENT
121
S. Thomas Foster Jr
A NEW MODEL FOR TEACHING SUPPLY CHAIN AND OPERATIONS
MANAGEMENT
135
Margaretha Gansterer and Richard F. Hartl
COMBINATORIAL AUCTIONS FOR COLLABORATIVE MULTI-LEVEL
LOTSIZING PROBLEMS
139
Joren Gijsbrechts and Robert Boute
A DEEP REINFORCEMENT LEARNING APPROACH FOR
SYNCHRONIZED MULTI-MODAL REPLENISHMENT
151
Robert W. Grubbström
APPLICATION OF THE LAPLACE TRANSFORM TO THE RISK
PREFERENCE EVALUATION OF RISKY INVESTMENTS
161
Po-Chien Hao, Kuan-Ting Lin, Tsung-Jung Hsieh, Huai-Che Hong,
and Bertrand M.T. Lin
APPROACHES TO SIMPLIFICATION OF JOB SHOP MODELS
173
Ying Hao, Lujie Chen, Xiande Zhao and Ou Tang
LENDING TECHNIQUES IN SUPPLY CHAIN FINANCE:
A STUDY BASED ON COMPUTER-AIDED TEXT ANALYSIS
185
M. Hasni, Mohamed Zied Babai, M. Aguir and Z. Jema
ON THE PERFORMANCE OF ADJUSTED BOOTSTRAPPING METHODS
FOR INTERMITTENT DEMAND FORECASTING
197
Hakan Karaosman and Alessandro Brun
PRODUCT MATRIX: A MODEL FOR SUSTAINABILITY ASSESSMENT
AT PRODUCT LEVEL
209
Qiang Li, Ibrahim Kucukkoc, Naihui He, David Zhang and Shilong Wang
ORDER ACCEPTANCE AND SCHEDULING IN METAL ADDITIVE
MANUFACTURING: AN OPTIMAL FORAGING APPROACH
225
Qiang Li, Ibrahim Kucukkoc, Naihui He, David Zhang and Shilong Wang
SCHEDULING OF MULTIPLE ADDITIVE MANUFACTURING AND 3D
PRINTING MACHINES TO MINIMISE MAXIMUM LATENESS
237
Qinyun Li and Stephen M. Disney
INVENTORY PERFORMANCE OF THE DAMPED TREND
FORECASTING METHOD
249
Giovanna Lo Nigro, Umberto Panniello and Paolo Roma
SHARING ECONOMY AND PRICE DISPERSION: THE IMPACT OF
AIRBNB ON THE HOSPITALITY INDUSTRY
261
Jie (Kitt) Ma, Ying Kei (Mike) Tse, Minghao Zhang, Yuji Sato and Jin Yu
EXPLORING THE PUBLIC PERCEPTION IN SOCIAL BIG DATA: AN
INVESTIGATION IN MARS RECALL SCANDAL
271
Karen Moons, Ernest Vandermeulen, Liliane Pintelon,
Geert Waeyenbergh and Paul Timmermans
OPERATING ROOM SUPPLY CHAIN MANAGEMENT: A SIMULATION
CASE STUDY
283

v
Boualem Rabta and Gerald Reiner
EFFECT OF THE PERTURBATION OF THE PARAMETERS OF
PRODUCTION AND MANUFACTURING MODELS ON THEIR
PERFORMANCE
295
Patricia Rogetzer, Lena Silbermayr and Werner Jammernegg
SUSTAINABLE SOURCING OF CRITICAL RAW MATERIALS:
INCLUDING RECYCLED MATERIALS IN THE SUPPLY CHAIN
303
Cevdet Utku Şafak and Görkem Yılmaz
SIMULTANEOUS LOT SIZING AND SCHEDULING INCLUDING
OVERTIME, SHIFT DECISIONS IN A SINGLE STAGE TOOL AND
MACHINE PRODUCTION ENVIRONMENT
315
Leila Schwab, Stefan Gold and Gerald Reiner
EXPLORING FINANCIAL SUSTAINABILITY OF SMES DURING
PERIODS OF PRODUCTION GROWTH: A SIMULATION STUDY
327
Samuel Fosso Wamba and Shahriar Akter
BIG DATA ENABLED DYNAMIC CAPABILITIES AND FIRM
OUTCOMES: EXPLORING THE MEDIATING EFFECTS OF ‘TRIPLE A’
IN SUPPLY CHAIN MANAGEMENT
339
Jinou Xu, Margherita Pero and Monica Rossi
TRIADIC SUPPLY NETWORK RELATIONSHIP IN NEW PRODUCT
DEVELOPMENT: A COMPARISON BETWEEN ITALY AND CHINA
349
Shilei Yang, Chunming (Victor) Shi and Yibin (Robbin) Zhang
THE BENEFIT OF SUPPLY CHAIN DECENTRALIZATION UNDER
SEQUENTIAL QUALITY CHOICE
361
Zeming Yuan, Tian Li , Tao Ma and Yuyuan Fu
THE ANALYSIS DRIVING FACTORS AND MODEL EXPLORATION FOR
SMES TRANSFORMATION AND UPGRADING
371
Yi Zhang, Guowei Hua, T.C.Edwin Cheng, Juliang Zhang
and Vicenc Fernandez
RISK POOLING THROUGH OFFLINE PROBABILISTIC SELLING
385

