Supply-side inoperability input–output model (SIIM) for risk analysis in manufacturing systems

Journal of Manufacturing Systems 41 (2016) 76–85

Contents lists available at ScienceDirect

Journal of Manufacturing Systems journal homepage: www.elsevier.com/locate/jmansys

Supply-side inoperability input–output model (SIIM) for risk analysis in manufacturing systems Lanndon Ocampo a,∗ , Jesah Grace Masbad b , Vianca Mae Noel b , Rauvel Shay Omega b a b

Department of Mechanical and Manufacturing Engineering, University of San Carlos, 6000 Cebu City, Philippines Department of Industrial Engineering, University of San Carlos, 6000 Cebu City, Philippines

a r t i c l e

i n f o

Article history: Received 9 December 2015 Received in revised form 3 June 2016 Accepted 26 July 2016 Keywords: Manufacturing systems Supply-driven inoperability input–output model Risk analysis Inoperability Manufacturing resilience

a b s t r a c t This paper proposes a methodological approach in risk analysis of interdependent manufacturing systems which is based on Ghosh model - a variation of the Leontief input-output model. The proposed approach is able to quantify the impact of supply perturbations in a manufacturing system in terms of cost-price increase in production output due to increase in prices of value-added input brought about by degraded supply resulting from natural or man-made disasters and sudden policy changes. Unlike demand-driven perturbation models presented in literature, the supply-driven inoperability input-output model (SIIM) appears to be more relevant particularly in make-to-order manufacturing systems as demand is usually pre-determined and production costs typically increase when prices of inputs increase. An actual case study was carried out in a furniture manufacturing firm in central Philippines and three scenarios were presented to illustrate the proposed approach: (1) a sudden log ban in the location of the supplier, (2) increase in labor costs and (3) metal shortage caused by severe weather condition. Results show that supply perturbation of upstream processes does not impact downstream processes as long as these processes remain independent of the perturbed upstream process as described in firm’s system structure and topology. This also shows that the magnitude of impact of non-perturbed process depends on its nature of interdependence of the perturbed process. The proposed approach is highly relevant for manufacturing practitioners in formulating and implementing mitigation and adaptation policies. © 2016 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

1. Introduction With increasing global competition and complexity, manufacturing firms nowadays strive not only to survive but also to remain competitive in their respective industries [1,2]. Hayes and Wheelwright [3] pointed out that manufacturing firms must exert effort to advance from being reactive to being competitive and maintaining a competitive advantage requires managers an effective decisionmaking process. From a manufacturing perspective, decisionmaking is required on various areas such as supplier selection, technology selection, production planning, production control, workforce management, inventory management, quality management, and process prioritization, among others [4]. Competitiveness in manufacturing along with the influx of sustainability issues has been comprehensively addressed in domain literature [1,3]. To sustain such competitiveness, manufacturing practitioners must be critical in various decision-making areas and an important input to any decision-making process in manufacturing systems is the

∗ Corresponding author. E-mail address: [email protected] (L. Ocampo).

analysis of risks brought about by disruptions of internal and external components where manufacturing firms are highly susceptible to. Thus, manufacturing firms must seek to understand risks making risk assessment and management become an emerging concern over the last decade [5]. The main argument adopted in this work is that assessment of potential losses caused by disruptions can be addressed by performing risk analysis which is significant to organizational decision-making in general and of production processes in particular. Such disruptions caused by unavailable worker, machine downtime, shortage of raw materials, natural disasters, etc. yield potential inoperability of a production process. Understanding how to mitigate these impacts from a systems approach advances current knowledge on manufacturing resilience research. Various approaches on risk analysis in the context of manufacturing at firm level have been proposed in literature. These include the analysis using strengths, weaknesses, opportunities and threats (SWOT), failure mode evaluation analysis (FMEA) and the analytic hierarchy process (AHP), system dynamics (SD) among others. See the works of Yang and Lee [6], Tukundane et al. [7] and Lolli et al. [8] for the application of these methods. Generally, these methods involve qualitative measures that are based on some value judgements of decision-makers which may potentially affect the

http://dx.doi.org/10.1016/j.jmsy.2016.07.005 0278-6125/© 2016 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

L. Ocampo et al. / Journal of Manufacturing Systems 41 (2016) 76–85

reliability of decision-making. SD, although a quantitative one, is a simulation tool that propagates different results due to certain parameters and conditions. However, a simulation tool is outweighed by an analytical tool in terms of situations that possess known and certain information. Thus, risk analysis of manufacturing systems lacks a rigorous tool that is based on hard data. On a macroeconomic scale, Santos and Haimes [9], Jiang and Haimes [10], Haimes et al. [11] and Santos [12] have successfully demonstrated a methodology for risk analysis in an economic system based on the award winning input-output model (IOM) developed by Leontief [13]. IOM demonstrates a promising approach because it characterizes relationships or interdependencies of system components, originally used for sectors within an economy. IOM is also able to address how changes in one system component, i.e. an economic sector, affect other sectors through quantitative measures - usually through a flow of goods in a closed-loop system. It has been widely adopted for interdependency analysis of sectors in a macro level, country-level, and even on a local level [14]. As a counterpart, Ghosh [15] has introduced a supply-driven perspective of Leontief’s IOM wherein changes in value-added inputs, rather than exogenous final demands, indicate changes in production output of sectors. The model developed by Santos and Haimes [9] provides the foundation of inoperability input-output model (IIM), an important extension of Leontief’s IOM for risk analysis, which assesses the inability of economic sectors to perform intended function known as inoperability which is caused by disruptions due to natural disasters, terrorism, etc. [9]. The strength of IIM lies in its capability in handling cascading effect of a perturbation to interdependent sectors or system components. While IIM works for risk analysis in economic systems, it also works for other similar interdependent systems such as manufacturing systems. Some attempts have been made to incorporate IOM in production processes [16] but its applicability in risk analysis has not been explored in current literature. IIM assesses the reduced final production output of all interdependent economic sectors brought about by a degraded exogenous demand of a sector. This makes IIM as a demand-driven approach. On the contrary, Leung et al. [17] developed the mathematical formulation of the supply-driven IIM which is based primarily from the Ghosh model. Unlike demand-driven IIM, supply-driven IIM assesses the risks associated with price increase in value-added inputs brought about by the decreased supply. This approach is fairly developed and adopted in domain literature. See Leung and Pooley [18], Park [19], Xu et al. [20], and Xu and Wang [21] for key papers focusing on this approach. When manufacturing systems are analogously considered as economic systems where each process is treated as economic sectors, the demand-driven IIM may be inappropriate because in most manufacturing systems individual processes other than the final process may have no exogenous demand except for processes that manufacture spare parts. For instance, the tire production process in a car manufacturing system produces spare tires aside from those tires that are directly used for the manufacturing of cars. With this, supply-driven IIM is

