A Decision Framework for Maximising Lean Manufacturing Performance

International Journal of Production ResearchVol. 50, No. 8, 15 April 2012, 2234–2251

A decision framework for maximising lean manufacturing performance

Varun Ramesh and Rambabu Kodali*

Mechanical Engineering Group, Birla Institute of Technology and Science, Pilani-333031, Rajasthan, India

(Received 26 May 2010; final version received 14 February 2011)

Since the development of the original value stream mapping (VSM) by Taichi Ohno at Toyota, a number ofauthors have suggested several additional VSM tools to understand and improve the value stream throughwaste reduction. A single best VSM tool, though effective in dealing with a certain waste type, becomesredundant as other wastes take centre stage and/or organisational priorities change. To overcome this, adecision framework based on a novel formulation of the integrated analytical hierarchy process (AHP) – pre-emptive goal programming (PGP) has been proposed. This framework not only guarantees accurate selectionof an ideal VSM tool, based on the current organisation’s priorities, but also aids the decision maker to arriveat the optimum implementation sequence of a chosen set of VSM tools to identify and reduce all wastespresent in the system, thereby maximising organisational performance in the shortest timeframe.

Keywords: lean manufacturing; waste; VSM; decision framework; lean competitive priorities; lean perfor-mance metrics; AHP; PGP

1. Introduction

The term ‘lean manufacturing’ was first used in The machine that changed the world by James Womack and DanielJones (1991) to describe the manufacturing philosophy pioneered by Toyota. The philosophy has been practised atToyota under the name of Toyota Production System (TPS), which has its origins in Kichiro Toyoda’s (the founderof Toyota) work way back in 1934 but has only recently (since 1990) received global attention. In a nutshell, leanmanufacturing is the endless pursuit of eliminating waste (Shingo 1989). Waste is anything that adds cost, but notvalue, to a product (Ohno 1988). Toyota categorises the different types of waste observed around its plant into sevencategories, also known as the ‘seven deadly wastes’ (Shingo 1988). Several authors have presented variousalternative typologies for different types of waste present in a system; Dennis (2007) has included the waste ofknowledge disconnection in addition to the seven wastes. Liker and Meier (2006) have introduced the waste ofunused creativity. The Kaizen Institute (2010) proposed reprioritisation waste as an additional category. Hines et al.(1998) have introduced power and and energy, human potential, environmental pollution, unnecessary overheadsand inappropriate design. In the present research, only the seven wastes as originally proposed by Shingo (1988)have been considered. These are the wastes created by: overproduction; inventory; waiting; overprocessing;transportation; excessive human motion; and defects.

1.1 Value stream mapping as a tool against waste

The concept of using a visual tool to represent the flow of material and information as a means to identify andeliminate waste was originally introduced by Taichi Ohno. Originally, this methodology was passed on in Toyotathrough the learning by doing process – mentors trained mentees by assigning them to projects – and remainedunknown to the outside world at large. Mike Rother and John Shook changed that, in their Learning to see (1999).According to Rother and Shook, a value stream is defined as all the actions (both value added and non-value added)currently required to bring a product through the main flows essential to every product: the production flow fromraw material into the arms of the customer and the design flow from concept to launch.

An alternative view to VSM has also been found in the literature. As proposed by Hines et al. (1998), valuestream management is a more strategic and holistic approach to waste identification and removal. By borrowingtechniques from diverse fields such as engineering, logistics and operations research, Hines and Rich (1997) have

*Corresponding author. Email: [email protected]

ISSN 0020–7543 print/ISSN 1366–588X online

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compiled a set of seven detailed value stream mapping tools (Table 1) to identify micro-level waste and subsequentlyreduce it. However, application of inappropriate mapping tools may result in the additional wastage of resourcessuch as time and money, and the reduction of employees’ confidence in the lean philosophy. Hence, Hines and Richhave also proposed a decision heuristic for selection of value stream mapping techniques using the Value StreamAnalysis Tool (VALSAT) approach. As part of the heuristic, Hines and Rich have developed a correlation matrixbetween various waste types and the seven value stream mapping tools. The current paper further develops thematrix to encompass lean value stream mapping (current state map/future state map), as shown in Table 2. Thispresents the organisation with the opportunity to compare the performance of value stream management tools with

Table 1. The seven value stream mapping tools.