Order Acceptance and Scheduling in Metal Additive Manufacturing:
An Optimal Foraging Approach
Qiang Li 1,3*, Ibrahim Kucukkoc2, Naihui He1, David Zhang 1,3 and Shilong Wang 3
1 College of Engineering, Mathematics and Physical Sciences, University of Exeter,
EX4 4QF Exeter, United Kingdom
q.li@exeter.ac.uk, n.he@exeter.ac.uk, d.z.zhang@exeter.ac.uk
2 Department of Industrial Engineering, Balikesir University, Cagis Campus, Balikesir, Turkey
ikucukkoc@balikesir.edu.tr
3 College of Mechanical Engineering, Chongqing University, 400044 Chongqing, China
slwang@cqu.edu.cn
Abstract
Metal Additive Manufacturing (MAM), as an advanced direct digital manufacturing method with shortened lead
time and increased performance, has been increasingly applied in industrial sectors, in particular those
characterised by small production batches but high level of demand customization. In a manufacturing company,
the first baffling problem faced is how to properly respond to the price and due date inquiries from customer s, i.e.,
the problem of Order Acceptance and Scheduling (OAS). OAS problem has been proved as NP-hard problem and
studied extensively by academic scholars and industrial practitioners in the past decades. However, the nature of
MAM process, e.g. serial-batching scheduling and inconclusive production time, makes the OAS problem in
MAM environment become more challenging.
This paper introduces the OAS problem faced by MAM companies for the first time in the literature and proposes
a novel decision model inspired by Optimal Foraging Theory (OFT) for solving this problem. The proposed model
combines scheduling optimization and order acceptance decision-making for the cases where the MAM machines,
following various optimal foraging strategies, compete for orders by providing attractive offers to maximize the
utilization of machine and optimize the payoff from an order acceptance decision as well.
Keywords: Metal Additive Manufacturing, Order Acceptance and Scheduling, Decision Making, Serial Batching,
Optimal Foraging Theory.
1. Introduction
Metal Additive Manufacturing (MAM), as an advanced direct rapid manufacturing method
with shorter lead time and higher flexibility, is rising particularly in industrial sectors with
small batch sizes and a high level of customization (Li et al., 2017; Schmidt et al., 2017). This
development will put practical problems regarding production planning and scheduling on to
the table. Typically, the order acceptance and scheduling (OAS) problem is one of the trickiest
challenges which must be faced by MAM service providers. The problem of OAS is defined
as a joint decision of which orders to accept for processing and how to schedule them (Slotnick,
2011). Over the last decades, the different versions of OAS problems have been studied with
different objective functions under different sets of manufacturing assumptions (Jiang et al.,
2017; Oguz et al., 2010; Slotnick, 2011; Zwier and Wits, 2016). Although the topic of OAS
has attracted considerable attention from those who study scheduling and those who practice
it, the OAS problems in MAM is barely discovered.
Traditionally, the OAS problem is motivated by practical situations in make-to-order (MTO)
production systems to optimize the use of the limited capacity through determining whether to
accept or reject orders from customers (Oguz et al., 2010). However, the nature of MAM makes
it more challenging for decision making in OAS problems due to high level of uncertainties in
production cost and lead time caused by different combinations of parts into a job. The
production planning and scheduling problem in MAM was defined for the first time in the
literature by (Kucukkoc et al., 2016; Li et al., 2017)and a mathematical model was proposed
for the optimization of parts regrouping and allocating jobs to minimize average production
225