77

more applicable in analysing risks of manufacturing systems than demand-driven IIM due to the following: (1) most manufacturing systems have processes with no exogenous demand, (2) exogenous or customer demand in manufacturing is usually agreed beforehand by all concerned parties such that demand reduction after the demand is placed is highly unlikely, and the (3) increase in prices of outputs due to increase in prices of value-added inputs is highly relevant in manufacturing systems. Thus, this work attempts to demonstrate risk analysis of manufacturing systems using supply-driven IIM. While former approaches provide insights on this problem domain, they fail to provide a quantitative analytical framework which is highly significant in manufacturing decision-making. The relevance of SIIM is on the analysis of interdependent components in a system. A case study of a process system in furniture manufacturing industry is reported in this work. The contribution of this study is in presenting a new methodological framework that holistically addresses risk analysis in manufacturing systems. 2. Preliminaries 2.1. Leontief input–output model The input–output (IO) model, which was developed by Leontief [13], is a quantitative tool which generally portrays the interrelationships of components within a system, e.g. sectors in an economy. It originally intends to address how changes in one economic sector may have an effect on other sectors thus providing a systems approach in viewing an economy. IOM consolidates production data of sectors comprising an entire economy and provides the required production output of a sector to satisfy the demand of final consumers and other sectors. Generally, the model developed by Leontief [13] is a demand-driven approach where the analysis is rooted from how the entire system is affected with demand changes from economic sectors [14]. IOM expresses the relationship between economic sectors through a simple yet so monumental linear equation also known as the Leontief balance equation as shown in Eq. (1). x = Ax + c

(1)

where x is an n × 1 vector containing the production output of n sectors, A is an n × n interdependency of sectors which is also known as the IO coefficients vector which is expressed as a proportion of the sector’s values of inputs with respect to its output, and c is the n × 1 vector of final demand. The flow of goods in monetary units is recorded in an IO table as in Table 1. The terms oij represent intermediate sales or the interindustry outputs of sector i, consumed by other sectors j, including itself, when i = j for the production of their own goods [14]. Value-added row as shown in Table 1 represents the external goods utilized by the different sectors. From the table, technological matrix A can be obtained by dividing individual elements oij by the total inputs y. As a basic rule of IOM, total inputs y must be equal to the required

Table 1 input–output table. Buying sector 1

Selling sector

Value-added Total inputs (y)

1 ... i ... n

o11 ... oi1 ... on1

... ... ...

j

...

n

o1j ... oij ... onj

...

o1n ... oin ... onn

... ...

v1

v2

v3

y1

y2

y3

Exogenous final demand (c)

Required production (x)

c1 ... ci ... cn

x1 ... xi ... xn

78

L. Ocampo et al. / Journal of Manufacturing Systems 41 (2016) 76–85

production x. Having matrix A and an identity matrix I, the vector of required outputs can be obtained by rewriting (1) into: x = (I − A)−1 c

(2) (I − A)−1

The matrix is widely known as the Leontief inverse or the total requirements matrix (TRM). This matrix may be a straightforward one; yet it is recognized to be one of the powerful strengths of the IO model for the identification of the key sector is done once the TRM is obtained [22]. The total output multiplier of any sector is calculated by adding the column values of (I − A)−1 and the sector with the largest total output multiplier value is considered as the key sector. The comprehensive discussion of IOM can be found in Miller and Blair [14]. 2.2. Risk analysis with input–output model The input–output model typically explains the behavior and relation of different economic sectors or the interdependencies between them. IOM identifies the key sector or the highly sensitive sector with respect to its dependence to the other sectors [14]. The inherent structure of IOM which is to address interdependencies of systems in general makes it attractive in risk analysis. Prioritization of the key sector entails implementation of preventive measures, policies, and investing for development. It is necessary for decisionmakers to prioritize sectors to reduce the impacts of the said risks [23]. An internal or external failure of one sector could make that sector unable to perform its intended function. With the inherent interconnectedness among sectors, the impact of this failure could propagate to the entire system which triggers to a system’s dysfunction [12]. Santos [12] coined this phenomenon as ‘inoperability’ leading to a new perspective in risk analysis. An extension of input–output model which focuses on assessing the possible impacts of a sector or system perturbation is known as inoperability input–output model (IIM) [9]. IIM describes the cascading effect of a perturbation to interconnected sectors through quantitative and verifiable data. Tan et al. [5] argue that organizations must seek to understand such disruptions and be able to quantify the impact of the disruption to a certain sector and to the whole system so as to mitigate it more effectively. IIM, adopted from the Leontief’s IOM, assesses inoperabilities of interdependent sectors caused by disasters, terrorism, etc. [9]. IIM has been widely used in different applications such as in evaluating the effect of terrorism attack [9], loss of natural resource inputs due to climate change [24,25], power blackout [23], influenza epidemic consequences in workforce sectors [26], etc. The simplicity of IIM has led to various developments and extensions by associating it to different methods in order to perform its purpose more effectively. The application of IIM to economic sectors allowed decision-makers of these sectors to implement policies, prevention methods and other investments to reduce the impacts of risk. However, the framework of IIM is not limited to economic sectors alone. Following its systems approach in analysing risk, it is thus applicable to other systems such as processes in production systems. Production processes transform raw materials into finished products [27] and these processes generate output that becomes an input to succeeding process or processes in order to convert the semi-finished product into finished product. Consequently, production processes establish interconnection with other processes making the entire system interdependent. 3. Inoperability input–output model 3.1. Conceptual and mathematical foundation Haimes and Jiang [28] developed the inoperability input–output model (IIM) based from the input–output model (IOM) established