Mapping tool Description

1. Process activity mapping An industrial engineering tool for the study of flow process, identification of waste,consideration of process rearrangement, consideration of flow rearrangement,analysis of the occurrence of activity.

2. Supply chain response matrix Portrays in a simple diagram the critical lead-time constraints for a particularprocess. It may plot a simple diagram indicating cumulative inventory lead timeversus process lead time at various stages. It helps in targeting each of theindividual inventory amounts and lead time at different stages for improvement.

3. Production variety funnel Plots the number of product variants at each stage of the manufacturing process.Helps in deciding where to target inventory reduction and making changes to theprocessing of products. Provides overview of the company.

4. Quality filter mapping This tool is designed to identify quality problems in the order fulfilment process orthe wider supply chain. The map shows the occurrence of the three types of defects(product defects, scrap defects and service defects) in the value stream.

5. Demand amplification mapping This graph shows the batch size of the product at various stages of the productionprocess (within a company or supply chain).It can also show the inventory holdingat various stages in time.

6. Decision point analysis Decision point analysis is of particular use for ‘T’ plants or for supply chains thatexhibit similar features, although it may be used in other industries. It indicatesthe point at which products stop being made according to actual demand andinstead are made against forecast alone.

7. Physical structure mapping Useful in understanding what a particular supply chain looks like at an overview orindustry level and how it operates; in particular, in directing attention to areas thatmay not be receiving sufficient development attention.

Source: Hines et al. (1997), adapted from Singh et al. (2006).

Table 2. 7þ 1 value stream mapping tools.

Mapping tools

Wastes

Processactivitymapping

Supplychain

responsematrix

Productionvarietyfunnel

Qualityfilter

mapping

Demandamplificationmapping

Decisionpoint

analysis

Physicalstructuremapping

Leanvaluestreammapping

Overproduction L M L M M HWaiting H H L M M MTransport H L LOver-processing H M L L MInventory M H M H M L HMotion H LDefects L H

Notes: H¼High correlation and usefulness; M¼Medium correlation and usefulness; L¼Low correlation and usefulness.Tools 1–7 adapted from Hines and Rich (1997).

International Journal of Production Research 2235

lean material and information flow mapping and, based on their priorities, to choose the best tool for wasteidentification and removal.

The VALSAT process, though simple in nature, is prone to judgemental inconsistency created by the biased viewof the decision makers while allocating emphasis to different alternatives (Singh et al. 2006). To overcome theseshortfalls, Singh et al. have proposed a fuzzy-based, multi-preference, multi-person and multi-criteria decision-support heuristic for the selection of value stream mapping tools.

Though the framework provides a logical and rational methodology for selection of detailed value streammapping tools, it fails to address long-term waste reduction. According to lean principles, if a manufacturing plantwants to deliver the highest quality, at the lowest cost, in the shortest time to its customers and also continuouslyimprove on them, then it must continuously identify and remove all the waste present in the system. Although asingle VSM tool may be effective in dealing with a certain type waste that currently is of the highest priority to theorganization, it becomes increasingly redundant as other wastes take centre stage and/or organisational prioritieschange. There is no one-time solution for highest quality at the lowest cost in the shortest time. This is thefundamental problem faced by the previously described decision process. Hence, there exists a need to develop aframework that not only guarantees selection of the most suitable VSM tool based on the current organisation’spriorities but also proposes the best sequence of application of VSM tools to remove other wastes present in thesystem and maximise the performance measures of the organisation.

This is the objective of the current paper: to develop a decision framework for the selection of the best sequenceof VSM tool application to maximise the performance of a lean manufacturer by removal of all waste types in theshortest time and with the minimum expenditure of resources. To do so, the paper describes a novel approach tointegrated AHP-PGP modelling using an iterative algorithm to solve the prioritised goal optimisation.

2. An overview of the case organisation

The organisation considered in this case study is a medium-sized, original equipment manufacturer (OEM) for manyautomobile manufacturers located in the northern part of India. It manufactures different types of automobilecomponent (base plates, separator assemblies, notch backs, etc.). These parts are predominantly used by majorautomobile manufacturers (for both two-wheel and four-wheel drive vehicles) across the country. Table 3 presents asummary of the case organisation.