cost per volume of material while satisfying certain constrains. According to our research, for
a specific part, the difference of production cost per volume of material could be more than
40% by scheduled into different jobs. In powder-bed based MAM, the machine can handle one
job at a time and the job consists of a batch of parts which will be started and completed
simultaneously. For each job, a specific machine set-up/clean-up time is required. However,
the time as well as the costs to produce parts included in the job is dynamic which depends on
the total material volume and maximum height of these parts. In other words, the production
time and costs are unknown before all the parts assigned to this job are confirmed. This will
make it hard to answer the questions from customers: when will a part can be delivered and
how much does it cost to produce this part?
This paper will introduce the OAS problem faced by MAM companies for the first time in the
literature and propose a novel decision model inspired by Optimal Foraging Theory (OFT).
The OFT is one of the major predictive theories of animal foraging behaviour (Pyke, 1984;
Pyke et al., 1977) and has inspired researches in decision making and optimization area
(Hayden, 2018; Sulikowski, 2017; Zhu and Zhang, 2017). Foraging decisions are accept-reject
decisions just like the decisions on order acceptance. The reminder of the paper is organized as
follows: Section 2 introduces the nature of OAS problem in MAM filed; Section 3 presents the
proposed decision model inspired by OFT; Section 4 discusses the simulation results based on
the proposed decision model and Section 5 concludes the paper.
2. The OAS problem in MAM
2.1 The nature of production with MAM
As one of the dominant applications of MAM processes, Selective Laser Melting (SLM) also
known as Direct Metal Laser Sintering (DMLS) has been widely adopted in a variety of
industries (Calignano et al., 2017; Schmidt et al., 2017). The general production process of
SLM/DMLS, as well as powder-bed based MAM technology, is illustrated in Figure 1.
Figure 1. The production process of SLM/DMLS.
The production with powder-bed based MAM is job-based and a batch of parts can be produced
simultaneously in one job. The MAM machine can handle one job at a time and, once the job
starts, any of the parts included in this job cannot be taken out before the job finishing.
Normally, a relative fixed time needs to be spent on setting up a new job and collecting the
produced parts from the machine. However, the time of powder laying and melting to produce
the parts is dynamic which depends on the total material volume and the maximum height of
the parts included in the job. Also, the average production cost of per volume of material is
dynamic due to all the parts in a job will share some of the fixed costs, such as the costs caused
by job setting up and powder laying, which is not related with their volume of materials.
Compared with traditional manufacturing processes, the major distinction of production with
a powder-bed based MAM process is that the production cost and lead time are dynamically
impacted by the combination of parts included in the same job. The cost and time of a job may
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vary when a part with a particular height, production area, and material volume is added. The
dynamics of production time and costs make it more challenging for the planning and
scheduling of MAM production jobs when considering the constraints of dynamic release time
and due date of orders.
2.2 OAS problem statement
This paper studies the OAS problem faced by MAM companies where the orders are
dynamically released on the market and the MAM companies compete for orders to maximize
their profits based on applied strategy. In a period of time , a set of distinct orders (= 1, … , )
are released on the market one by one in time sequence and a set of MAM machines (=
1, … , ) with different specifications, including operation cost, production efficiency and
maximum supported production area and height, are available at the beginning. The orders in
this paper will be dispersed on a part by part basis using specific height , width , length ,
material volume , release time , expected due date , expected production price , and
sale price . The MAM machines monitor the orders released on the market and provide offers
to the selected orders based on their situation and applied strategy. Meanwhile, the orders will
compare the received offers from different MAM machines and make choice based on applied
strategy. Once an offer is accepted, the order who accepted this offer will be assigned to the
MAM machine within one of its jobs.
Index/Parameters
/Variables
Descriptions

Order index (= 1, … ,   )

Job index (= 1, … ,   )

Machine index (= 1, … ,   )
,,,
Height, length, width, and material volume of part 
,
Release date and expected due date of part 
,
Expected profit and sale price of part 

Cost per unit volume of material

Operation cost per unit time for machine 

Time for forming per unit volume of material for machine 

Accumulated interval time per unit height for machine 

Cost of human work per unit time for machine 

Set-up time needed for machine 

Production price per unit volume of material for machine 
,,
Maximum height, width, and length of part that machine  can process
,
Price and due date offered to part  by machine 

Profitability expected by machine 

Production cost of job  on machine 

Profit of job  on machine 

Production time of job  on machine 

Start time of job  on machine 
Table 1. Index, parameters and variables used for OAS problem.
Each MAM machine () aims to win as many as possible orders to maximize its total
profit within a time duration. To do this, the machine must carefully considere the decisions on
the price and due date of the offer as well as the selection of target order who will receive the
offer. The index, parameters and variables used for describing the above model are shown in
Table 1.
In terms of the notations given in Table 1, the profit of job  on machine , represented by
, can be formulated as follows:
227