by Wassily Leontief in 1936. IOM provides an overview on the interdependencies of an economic sector to another sector as the output of one sector becomes the input of another thus creating interdependency within the system. IIM, on the other hand, is a simple tool which is used to analyze and quantify the impact of man-made or natural disasters of the affected sector and its cascading effect due to the interdependencies of other sectors within the system. IIM is applied in macroeconomic and in country level analysis. It provides a framework on how the interdependencies of different sectors contribute to the spread of disruption [11]. IIM defines inoperability as the inability of a system to perform its intended function due to internal failure or external perturbation. It uses the inoperability metric which is a dimensionless index whose values range from 0 (system on normal state) to 1 (system on total failure) in quantifying risk [12]. Santos and Haimes [9] later expanded IIM focusing on the demand-side inoperability which can be expressed as the percentage of economic loss due to a reduced final demand. IIM was used to quantify the economic loss triggered by terrorism of interconnected infrastructures. The conceptual and mathematical foundations of this approach were elaborated by Jiang and Haimes [10], Haimes [29] and Haimes et al. [11]. The simplicity of the IIM structure has made opportunities possible in developing additional capability for analysing the impact of disruptions [30]. Several extensions up to date have been made with IIM as its core in analysing the cascading effect of the disruptions which aid decision-makers in providing risk mitigation policies. Santos and Haimes [9] first expanded IOM by looking into the effects of a disruption in an interdependent system and coined it as inoperability input–output model (IIM). The mathematical methodology of IIM was explicitly presented in their first publication. The inoperability input–output model, from the data obtained in IOM, can then be constructed as follows:

q = A∗ q + c ∗

(3)

where:

demand-side perturbation vector expressed in terms of normalized degraded final demand of industry sector i interdependency matrix that indicates the degree of coupling of the industry sectors is the inoperability vector expressed in terms of normalized economic loss

c* A* q

3.2. Demand-side perturbation The scalar element of the ith sector of the demand-side perturbation vector can be calculated as “as-planned” final demand cˆi minus actual final demand c˜i , divided by the “as-planned” production level xˆ i , as follows:

ci∗ =

cˆi − c˜i xˆ i

(4)

 Note that (diag(ˆx))

−1

: xˆ i = / 0,



∀i = 1, 2, . . ., n always exists

due to “economic significance” which states that the ‘as-planned’ production of all sectors do not have zero values. Subsequently,

L. Ocampo et al. / Journal of Manufacturing Systems 41 (2016) 76–85

diag(ˆx) is always a non-singular matrix which implies that −1 (diag(ˆx)) exists. Conversely, Eq. (4) can be represented by Eq. (5)



−1

c ∗ = diag(ˆx)

(ˆc − c˜ )

⎡ 1 ⎢ xˆ 1 ⎢ ⎥ ⎢ ⎢ ⎥ ⎢ ⎢ .. ⎥ ⎢ 0 ⎢ . ⎥ ⎢ ⎢ ⎥ ⎢ . ⎢ ⇔ ⎢ c ∗ ⎥ = ⎢ .. ⎢ i⎥ ⎢ ⎢ ⎥ ⎢ ⎢ .. ⎥ ⎢ . ⎣ . ⎦ ⎢ .. ⎣ ∗ ⎡

c1∗

⎤

cn

···

..

.

..

..

.

···

0 .. .

.

1 xˆ i

..

.

..

.

..

.

···

0

.. . 0 1 xˆ n

⎤

⎡ ⎥ cˆ1 ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ cˆi ⎥⎢ ⎥⎢ ⎥⎣ ⎥ ⎦

c˜1

–

⎤

The demand-side inoperability vector q, can be expressed as the percentage economic loss due to a reduced final demand. The scalar elements of vector q can be calculated by:

⎥ ⎥ ⎥ ⎥ ⎥ – c˜i ⎥ ⎥ ⎥ ⎥ .. ⎦ . .. .

cˆn

(5)

c˜n

–

The demand-side interdependency matrix, denoted by A* is associated with the Leontief technical coefficient matrix A and the “as-planned” productions xˆ . The elements of matrix A* can be derived as follows:

xˆ i xˆ j

(6)

where xˆ i the “as-planned” production of industry i, xˆ j is the “asplanned” production of industry j and aij as the Leontief coefficient. A matrix representation of these elements is shown as follows:

⎡

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⇔⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

1 xˆ 1 0 .. .

...

..

..

..

. .

...



⎡ a

Adiag(ˆx)

0

.. . 0

−1

xˆ 1

...

⎤ 0 .. .

.

1 xˆ 1

..

.

..

.

..

.

...

0

.. . 0 1 xˆ 1



...

a

...

anj

⎡ ⎥ a11 ⎥ ⎥⎢ ⎥⎢ ⎥ ⎢ .. ⎥⎢ . ⎥⎢ ⎥ ⎢ ai1 ⎥⎢ ⎥⎢ ⎥ ⎢ .. ⎥⎣ . ⎥ ⎦ an1 xˆ j

···

a1j

xˆ n

(8)

q = (diag(ˆx))

−1

..

a1n

.. .

ajn

···

ann



⎤

.

···

aij .. .

···

...

a

xˆ n

...

ann

(ˆx − x˜ )

⎡ 1 ⎡ ⎤ q1 ⎢ xˆ 1 ⎢ ⎥ ⎢ ⎢ ⎥ ⎢ ⎢ .. ⎥ ⎢ 0 ⎢ . ⎥ ⎢ ⎢ ⎥ ⎢ .. ⇔⎢q ⎥=⎢ . ⎢ i⎥ ⎢ ⎢ ⎥ ⎢ ⎢ ⎢ .. ⎥ ⎢ . ⎣ . ⎦ ⎢ .. ⎣ 0

0

···

..

.

..

..

.

···

···

0 .. .

.

1 xˆ i

..

.

..

.

..

.

···

0

.. . 0 1 xˆ n

⎤

⎡ ⎥ xˆ 1 ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ xˆ i ⎥⎢ ⎥⎢ ⎥⎣ ⎥ ⎦ xˆ n

–

xˆ 1

⎤

⎥ ⎥ ⎥ ⎥ ⎥ – xˆ i ⎥ ⎥ ⎥ ⎥ .. ⎦ . .. .

–

(9)

xˆ n

The difference between (ˆx) and (˜x) is the deviation of the “asplanned” production. It can be shown that by dividing the economic loss by x˜ i , the demand-side inoperability is bounded in the closed interval 0 ≤ qi ≤ 1 where a value of 0 means that the sector is at its normal state and a value of 1 means that the sector is completely inoperable of production. With the general equation of IIM expressed in matrix notation as q = A*q + c* the inoperability is then obtained and can be analyzed.