The organisation is currently facing a lot of problems in terms of not being able to meet its competitive priorities.A few of the critical problems are high variety and low volume, quality, delivery and cost of production. Hence, theorganisation chose to streamline its processes to achieve its objectives of improving productivity, quality, deliveryand minimum cost. The organisation has a strong focus on the safety and morale of its workforce and would like toachieve its business objectives without comprising its safety standards.

Top management was open to implementing management philosophies such as lean manufacturing. This isbecause, as an OEM to some of the biggest automobile manufacturers in the country, they had obtained the ISO9000 certification of quality, which had produced good results in the past in terms of standardising various processesas well as reducing defects. Hence, they were contemplating implementing such manufacturing managementpractices and philosophies. The first step to streamlining its process was to identify appropriate mapping tools tomap the current organisational processes and identify waste. The issue here was how to choose the best VSM toolsto map and reduce all the various forms of waste in the organisation with the least expenditure of time and energy.

Table 3. Summary of case organisation.

Industry characteristics Details about the case organisation

Industry type Discrete type manufacturingIndustry sector ManufacturingProduct Different types of automobile parts for two-wheel and four-wheel drive vehiclesProduct type Critical componentsProduction volume and variety High variety and low volumeCompany vision To be a star performer and market leaderMission Continuous improvement of products, processes and people

2236 V. Ramesh and R. Kodali

This dilemma was resolved by the application of the developed decision frame for lean tool selection so as tomaximise the performance of lean manufacturing.

3. Development of the decision framework

The decision framework selects the best sequence of VSM tool application to maximise the performance of a leanmanufacturer by removal of all waste types in the shortest time and with the minimum expenditure of money andenergy.

The steps involved in the decision framework process are as follows:

(1) Identification of performance measures (PM) for lean manufacturing that need to be maximised.(2) Identification of VSM tools for the lean manufacturer that will aid in the improvement process.(3) Selection of VSM tool for current priority: using AHP to select the best VSM tool to maximise the current

priority with minimum expenditure of time and effort.(4) Identification of performance metrics for each PM and prioritisation of them with respect to the

corresponding PM.(5) Selection of VSM tools for future priorities: using PGP to identify the best sequence of VSM tool application

to maximise all PMs by identification and subsequent reduction of all waste types with minimumexpenditure of time and money. PGP also outputs the optimum value of performance metrics that maximisethe corresponding PM under the given constraint.

(6) Comparison of the optimum value of the metrics with real time performance metrics to help decide when acertain VSM tool has attained the limit of its ability to effect improvement and that it is time to apply thenext VSM tool in the sequence as defined by PGP. Figure 1 shows the flowchart for the decision framework.

Figure 1. Flowchart for decision framework.


3.1 Performance measurement

The objective of lean manufacturing is to maximise performance by eliminating waste. Hence, performancemeasures and waste serve as the attributes and sub-attributes of the AHP model, described in a later section, whichaid the decision maker in converting information (knowledge, judgements, values, opinions, needs, wants, etc.) tonumerical values by establishing priorities. These will also serve as elements (objective function and constraints) forthe PGP model and hence defining a comprehensive set of performance measures that provide an all-round view ofthe organisation’s priorities and preferences is the most critical section of the decision framework.

In lean philosophy, measures give a sense of direction as we move from the current state to the future state bykeeping our actions aligned with the business’s long-term goals (Rother 2010). Dennis (2007) has suggested sixprimary customer focus or performance measures (PM) for a lean manufacturer: productivity, quality, cost,delivery, safety and and environment and morale. There also exists a need to define a new set of lean performancemetrics so as to measure the intensity of the PM along different dimensions. Traditional metrics (related to massproduction) cannot be used in a lean environment because these will cause people to resist changing the habits forwhich they were previously rewarded and hence performance will depreciate accordingly (Total SystemsDevelopment Inc. 2001). The most common metric in mass manufacturing is the desire to produce as much aspossible to improve the efficiency or utilisation of personnel and equipment. This leads to the waste created byoverproduction, if what is produced is not synchronised with what is required (customer demand). Ideal efficiency(lean) is to make exactly what is needed, when it is needed, in the quantities required and at the lowest cost.