= , (1)
where  is the set of parts assigned to job  () on machine  (), and  is
the production cost of job  which can be formulated as follows:
=(+) +max
{}+. (2)
The production time of job  on machine , represented by , can be formulated as
follows: = +max
{}+. (3)
Therefore, the objective function of machine  can be formulated as follows:
max =
,(4)
where  is the set of jobs processed on machine .
With the objective function given above, the MAM machine would be able to make decision
on order selection and offer generation. The details of decision model will be described in
Section 3.
3. Decision Model Inspired by OFT
3.1 Foraging decision-making
Animals forage and feed to obtain energy for survival and successful reproduction. However,
foraging and processing of the food require both energy and time. To maximize the benefit
(energy) with the lowest cost, the animal needs to make decision on whether to pursue or ignore
a prey item during foraging. OFT addresses the kinds of decisions faced by animals. The
animals (predators) make decisions under the constraints of the environment and take optimal
decision rule, or the best foraging strategy, to maximize a variable known as the currency, such
as the value of an item by taking into account the cost and time to acquire the item (Sinervo,
1997), which can be presented as follows:
  =       
      (5)
The profitability of a prey provides decision-making basis for a predator on the chosen of prey
item. Generally, the predator will gain more energy by eating large prey provided that the prey
is not too large so that the predator runs into processing constraints, while the handling time,
or the time taken to catch, subdue, and consume prey, will increase with prey size and prey
armour (Sinervo, 1997). The handling time will be more crucial for some species, such as
snakes, due to mobility impairment during feeding. Once a snake swallowed a prey, it will be
not able to attack another prey before the prey was digested, and the other preys may have
escaped or been captured by other predators. Therefore, in a competitive environment with
limited food source, a snake must be more careful on the selection of preys to capture by
considering the total potential benefits it will obtain over a period.
Given that a snake with intelligence, a possible smart way to maximize the total benefits from
foraging is to trap preys and consume the captured preys in packaged form based on snake’s
228

maximum size threshold. A prey with ability of activity will not stay there to be captured. The
prey will be captured only when it has chosen and eaten a bait. A concept of trap-based foraging
is illustrated in Figure 2. The predator releases a bait to attract a prey and capture it if it eaten
the bait. The captured preys will be packaged, when their total size reached the expected goal,
and stored as food packages which will be consumed on schedule. However, the value of a
prey has timeliness which means the prey, if dead or decayed, may become valueless even
harmful to the predator. Therefore, the crucial decision a snake needs to make is how to set a
competitive bait to attract target preys and how to determine the boundary conditions of a food
package to meet the maximum size threshold?
Figure 2. The illustration of trap-based foraging concept.
3.2 Decision model for OAS in MAM
The nature of order competition and production scheduling in MAM is extremely similar to the
trap-based foraging behaviour of snakes. For the OAS problem stated in Section 2.2, a MAM
machine monitors the orders appeared on the market and competes for an order by providing
an offer. The customer determines whether to accept an offer through comparing the price and
due date of the offers provided by different MAM machines. Once the MAM machine obtains
(or wins) enough orders, the orders will be grouped as a MAM production job which will be
processed on a schedule. The MAM machine aims to compete orders as many as possible to
maximize the utilization as well as the total profit obtained within a given period.
To achieve this objective, the MAM machine needs to make optimal decision rules. The most
important decision faced by MAM machine is to determine the price and due date of the offer
and which order it should provide to? As mentioned previously, the parts included within one
MAM production job will be produced simultaneously with same due date (completion time).
However, the due date of a job is dynamic which depends on the combination of parts assigned
to this job. At the time of making an offer, the MAM machine does not know if the offer would
be accepted and does not know what orders it can obtain from the market in the future.
Therefore, the MAM machine has to estimate the due date as well as the start time of the job
based on its expected profitability. For machine , its expected profitability 
 of job  can
be formulated as follows:

=


=()




, (6)
where 
 and 
 are the estimated total material volume and maximum height, respectively,
for job  on machine . The value of 
 can be calculated as follows:
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
=
()
 , (7)
where  is the total material volume already assigned to job  and  is the expected
utilization of the total production area of machine .
Given the value of expected profitability 
, the allowed maximum height 
 , which will
not lower the expected profitability, can be calculated based on formulation (6) as follows:

 =

(
)
(
). (8)
However, the currently real maximum height  of job  based on already assigned parts is
presented as follows: =max
{}. (9)
It can be mentioned that a part is profitable to job  if 
  after including this part into
the job. Therefore, the value of (
 )/
 as a function of part , termed as the
profitability of part  to job  (marked as 
), can be a decision variable for the selection of
part to be offered. The estimated due date of job  on machine , also the due date offered to
the parts which will be included in this job, will be determined based on the first part  who
accepted the offer. The offered due date  for a new job  by machine  can be calculated
based on the first part  as follows:
=+
+
+, (10)
where  is the start time of a new job , 
=() /()is the
estimated total material volume based on part , and 
=min{,
 } is the estimated
maximum height.
For the price offered to a part, the MAM machine can determine it with various strategies. One
of practical strategy, termed as “FIX_PRICE”, is pricing based on the material volume of the
part where the price is fixed relative to per unit volume of material. Alternatively, the MAM
machine can adopt a “FLEX_PRICE” strategy where the price offered to each part can be
flexible by considering the material volume and the profitability of the part together. Given a
reference price per unit volume of material , the flexible price  offered to part  can be
calculated as follows: =1

, (11)
where 
[0, 1] is the weight factor related to the profitability of part . The offered price
will be cheaper than  if a part has a positive profitability so that the offer will be more
competitive.
On the customer side, the offers provided by different MAM machines will be compared and
selected to accept based on the customer’s strategy. The customers aim to produce their parts
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through buying MAM service and make profit through selling the parts. The profit obtained
from part  produced with machine  can be calculated as follows:
=(). (12)
In the case of existing multiple offers which make positive profit, the customer may prefer the
offer either with the lowest price (“PRICE” strategy) or with the shortest due date (“TIME”
strategy). However, a “BLANCE” strategy, by considering the price and due date together, may
be more practical if the sale price is highly time-sensitive which means the sale price will be
higher if the part can be available earlier.
Figure 3. The principle of decision-making in OAS problem of MAM.
By now, the principle of decision-making in OAS problem of MAM can be illustrated as Figure
3.The MAM machine will make an offer to the part with positive profitability to current job
of scheduling and determine the price and due date to be offered to the part based on applied
strategy. Meanwhile, the part who received the offer will consider whether to accept the offer
if it can make positive profit. The decision of acceptance or rejection depends on the strategy
applied by the customer. The part who accepted the offer will be assigned to a job of the
machine who made the offer. However, the machine will withdraw the offer if it is rejected,
and make a new offer to another available part on the market. The due date offered by the
machine will be updated based on a new job to be scheduled if the obtained parts have reached
expected level or the moment for starting the job has come.
4. Simulation of OAS in MAM
4.1 OAS simulation system
The method of simulation-based optimization becomes more and more important because of
its flexibility and the capability to represent complex real world systems (Frantzé N et al., 2011;
Klemmt et al., 2009). According to the decision model proposed in Section 3, a simulation
system was developed using SimPy which is a process-based discrete-event simulation
framework based on standard Python (“SimPy,” n.d.). Also, a graphic user interface was
developed using Kivy which is an open source Python library for creating GUIs (“Kivy,” n.d.).
An example of result generated with developed OAS simulation system is shown in Figure 4.
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Figure 4. An example of result generated with OAS simulation system.
With the developed OAS simulation system, various MAM machines with different strategies
can be generated at the beginning and the parts with selected strategy will be generated
randomly in sequence during the simulation. The MAM machines monitoring the arrived parts
(coloured in green) provide offers based on their strategies for competition. A part is coloured
in red if it has accepted an offer or in blue if it has rejected all the offers. The scheduled jobs
are displayed as rectangles with different size and colours based on their start time, due date,
and status (red for completed, green for in printing, and blue for in scheduling).
4.2 Application of the OAS simulation system
The potential applications of the developed OAS simulation system are various. It can be used
for the investigation of the competitivity of different pricing strategies and the analysis of
sensitivities of various influencing factors including waiting time to start a new job, estimated
due date, priority of orders, etc. To demonstrate the basic application of this system, a scene
where 2 MAM machines with different strategies to compete 100 parts dynamically released
on the market within 30 days was simulated. The 2 MAM machines with the same
specifications as shown in Table 2 and the 100 parts are generated randomly with different size,
material volume, sale price, release data and expected due date (details of the first 10 parts are
shown in Table 3).
Parameters
M1
M2
, (hour/cm3)
0.030864
0.030864
, (hour/cm)
0.7
0.7
, (hour)
2
2
,, (GBP/hour)
60, 30
60, 30
,,, (cm)
32.5, 25, 25
32.5, 25, 25