⎤ ⎡ xˆ 1 0 . . . . . . 0 ⎤ ⎥ ⎥ ⎢ ⎥ ⎥ ⎢ . . . ⎢ .. ⎥ ⎢ .. .. .. ⎥ ⎥ 0 ⎥ . ⎥ ⎥ ⎢ ⎢ .. ⎥ .. .. × ⎢ .. · · · ain ⎥ . . xˆ n . ⎥ ⎥ ⎢ . ⎥ ⎥ ⎢ ⎥ .. ⎥ ⎢ . .. ⎥ .. .. . . ⎦ ⎣ .. . . 0 ⎦ ···

xˆ n

1n 1j ⎢ 11 xˆ 1 xˆ 1 xˆ 1 ⎥ ⎢ ⎥ ⎢ ⎥ .. .. .. .. ⎢ ⎥ . ⎢ ⎥ . . . ⎢ ⎥ ⎢ xˆ j xˆ 1 xˆ n ⎥ ⎥ ⇔⎢ . . . aij . . . ain ⎢ ai1 xˆ i ⎥ xˆ i xˆ i ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ .. .. .. .. ⎢ ⎥ . . . ⎢ . ⎥



⎣ xˆ j xˆ 1 xˆ n ⎦

an1

xˆ i − x˜ i xˆ i

qn

3.3. Interdependency Matrix

A∗ = (diag(ˆx))

qi =

The economic loss can be described as the difference between the “as-planned” production (ˆx) and the reduced level of production (˜x). By normalizing economic loss in terms of the “as-planned” production (ˆx), q can be expressed as follows:

The value of the final demand for industry i must be cˆi = c˜i in order to determine the upper and lower limits for the normalized reduced final demand. The lower limit is ci∗ = 0 which represents that industry i is completely inoperable. The worst value of the final demand in sector i would be c˜i = 0, i.e. the worst scenario that could happen to the final demand of sector i is for its customers to give up on that sector’s products. As can be seen in Eq. (4), the upper limit would be ci∗ = (ˆci /ˆxi ). Thus, demand-side perturbation of any sector i has 0 ≤ ci∗ ≤ (ˆci /ˆxi ).

a∗ij = aij

Normalized values result to the inoperability metric where it is expressed as the ratio relative to “as-planned” production level. 3.4. Inoperability

0

···

0

79

xˆ n

0

...

...

0

xˆ n (7)

80

L. Ocampo et al. / Journal of Manufacturing Systems 41 (2016) 76–85

3.5. Supply-driven input–output model (SIOM) IOM is a demand-driven analysis that is widely used in the macro-economic context however, several studies exploring supply-sided models are now being conducted and its applications in current literature extended to different issues. Ghosh [15] introduced the supply-driven perspective of the input–output model. The SIOM is concentrated on value added inputs rather than final demand. The variable xij represents the input in terms of the observed monetary value of the commodity flow from sector i to sector j and the matrix of commodity flows is X = (xij )nxn [20,21]. Similar to the demand-driven IOM, the technical coefficient is defined in Eq. (10): aij =

xij

(10)

xi

Eq. (11) is the traditional input–output Ghosh model. x = A(s) x + z ⇒ x = (I − A(s) )

−1

z

(11)

This relationship among all n sectors is represented as a matrix, (s) as shownin Eq.  (11), where x is the vector of total inputs A = (aij )Tnxn =

(s)

aji

is the interdependency matrix derived from the



nxn

economic input–output data, where

(s)

aij



specifies the propor-

tionality coefficient corresponding to the input from sector i to sector j, with respect to the total output of sector i and z is the column vector of value added inputs. 3.6. Supply-side inoperability input–output model (SIIM)

1. Form the matrix O = (oij )nxn where oij is the output of process i that becomes the input of process j. This is expressed in monetary values which represent the aggregate value of all products, i.e. work-in-process inventories, which flow from process i to process j. These values can be acquired from the firm’s accounting department and/or production planning and control department. 2. Establish the matrix A = (aij )nxn where aij = (oij /xi ) represents the ratio of output generated by process i to be used by process j over the required production output of process i. It follows the Leontief balance equation as shown in Eq. (1) where x is the production output vector and c is the final demand vector of all processes. ci = / 0 if process i contains output products which are eventually the finished goods required by the customer or products that are used for spare parts, etc. For instance, in a car manufacturing firm, tire production process has output products that are sold directly to the customers. Otherwise, ci = 0. 3. Form the interdependency matrix A(s) = AT to form the input–output Ghosh model as shown in Eq. (11) where z represents the vector of value added input to all manufacturing processes. 4. Compute for the supply interdependency matrix A(s)* using (15). −1

using MATLAB® software or 5. Compute for the (I − A(s)∗ ) Microsoft Excel® . 6. To determine the cost price change of output or the inoperability vector p, an initial perturbation expressed in percentage as represented by z* is calculated using (13) or assumed as in Santos and Haimes [9]. Compute p using (12) by performing matrix multiplication in MATLAB® software or Microsoft Excel® . 7. Interpret the inoperability vector p in the context of the initial perturbation vector z*.

The supply-driven static IIM was derived by Leung et al. [17], and it is represented by the equation: p = (I − A(s)∗ )

5. Case study

−1 ∗

z

(12)

where p is the vector of the cost change in output due to value added perturbation, A(s)* is the interdependency matrix which is derived from the economic input–output data, and z* is the value added or supply perturbation vector whose elements represent the difference between the planned supply or nominal production and the perturbed value added divided by nominal production, which is equivalent to the increase of value added as a proportion of total planned input. Suppose that (I − A(s)∗ ) z ∗ = (diag(ˆx)) p = (diag(ˆx))

−1

−1

−1

(˜z − zˆ )

(˜x − xˆ )

A(s)∗ = (diag(ˆx))

−1 (s)

A diag(ˆx)

= (bij )nxn and (13) (14) (15)

The variable zˆ is the value of nominal value added and z˜ is the value of degraded value added after perturbation. The supplydriven IIM is used to determine the inoperability of a process of a value-added input perturbation. A supply-driven IIM (SIIM) is more suitable in a manufacturing system as the processes involved in the case study, for instance, do not have final demand that could be perturbed. This is contrary to relevant demand-driven IIM applications in economic systems where economic sectors have final demand. Additionally, the value added inputs such as the raw materials, labor and machineries are elements that could be controlled. 4. Methodology In general, the proposed methodology in assessing risk in manufacturing systems can be described as follows:

A case study was conducted in one of the premier furniture manufacturing firms in the Philippines – an internationally recognized manufacturing firm which produces a wide variety of furniture products at the highest quality. The case firm, situated in Cebu City, Philippines, distributes intricately designed pieces across the globe. Across the furniture manufacturing industry, the case firm has fairly similar processes used in any production floor since wood is the baseline material in the industry. With stiff competition in the industry, the case firm led the innovation with unique furniture designs. This has made the manufacturing processes more complex and susceptible to risk factors such as disruption caused by natural disasters, labor issues, supply shortage, etc. as the country faces these challenges more often. The case firm has 16 different processes such as: milling, veneering, assembly, carving, carpentry, fiber/stone casting, metal framing, powder coating, weaving, retouching, sanding, finishing, upholstery, final fitting, final quality check and final packing process. Due to the high customization of manufactured products, not all products go through the same set of processes. The volume of products manufactured by the firm for the current year 2015 has a total of 183 units and all of these products undergo final fitting, final quality check, and final packing while the least utilized process is fiber/stone casting. Appendix 1 shows the process flows of the products manufactured by the case firm. For instance, Product A undergoes processes 4 through 7 and then skips processes 8 and 9 but proceeds with processes 10 through 13. From Appendix 1, the input–output transactions matrix is developed in Appendix 2. Values in Appendix 2 were obtained from the accounting department of the case firm with some degree of confidentiality. For example, process 1 (milling) delivers Php 998, 189.37 worth of work-in-process inventory to process 2 (assembly).

L. Ocampo et al. / Journal of Manufacturing Systems 41 (2016) 76–85

81

Table 2 Input–output technical coefficient matrix A. Processes

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[1] Milling [2] Assembly [3] Fiber/stone casting [4] Metal framing [5] Powdercoating [6] Weaving [7] Retouching [8] Sanding [9] Finishing [10] Upholstery [11] Final fitting [12] Final quality check [13] Packing

– 0.1450 – – – – – – – – – – –

0.8570 – – – – – – – 0.0738 – – – –

– – – – – – – – – – – – –

0.0029 – – – – – – – – – – – –

– – – 0.6877 – – – – – – – – –

– – – – 0.5072 – – – 0.0342 – – – –

– – – – – 0.4732 – – – – – – –

0.0260 0.8550 – – – – – – – – – – –

0.1141 – – 0.3123 0.4928 0.5628 – 0.9650 – – – – –

– – 1 – – – 1 – 0.3983 – – – –

– – – – – – – – 0.4937 1 – – –

– – – – – – – – – – 1 – –

– – – – – – 0.0350 – – – 1 –

Table 2 shows the matrix A = (aij )nxn which is derived from the Leontief balance equation as shown in (1). These values were obtained by dividing each entry in Appendix 2 by its corresponding required output column value. For instance, milling to assembly has an entry in the technical coefficient matrix A of (998, 189.37/1, 164, 712.10) = 0.8570. The transpose of A = (aij )nxn denoted as AT = (aji )nxn is the inter-

dependency matrix in the Ghosh model and is denoted as A(s) . This is shown in Table 3. −1 The diag(ˆx) and its inverse (diag(ˆx)) are shown in Tables 4 and 5, respectively. The values in Table 5 were obtained by computing for the inverse matrix of diag(ˆx) which is a diagonal matrix where diagonal elements represent the corresponding required output of the processes as shown in Appendix 2. The supply interdependency matrix A(s)* is thus computed using (15) −1

and is shown in Table 6. Its corresponding matrix (I − A(s)∗ ) is presented in Table 7 which is obtained by computing for the inverse matrix of the difference of the identity matrix I and the supply interdependency matrix A(s)* . The impacts of different supply disruptions are presented and discussed under different scenarios in the next section. 6. Results and discussion 6.1. Scenario 1: The impact of local logging ban policy In the case of the furniture firm which primarily produces first class pieces made of high quality wood, a supposed log ban in the Philippines would affect the firm in its acquisition of raw materials. Log ban policies cause suppliers to increase their prices of wood. It also causes loss of jobs to forest dependent communities. This is prevalent in the country as the government is trying to protect its natural resources [31] and to mitigate deforestation problems [32].

For instance, over the last three decades, 20 policies on logging ban have been issued on specific locations of the country [31]. This has made the country as the net importer of logs since the late 1980s [31]. Furniture manufacturers are considered the direct stakeholders that may be affected in any case of a logging ban. With the proposed SIIM model, an z* = 0.10 initial perturbation in the milling process is assumed that is mainly caused by an implementation of a local logging ban policy. This means that, as a result of sudden limited supply, a 10% increase of prices of logs or wood products is expected. This perturbation represents an increase of value added as a proportion of total planned input. This is just a conservative estimate as in the long run, Bugayong [31] pointed out that a 40% increase of prices has been observed due to a number of logging ban policies. Here in this scenario, a localized log ban policy is assumed and the impact on prices in the market is relatively small as furniture manufacturers may find alternative suppliers immediately. Using Eq. (12), results of final perturbation are presented in Table 8. Having a value-added perturbation of 10% in the milling process that is caused by s local logging ban policy yields the price-cost change vector p as shown in Table 8. This vector p represents the final value-added perturbation of the processes in this manufacturing system. As expected, the milling process has the largest price-cost change since it is the only process being perturbed. Other processes also incur price-cost changes due to the interdependencies of the processes in the furniture manufacturing system. On the other hand, the final perturbation in the fiber/stone casting has a value of zero because this process does not have inputs from other processes as shown in matrix A of Table 2. Except for the milling process, significant perturbation is observed in assembly, retouching and sanding processes. Total value-added price-cost of these processes is expected to increase by a factor of p. The inputs for these processes are value-added inputs which consist of materials and labor.