3.2 Lean performance metrics

A performance metric is a verifiable variable that is expressed in either quantitative or qualitative terms. Neely et al.(2005) defined performance metrics as a variable used to quantify the efficiency and effectiveness of an action.Daum and Bretscher (2004) extended the definition of performance metric to include a qualitative aspect becausedifferent stakeholders put different values on the same outcome, which cannot be quantified. Also, intangiblemeasures to a large extent cannot be quantified, and thus require a qualitative metric (Lev 2001). A performancemetric should be based on an agreed-upon set of data and a well-understood and well-documented process forconverting that data into the metric. Given the data and process, independent sources should be able to arrive at thesame metric value (Melnyk et al. 2004). To interpret meaning from a metric, however, it must be compared to atarget (Mahindhar 2005). Based on these parameters, 29 key performance metrics for lean manufacturing wereidentified (Total Systems Development Inc. 2001; Anand and Kodali 2008) through a thorough literature survey(Table 4). The performance metrics for the six PM of lean manufacturing are described below: Lean metrics forproductivity:

(1) Wait Kanban Time (WKT): In a lean manufacturing company (using Kanban or pull methods), productionmust be stopped to avoid the waste of overproduction. The line is in Wait Kanban Time mode when it awaitsthe order to resume making the products required by the customer. Consistently high amount of WaitKanban Time indicates an imbalance between processes, caused by greater capacity than required to meetthe customer demand.

(2) Parts per labour hour (PLH): This considers the variability of the workforce, as well as the overall efficiencyof the production line. This calculation is the total number of good (non-defective) parts produced, dividedby the total labour hours worked, minus any scheduled non-production time (including Wait Kanban Time)

(3) Total parts produced (TPP): This is necessary to understand the production process because allmeasurements, such as yield or scrap rate, are compared to the total parts produced and expressed as apercentage of this total.

(4) Line stop time (LST): This is the amount of time the line is stopped for any reason other than equipmentdown time or Wait Kanban Time. Causes include part shortage, quality issues, etc. It is normally reported asa percentage of standard operating time minus Wait Kanban Time.

(5) Equipment downtime (EDT): It is the percentage of time the machine is unable to produce product duringscheduled operation time.

(6) Shorting customer process (SCP) and: This measure indicates a process’s ability to produce what is needed,when it is needed and according to the process Takt time. It should be used only if there is an ongoingproblem, or if it is the best measure of process capability. It can be calculated by dividing the amount of stoptime by standard operation time, minus the Wait Kanban Time.


(7) Stopping supplier process (SSP): This is the same as the shorting customer process (SCP).(8) Changeover time (C/T): A lengthy changeover time contributes to a lack of efficiency. Time lost is generally

compensated for by running larger batch sizes. It is the time recorded in minutes from the last good of onepart type to the first good of another part type.

Lean metrics for quality:

(9) Customer satisfaction (CUS): This is defined as the number of defective parts returnedfrom the following process or customer. It is calculated as a percentage of the total parts produced by aprocess.

Table 4. List of key PM metrics for lean manufacturing.

Performance metric Quantitative Qualitative Reference

1 Wait Kanban Timep

Total Systems Development Inc. (2001)2 Parts per labour hour

pTotal Systems Development Inc. (2001)

3 Total parts producedp

Total Systems Development Inc. (2001);Anand et al. (2008)

4 Line stop timep

Total Systems Development Inc. (2001)5 Equipment downtime

pTotal Systems Development Inc. (2001);

Anand et al. (2008)6 Shorting customer process


7 Stopping supplier processp

Total Systems Development Inc. (2001)8 Changeover time


Dennis (2007); Anand and Kodali (2008);Shingo (1989)

9 Customer satisfactionp

Total Systems Development Inc. (2001);Anand et al. (2008)

10 Defects repaired in processp

Total Systems Development Inc. (2001);Anand and Kodali (2008)