, (GBP/cm3) 5 5
Table 2. The specifications and parameters of the MAM machines.
With the test data given above, the situations where the 2 MAM machines applied with different
strategies were simulated. The parts were applied with “PRICE_TIME” strategy for the
acceptance of offers, where the offer with lowest price and satisfied due date will be accepted.
The simulated results as shown in Table 4.
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Part
Size    (cm)
Volume  (cm3)
Arrive 
Due date 
Price  (GBP/cm3)
P1 15.4*3*15.2 229.21 512 9602 16.41
P2 11.2*24.8*20.3 3559.27 895 30885 15.17
P3 7.9*17.3*10.8 476.61 944 20439 20.15
P4 25.7*8.6*18.3 2456.64 980 18182 15.9
P5 28*23.5*15.4 7681.96 1356 34689 17.68
P6 17.6*5.2*6.1 360.00 1615 25688 21.05
P7 28*20*11.2 3689.05 1640 36063 21.99
P8 2.8*8.6*24.5 469.36 2258 12749 24.9
P9 19.9*12.3*11 1734.38 2912 20199 23.66
P10 31.6*11*5 791.85 3339 16825 23.47
Table 3. Sample data related to parts.
Applied
strategy
Number of
parts
Volume
(cm
3
)
Makespan
(hours)
Profit
(GBP)
Profit/volum
e
(GBP/cm
3
)
Profit/time
(GBP/hour)
M1
FIX_PRICE
15
30756.47
1123.48
58229.45
1.89
51.83
M2
FIX_PRICE
5
27960.74
970.78
56233.82
2.01
57.93
M1
FIX_PRICE
15
29011.10
1081.58
54320.14
1.87
50.22
M2
FLEX_PRICE
8
32713.52
1148.33
31679.97
0.97
27.59
M1
RANDOM
12
29080.08
1029.37
57051.65
1.96
55.42
M2
RANDOM
14
29237.34
1058.82
56472.80
1.93
53.34
Table 4. Simulation settings and results.
The machine M1 and M2 obtained 15 and 5 parts from the market respectively although they
were applied with the same strategy of “FIX_PRICE” – the part with best profitability will be
selected to provide offer. However, they obtained 12 and 14 parts respectively when applied
with strategy of “RANDOM” – available parts will be randomly selected to provide offer. For
the former situation, M1 and M2, with the same specifications, are likely to compete for the
same part on the same price and due date. The winner will gain superiority in the follow-on
competition. While for the latter situation, the competition on the same part is likely avoided
due to randomly selection of parts to offer. Although the total profit and makes pane are
different, M1 and M2 achieved similar profitability when applied with the same strategy. The
results indicated that the selection of the first part to be assigned to a new job will affect the
final competition results.
Another factor which will affect the competition results is the price offered to a part. As shown
in Table 4, M1 and M2 obtained 15 and 8 parts by applying strategy of “FIX_PRICE” and
“FLEX_PRICE”, respectively. For the same part, M2 will provide an offer with lower price
than M1 and this will give M2 more compactivity. As the result, the total profit achieved by
M2 increased about 17% although the profitability decreased about 50%. The strategy of
“FLEX_PRICE” will be useful when the manufacturers want to improve the utilization of their
machines.
5. Conclusions
In this paper, the OAS problem faced by MAM companies was introduced and a novel decision
model inspired by OFT was proposed for the first time. The nature of production with MAM,
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particularly the dynamism in the cost and time of a production job, makes it hard to determine
on which order should be accepted and how to schedule the accepted order to maximize profit
within a competitive market environment. The authors inspired by the trap-based foraging
behaviour of animals, proposed a competition behaviour mechanism of MAM machines which
aim to obtain as many orders as possible from the market to maximize their profit through
providing competitive offers. Further, a simulation system based on the proposed competition
mechanism was developed and the application for the investigation of different strategies was
demonstrated.
As a first attempt to handle the OAS problem in MAM, this study provided a principle decision
making model as well as a novel simulation tool for the future studies in this emerging research
field. A lot of efforts need to be undertaken to perfect the optimal decision rules for MAM
machines to generate competitive offers based on their business strategy and objectives. Further,
advanced theories such as the game theory will be considered in future for the study of
cooperation and competition behaviours of MAM machines, while the machine learning theory
will be considered to help the MAM machines to make more accurate estimations for decision
making.
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