Table 3 Interdependency matrix A(s) . Processes

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[1] Milling [2] Assembly [3] Fiber/stone casting [4] Metal framing [5] Powdercoating [6] Weaving [7] Retouching [8] Sanding [9] Finishing [10] Upholstery [11] Final fitting [12] Final quality check [13] Packing

– 0.8570 – 0.0029 – – – 0.0260 0.1141 – – –

0.1450 – – – – – – 0.8550 – – – – –

– – – – – – – – – 1 – – –

– – – – 0.6877 – – – 0.3123 – – – –

– – – – – 0.5072 – – 0.4928 – – – –

– – – – – – 0.4732 – 0.5628 – – – –

– – – – – – – – – 1 – – –

– – – – – – – – 0.9650 – – – 0.035

– 0.0738 – – – 0.0342 – – – 0.3983 0.4937 – –

– – – – – – – – – – 1 – –

– – – – – – – – – – – 1 –

– – – – – – – – – – – – 1

– – – – – – – – – – – – –

82

Table 4 The diag(ˆx) matrix. [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[1] Milling [2] Assembly [3] Fiber/stone casting [4] Metal framing [5] Powdercoating [6] Weaving [7] Retouching [8] Sanding [9] Finishing [10] Upholstery [11] Final fitting [12] Final quality check [13] Packing

1,164,712.10 – –

– 1,185,715.30 –

– – 38,008.08

– – –

– – –

– – –

– – –

– – –

– – –

– – –

– – –

– – –

– – –

–

–

–

91,874.17

–

–

–

–

–

–

–

–

–

–

–

–

–

145,449.06

–

–

–

–

–

–

–

–

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

307,345.68 – – – – –

– 140,623.16 – – – –

– – 1,080,750.13 – – –

– – – 1,752,048.74 – –

– – – – 1,159,800.23 –

– – – – – 2,254,449.47

– – – – – –

– – – – – –

–

–

–

–

–

–

–

–

–

–

–

2,298,587.29

–

–

–

–

–

–

–

–

–

–

–

–

–

5,025,280.36

Table 5

 −1

The diag xˆ

matrix.

Processes

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[1] Milling [2] Assembly [3] Fiber/stone casting [4] Metal framing [5] Powdercoating [6] Weaving [7] Retouching [8] Sanding [9] Finishing [10] Upholstery [11] Final fitting [12] Final quality check [13] Packing

8.58581E−07 – –

– 8.43373E−07 –

– – 2.63102E−05

– – –

– – –

– – –

– – –

– – –

– – –

– – –

– – –

– – –

– – –

–

–

–

1.08845E−05

–

–

–

–

–

–

–

–

–

–

–

–

–

6.87526E−06

–

–

–

–

–

–

–

–

– – – – – –

– – – – – –

– – – – – –

– – – – – –

– – – – – –

3.25367E−06 – – – – –

– 7.1112E−06 – – – –

– – 9.25283E−07 – – –

– – – 5.7076E−07 – –

– – – – 8.62217E−07 –

– – – – – 4.43567E−07

– – – – – –

– – – – – –

–

–

–

–

–

–

–

–

–

–

–

4.3505E−07

–

–

–

–

–

–

–

–

–

–

–

–

–

1.98994E−07

L. Ocampo et al. / Journal of Manufacturing Systems 41 (2016) 76–85

Processes

L. Ocampo et al. / Journal of Manufacturing Systems 41 (2016) 76–85

83

Table 6 Supply interdependency matrix A(s)* . Processes

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[1] Milling [2] Assembly [3] Fiber/stone casting [4] Metal framing [5] Powdercoating [6] Weaving [7] Retouching [8] Sanding [9] Finishing [10] Upholstery [11] Final fitting [12] Final quality check [13] Packing

– 0.8418 – 0.0370 – – – 0.0280 0.0759 – – – –

0.1476 – – – – – – 0.9381 – – – – –

– – – – – – – – – 0.0328 – – –

– – – – 0.4344 – – – 0.0164 – – – –

– – – – – 0.2400 – – 0.0409 – – – –

– – – – – – 0.9556 – 0.0987 – – – –

– – – – – – – – – 0.1212 – – –

– – – – – – – – 0.5953 – – – 0.0075

– 0.1091 – – – 0.1948 – – – 0.6017 0.3837 – –

– – – – – – – – – – 0.5144 – –

– – – – – – – – – – – 0.9808 –

– – – – – – – – – – – – 0.4575

– – – – – – – – – – – – –

Table 7 −1 The matrix (I − A(s)∗ ) . Processes

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[1] Milling [2] Assembly [3] Fiber/stone casting [4] Metal framing [5] Powdercoating [6] Weaving [7] Retouching [8] Sanding [9] Finishing [10] Upholstery [11] Final fitting [12] Final quality check [13] Packing

1.1549 1.0495 0.0000 0.0427 0.0186 0.1424 0.1361 1.0168 0.7084 0.4428 0.4996 0.4900 0.2318

0.1818 1.2314 0.0000 0.0067 0.0029 0.1407 0.1344 1.1602 0.7185 0.4486 0.5065 0.4968 0.2360

0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0328 0.0169 0.0165 0.0076

0.0009 0.0061 0.0000 1.0000 0.4344 0.1138 0.1087 0.0057 0.0489 0.0426 0.0407 0.0399 0.0183

0.0013 0.0088 0.0000 0.0000 1.0000 0.2539 0.2426 0.0083 0.0710 0.0722 0.0644 0.0631 0.0290

0.0020 0.0135 0.0000 0.0001 0.0000 1.0212 0.9758 0.0127 0.1086 0.1836 0.1361 0.1335 0.0612

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.1212 0.0624 0.0612 0.0280

0.0120 0.0815 0.0000 0.0004 0.0002 0.1275 0.1219 1.0768 0.6545 0.4086 0.4613 0.4525 0.2151

0.0202 0.1370 0.0000 0.0007 0.0003 0.2143 0.2047 0.1290 1.0995 0.6864 0.7750 0.7601 0.3487