11 Yieldp


12 Scrap %p

Total Systems Development Inc. (2001)13 Scrap cost


Anand and Kodali (2008)14 Total inventory


Anand and Kodali (2008)15 Labour content


Anand and Kodali (2008)16 Raw material variance


17 Missed delivery cyclesp


18 Quick response to customerp

Total Systems Development Inc. (2001)19 Delivery reliability


Anand and Kodali (2008)20 Number of work-related injuries


21 Lost work daysp

Total Systems Development Inc. (2001)22 Number of medical visits


23 Work-related restrictionsp

Total Systems Development Inc. (2001);Dennis (2007)

24 Employment securityp

Total Systems Development Inc. (2001);Dennis (2007); Anand and Kodali (2008)

25 Employee training andand developmentp

Total Systems Development Inc. (2001);Dennis (2007); Anand and Kodali (2008)

26 Number of awards andandrewards disbursed


Dennis (2007); Anand and Kodali (2008)27 Employee involvement


Dennis (2007)28 Culture

pDennis (2007)

29 Governancep

Dennis (2007); Thompson and Wallace (1996)


(10) Defects repaired in process (DEF): Products are categorised as either acceptable parts as produced (first run

or first time through), parts requiring rework or scrap parts. The second category of parts is recorded in this

metric and represented as a percentage of total parts produced.(11) Yield (YLD): This refers to the percentage of total parts produced that are accepted as is, i.e. without any

rework.(12) Scrap % (SCR): These parts require excessive rework and hence are scrapped and recycled into raw

materials (if possible) than rectified back into the flow. This metric is related to defects repaired in process

(DEF) and Yield (YLD) by the following equation:

SCR ¼ 1� YLD�DEF ð1Þ

Lean metrics for cost:

(13) Scrap cost (SCC): Total cost associated with scrapped parts/discarded materials.(14) Total inventory (TIN): The total cost associated with any standing inventory (finished goods, WIP, raw

materials). Traditionally, inventory has been viewed as an asset but lean philosophy focuses on complete

reduction of all types of inventory.(15) Labour content (LCN): For a lean manufacturer, labour is a fixed cost. This is derived from the practice

within Toyota of lifetime employment. Labour content is the number of workers required to successfully

operate a line after Takt time and standardised work considerations.(16) Raw material variance (RMV): Standards are developed for the amount of raw material per part. Total raw

material consumption should be compared to the standard quantity-per-part multiplied by the total parts

produced, which will provide a variance to the standard. This multiplied by the average cost of raw materials

gives the variance in cost terms. High variance may be caused by over-processing waste, high scrap rate or

material wastage (spillage, excess trim scrap).

Lean metrics for delivery:

(17) Missed delivery cycles (MDC): This metric measures the efficiency of material handlers working in a pull-

based production operation. Failure to complete a delivery cycle results in fluctuations in the material

process, and the customer process does not have sufficient parts at the operation to continue production.

Excess missed delivery cycles also increases the number of production kanbans deposited in the supply

operation, which may overwhelm it.(18) Quick response to customer (QRC): This metric measures the ability of the process to meet fluctuations in

customer demand. The number of orders over and above the average order size is recorded and the number

of such orders met is measured as a percentage of the latter.(19) Delivery reliability (DRL): Delivery reliability is a more comprehensive metric as compared to past due

orders used in traditional manufacturing setups. It includes the percentage of orders delivered on time that

are correct and complete (not partial shipment). This number provides the most accurate reflection of

customer satisfaction.

Lean metrics for safety:

(20) Number of work-related injuries (INJ): These typically fall into two broad categories – accidents or sudden

injuries, including cuts, contusions, etc., and cumulative trauma disorders or repetitive motion injuries,

including carpel tunnel syndrome and thoracic outlet syndrome.(21) Lost work days (LWD): Operational downtime resulting from work-related injuries of personnel and/or

health and and safety hazards.(22) Number of medical visits (MDV): Number of visits to a medical facility due to injuries and/or possible or real

health hazards.(23) Work-related restrictions (WRR): Number of work-related restrictions resulting from the general

operational environment in the plant.