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.5144 0.5046 0.2308

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.9808 0.4487

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.4575

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000

6.2. Scenario 2: The impact of increase in labor costs Due to the highly customized furniture products the firms manufacture, the case firm and its industry to some extent is labor intensive. An increase of the costs of labor in the Philippine market impacts all firms in general. This cost-price change would certainly affect the firm since it requires highly manual labor to manufacture its furniture products. In this scenario, an 8% increase in the standard minimum rate of a regular worker is applied to all processes. This estimate is a close projection of the average increase of 6.1% in labor wages from 1980–1997 reported by Hernandez [33]. Table 9 presents the perturbation of the processes imposed by a possible increase in labor costs. Scenario 2 depicts how the 8% increase in labor rate changes the cost-price values of the different production processes. The z* values shown in Table 9 are obtained after having the change in total value-added brought by the change in labor. As observed in Table 9, change in labor produces less than one percent value-added perturbations to all the processes. Fiber/stone casting, metal framing, and powdercoat have no values for z* as these processes are outsourced. The resulting cost-price change values are also minimal. Fiber/stone casting still has no cost change as this process does not need the outputs of the other processes to be its inputs. Thus, fiber/stone casting is not affected in the given scenario. 6.3. Scenario 3: The impact of metal shortage caused by severe weather condition The furniture manufacturing firm in this case study uses metals in its metal framing process. There are instances where the price of metal fluctuates due to changes in supply and demand and with the cost of production as well. The effect on the firm brought about

by the change in price of the metals can be investigated with the use of the supply-driven input–output model. In this case, a 10% increase on the price of metal is assumed. This is a conservative estimate based on the report of Garcia and Vicente [34] which highlighted 19% increase of scrap metals over the years. Table 10 shows the value added perturbation caused by an increase in the price of metals. A 10% value-added perturbation in metal framing process caused by a change in supply-demand and cost of production which yields a small value of p in the other processes. The metal framing process has the highest value of p mainly because it is the process being perturbed. This process requires inputs from other processes but its output is needed as to only one process in the system. With this, a perturbation in metal framing would give change in cost-price although it is not very significant due to its weak interrelationship with the other processes.

Table 8 Value-added perturbation caused by local logging ban policy scenario. Processes

z* (initial perturbation)

p (final perturbation)

Milling Assembly Fiber/stone Metal framing Powder coating Weaving OD retouching Sanding Finishing Upholstery Final fitting Final QC Packing

0.10 0 0 0 0 0 0 0 0 0 0 0 0

0.115 0.105 0.000 0.004 0.002 0.014 0.014 0.102 0.071 0.044 0.050 0.049 0.023

84

L. Ocampo et al. / Journal of Manufacturing Systems 41 (2016) 76–85

Table 9 Value-added perturbation caused by increase in labor costs scenario. Processes

z* (initial perturbation)

p (final perturbation)

Milling Assembly Fiber/stone casting Metal framing Powder coating Weaving OD retouching Sanding Finishing Upholstery Final fitting Final QC Packing

0.00117 0.00146 0.00000 0.00000 0.00000 0.00655 0.00075 0.00090 0.00115 0.00074 0.00005 0.00002 0.00007

0.002 0.003 0.000 0.000 0.000 0.007 0.008 0.004 0.004 0.004 0.004 0.004 0.002

Table 10 Value-added perturbation caused by increase metal prices scenario. Processes

z* (initial perturbation)

p (final perturbation)

Milling Assembly Fiber/stone Metal framing Powdercoat Weaving OD retouching Sanding Finishing Upholstery Final fitting Final QC Packing

0 0 0 0.10 0 0 0 0 0 0 0 0 0

0.000 0.001 0.000 0.100 0.043 0.011 0.011 0.001 0.005 0.004 0.004 0.004 0.002

7. Conclusion and future work This work presents a systems approach in analysing risks of a manufacturing system due to perturbations in its supply brought about by natural disasters, economic conditions, government policies, etc. A supply-driven inoperability input–output model (SIIM) initially used in literature in risk analysis of an economic system from the perspective of supply changes. This approach is most suitable for a production process system rather than the highly regarded demand-driven approach mainly because each process in a manufacturing system generally does not have any final exogenous demand unlike economic sectors where final demand is naturally present. The proposed approach is highly significant to manufacturing and risk practitioners as it determines the total impact of a certain supply change in terms of price increase. This total impact is not a straightforward approach since similar to economic systems, manufacturing systems have interdependencies that must be considered. To illustrate the proposed approach, an actual case study was conducted in one of the leading furniture manufacturing firms in the Philippines that is also globally acknowledged for its excellent products. Three scenarios were presented in the study. The first scenario illustrates the cost-price change brought about by the change in price of the wood used in the milling operation due to a local logging ban policy. The second scenario shows how the change in labor costs affect the manufacturing system. Finally, the third scenario illustrates the cost-price change brought about by the change in price of the metals used in the metal framing process. The results of the three scenarios have shown that perturbations on processes produce cost-price change on each process, thus on the entire manufacturing as well. The proposed approach effectively quantifies the actual impact on each process after a perturbation has occurred. Unlike previous demand-driven IIM applications adopted

in economic systems where perturbations represent percentage of reduced final output brought about by degraded exogenous demand, the supply-driven IIM model adopted in this work determines perturbations as cost-price increase in production output due to increase in prices of value-added input brought about by degraded supply which may be caused by disasters or policy implementation as shown in the case study. Supply-driven IIM, as demonstrated in the case study, is more plausible than demand-driven IIM because in most manufacturing systems particularly with make-to-order systems, demand is fixed beforehand and agreed upon by all concerned parties. Thus, “degraded demand” concept used in demand-driven IIM cases becomes irrelevant while the concept on “increase in production output” is more applicable as production costs of outputs typically increase when prices of inputs increase. Using the proposed approach, the interrelationships of the different processes in a manufacturing context are concretely defined and the underlying risks of perturbations can be observed. Thus, management would be able to plan out ahead mitigating policies both at the strategic and tactical levels in order to attain a resilient manufacturing systems. This paper paves interesting research questions in manufacturing system risk analysis. Future work might extend the proposed approach to quantify the total impact of a supply perturbation from the time it has occurred to the time that the manufacturing system attains a normal production. Another work may address the imprecision of values in the output–input table in order to provide more reliable results. Acknowledgement We are thankful for the support provided by the management and staff of the case firm. We are also grateful with the two anonymous reviewers who helped us improve the quality of this paper. L. Ocampo acknowledges the support provided by the University of San Carlos in terms of resource use. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jmsy.2016.07. 005. References [1] Ocampo L, Clark E. A sustainable manufacturing strategy framework: the convergence of two fields. Asian Acad Manag J 2015;20(2):29–57. [2] Ocampo L, Clark E. A sustainable manufacturing strategy decision framework in the context of multi-criteria decision-making. Jordan J Mech Ind Eng 2015;9(3):177–86. [3] Hayes RH, Wheelwright SC. Restoring our competitive edge: competing through manufacturing. New York: John Wiley and Sons; 1984. [4] Bates KA, Amundson SD, Schroeder RG, Morris W. The crucial interrelationship between manufacturing strategy and organizational culture. Manag Sci 1995;41:1565–80. [5] Tan CS, Tan PS, Lee SSG, Pham MT. An inoperability input–output model (IIM) for disruption propagation analysis. In: IEEE International Conference on Industrial Engineering and Management. 2013. p. 186–90, http://dx.doi.org/10.1109/ IEEM.2013.6962400. [6] Yang J, Lee H. An AHP decision model for facility location selection. Facilities 1997;15(9):241–54. [7] Tukundane C, Minnaert A, Zeelen J, Kanyandago P. Building vocational skills for marginalised youth in Uganda: a SWOT analysis of four training programmes. Int J Educ Dev 2015;40:134–44, http://dx.doi.org/10.1016/j.ijedudev. 2014.10.007. [8] Lolli F, Ishizaka A, Gamberini R, Rimini B, Messori M. FlowSort-GDSS – a novel group multi-criteria decision support system for sorting problems with application to FMEA. Expert Syst Appl 2014;42(17–18):6342–9. [9] Santos J, Haimes Y. Modeling the demand reduction (IO) inoperability due to terrorism of interconnected infrastructures. Risk Anal 2004;24(6):1437–51. [10] Jiang P, Haimes Y. Risk management for Leontief-based interdependent systems. Risk Anal 2004;24(5):1215–29.

L. Ocampo et al. / Journal of Manufacturing Systems 41 (2016) 76–85 [11] Haimes Y, Horowitz B, Lambert J, Santos J, Lian C, Crowther K. Inoperability input–input–output model (IIM) for interdependent infrastructure sectors: theory and methodology. J Infrastruct Syst 2005;11:67–79. [12] Santos JR. Inoperability input–output modeling of disruptions to interdependent economic systems. Syst Eng 2006;9(1):20–34, http://dx.doi.org/ 10.1002/sys.20040. [13] Leontief W. Quantitative input and output relations in the cconomic system of the United States. Rev Econ Stat 1936;18:105–25. [14] Miller R, Blair P. Input–output analysis: foundations and extensions. New York, NY: Cambridge University Press; 2009. [15] Ghosh A. Input–output approach to an allocative system. Economica 1958;25(1):58–64. [16] Lin X, Polenske K. Input—output modeling of production processes for business management. Struct. Change Econ. Dynam 1998;9(2):205–26. [17] Leung M, Haimes YY, Santos JR. Supply- and output-side extensions to the inoperability input–output model for interdependent infrastructures. J Infrastruct Syst 2007;13(4):299–310. [18] Leung P, Pooley S. Regional economic impacts of reductions in fisheries production: a supply-driven approach. Mar Resour Econ 2002;16:251–62. [19] Park J. Application of a price-sensitive supply-side input–output model to an examination of the economic impacts: The Hurricane Katrina and Rita disruptions of the US oil-industry. Ecol Econ 2009. [20] Xu WP, Hong L, He LG, Wang SL, Chen XG. Supply-driven dynamic inoperability input–output price model for interdependent infrastructure systems. J Infrastruct Syst 2011;17(4):151–62. [21] Xu W, Wang Z. The uncertainty and sensitivity analysis of the interdependent infrastructure sectors based on the supply-driven inoperability input–output model. Int J Innov Comput Inf Control 2015;11(2):616–7. [22] Resurreccion J, Santos J. Stochastic modeling of manufacturing-based interdependent inventory for formulating sector prioritization strategies in reinforcing disaster preparedness. IEEE Syst Inf Des Symp 2012:134–9, http://dx.doi.org/10.1109/SIEDS.2012.6215127. [23] Anderson C, Santos J, Haimes Y. A risk-based input–output methodology for measuring the effects of the August 2003 Northeast Blackout. Econ Syst Res 2007;19(2):183–204.

85

[24] Tan R, Aviso K, Promentilla M, Yu K, Santos J. Fuzzy inoperability input–output analysis of mandatory biodiesel blending programs: the Philippine case. Energy Proc 2014;61:45–8. [25] Tan R, Aviso K, Promentilla M, Yu K, George T. Development of a fuzzy linear programming model for allocation of inoperability in economic sectors due to loss of natural resource inputs. DLSU Bus Econ Rev 2015;24(2):1–12. [26] Santos JR, May L, El Haimar A. Risk-based input–output analysis of influenza epidemic consequences on interdependent workforce sectors. Risk Anal 2013;33(9):1620–35. [27] Setola R, De Porcellinis S, Sforna M. Critical infrastructure dependency assessment using the input–output inoperability model. Int J Crit Infrastruct Prot 2009;2(4):170–8. [28] Haimes YY, Jiang P. Leontief-based model of risk in complex interconnected infrastructures. J Infrastruct Syst 2001;7(1):1–12. [29] Haimes Y. Risk modeling, assessment, and management. 2nd ed. New York: Wiley & Sons; 2004. [30] Jung J, Santos J, Haimes Y. International trade inoperability input–output model (IT-IIM): theory and application. Risk Anal 2009;29(1):137–54. [31] Bugayong LA. Effectiveness of logging ban policies in protecting the remaining natural forests of the Philippines. In: Proceedings of the Berlin Conference on Human Dimensions of Global Environmental Change–Resource Policies: Effectiveness, Efficiency, and Equity. 2006. [32] Tumaneng-Diete T, Ferguson IS, MacLaren D. Log export restrictions and trade policies in the Philippines: bane or blessing to sustainable forest management? For Policy Econ 2005;7:187–98. [33] Hernandez J. Competitiveness and unit labor cost. In: Business Focus Series, De La Salle University Center for Business Research and Development. 2005. Accessed from: http://www.dlsu.edu.ph/research/centers/cberd/pdf/ bus focus/2005/competitiveness-laborcost.PDF. [34] Garcia MC, Vicente S. Competitiveness in the Philippines steel industry. In: Technical Workshop on Industry Studies for the Meeting the Challenges of Globalization: Production Networks, Industrial Adjustment, Institutions and Policies, and Regional Cooperation Project. 2005. Accessed from: http://www.dlsu.edu.ph/research/centers/aki/ pdf/ concludedProjects/ volumeI/GarciaVicente.pdf.