Lean metrics for morale:

(24) Employment security (EMS): Job security is one of the core values of a lean manufacturer. Lean

manufacturing does not mean eliminating jobs. It means reducing the labour content of operations so that


workers are free to be involved in improvement activities around the plant. The number of

employment contracts terminated in a fixed period is a good measure of the sense of job security in the

organisation.(25) Employee training andand development (ETD): Number of employee training and developmental

programmes undertaken in an organisation in a fixed period of time.(26) Number of awards and and rewards disbursed (A/R): The number of awards (best employee of the month,

year, etc.), bonuses for performance and so on.(27) Employee involvement (EMI): This is a combined measure of all the group activities an average

employee may be involved in, e.g. number. of Kaizen circles, average number of suggestions per

employee, etc.(28) Culture (CUL): The culture of lean production comprises PDCA, standardisation, visual management,

teamwork, intensity, paradox and lean production as a do path. The level of awareness and intensity of

involvement of the employees in these activities defines the quality of the culture. Since this is a qualitative

measure, a Likert scale-based questionnaire (Trochim 2006) will be the most appropriate tool to quantify the

quality of culture in an organisation.(29) Governance (GOV): Corporate governance is defined as the set of processes, customs, policies, laws and

institutions affecting the way a corporation (or company) is directed, administered or controlled (Wikipedia

2010). In a lean manufacturer, governance has a critical impact on how a team is organised, functions and

behaves (Thompson and Wallace 1996), and since a team forms the heart of lean improvement operations

(Total Systems Development Inc. 2001; Dennis 2007), the quality of governance is a critical measure of team

morale. The previously mentioned Likert scale-based questionnaire may be applied here as well to adjudge

the quality of governance in a lean manufacturer.

For the decision framework, each of the 29 performance metrics is calculated in real time and, after comparing it

with an achievable target performance (Melnyk et al. 2004), is scaled to a value between 0 and 1. This is done so as

to standardise the dimensions for each performance metric.

3.3 Development of AHP

The AHP has been well received in the literature (Roger 1987). Applications of this methodology have been reported

in numerous fields (Chandra 1998). The general approach of the AHP model is to decompose the problem and to

make pair-wise comparisons of all the elements on a given level with reference to related elements in the level just

above. A highly user-friendly computer model has been developed, which assists the user in evaluating their choices.

The schematic of the model is shown in Figure 2.

Figure 2. Schematic of the AHP model.


Description of the modelA thorough analysis of the problem is required, along with the identification of the important attributes/criteria

involved. The attributes/criteria (level 2) used in AHP to achieve the goal are the six performance measures of a lean

manufacturer. These are:

. Productivity (PRD)

. Quality (QUA)

. Cost (COS)

. Delivery (DLV)

. Safety (SFT)

. Morale (MRL)

The seven wastes (refer to section 1) are the sub-attributes/criteria for each of the PM of lean manufacturing, i.e. the

attributes at level 2 used in the AHP model. These are:

. Overproduction (OPD)

. Waiting (WTG)

. Transport (TRN)

. Over-processing (OPR)

. Inventory (INV)

. Motion (MOT)

. Defects (DEF)

The VSM tools are the alternatives amongst which the AHP aids the decision maker to choose the best tool for their

industry based on the current priority. The VSM tools considered in the present model (see Table 1 for a detailed

description) are:

. Process activity mapping (PAM)

. Supply chain response matrix (SCR)

. Production variety filter (PVF)

. Quality filter mapping (QFM)

. Demand amplification mapping (DAM)

. Decision point analysis (DPP)

. Physical structure mapping: (a) Volume versus (b) Value (PSM)

. Lean value stream mapping (LVS)

Analytical hierarchy process methodologyThe analytical hierarchy process (Satty 1982) is a practical approach to solving relatively difficult problems. The

AHP enables the decision maker to represent the simultaneous interaction of many factors in complex, unstructured

situations. Judgements were collected through a complete plant-level survey and multiple rounds of personal

interviews with the top management of the case organisation. These were primarily focused on eliciting the

preferences that they believe were important for sustaining the company’s position as a market leader in the

automotive parts industry. These were included in AHP for each criterion and subcriterion for all levels of

hierarchy. Pair-wise comparisons of criterion at each level was done on a 1–9 point scale: 1 reflecting equal weight

and 9 reflecting absolute importance of one over another.Below are the steps to follow in using the AHP (Roger 1987):

(1) Define the problem and determine the objective.(2) Structure the hierarchy from the top through the intermediate levels to the lowest level (Figure 2).(3) Construct a set of pair-wise comparison matrices for each of the lower levels, taking into consideration the

previous level as a goal to which these sub-criteria belong. Level II factors are decomposed into sub-criteria.

If element ‘a’ dominates over element ‘b’, then the whole number integer is entered in row A, column B, and

the reciprocal is entered in row B, column A. If the elements being compared are equal, 1 is assigned to both

positions.(4) Utilise the nðn�1Þ

2 judgements to develop the set of matrices in Step 3.(5) Determine the consistency of the pair-wise comparisons using eigenvalues. To do so, normalise the column

of numbers by dividing each entry by the sum of all entries. Then sum each row of the normalised values and


take the average. This provides the principal vector. Table 5 tabulates the normalised comparison matrix. To

check the consistency of the judgements, let the pair-wise comparison matrix be denoted by M1 and the

principal vector by M2.

Then define M3 ¼M1 �M2; and

M4 ¼M3

M2;

�max ¼ average of the elements of M4;

Consistency IndexðCIÞ ¼�max�N

N� 1;

Consistency RatioðCRÞ ¼CI

RCI;

corresponding to N where

RCI : Random Consistency Index; and

N : Number of elements

The Random Index Table is as follows:

If CR is less than 10%, the decision maker’s judgement may be consistent enough to give useful weightingestimates for various decision-making criteria. If CR is greater than 10%, there are inconsistencies in thejudgements, i.e. in the pair-wise comparison matrix, and these should be improved such that the CR isalways less than 10%.

(6) Perform Steps 3–5 for all levels and clusters in the hierarchy.(7) Next examine the effect of sub-criterion of level III on the respective criteria of level II. The procedure is

identical to the pair-wise comparison analysis above. See Table 6 for attribute weights.(8) Analyse the matrix for the pair-wise comparisons of the alternatives for the bottom-most sub-criteria using

the approach above. For the pair-wise comparison of each of the alternatives under each Level III sub-criterion, use the correlation matrix developed by Hines et al. (1998) between the wastes and mapping tool(see Table 2). See Table 7 for data summary.

(9) Calculate the desirability index for each alternative by multiplying each value in ‘weight of sub-criteria’column by the respective value in ‘criteria weight’ column, and then multiplying by the value for eachrespective alternative and summing the results (see Table 8).

3.4 Development of PGP

The decision framework developed in this study is based on a novel integrated AHP-PGP model. Integrated AHP-PGP approaches have been extensively used by Schniederjans and Gravin (1997), Badri (2001), Radcliffe and

N 1 2 3 4 5 6 7 8 9

RCI 0 0 0.6 1 1.1 1.24 1.41 1.45 1.51

Table 5. Normalised comparison matrix.

hPRDi hQUAi hCOSi hDLVi hSFTi hMRLi hSUMi Principal vector

hPRDi 0.427 0.645 0.208 0.300 0.281 0.285 2.146 0.358hQUAi 0.142 0.215 0.375 0.300 0.469 0.475 1.976 0.329hCOSi 0.085 0.024 0.042 0.014 0.031 0.032 0.228 0.038hDLVi 0.061 0.031 0.125 0.043 0.031 0.019 0.310 0.052hSFTi 0.142 0.043 0.125 0.129 0.094 0.095 0.628 0.105hMRLi 0.142 0.043 0.125 0.214 0.094 0.095 0.713 0.119

Notes: Consistency index (CI)¼ 0.1206; Consistency ratio (CR)¼ 0.0972.


Schniederjans (2003), Cebi and Bayraktar (2003), Percin (2006) and Bhagwat and Sharma (2009) to explore the

various preferences of firms. In these studies, integrating AHP with the PGP model made it possible for decision

makers to incorporate adjusted weightings on selected decision criteria. Then, the PGP model permitted an added

priority structure reflecting the added mathematical weighting. The PGP methodology for performance measure

improvement is developed in the following section.

Performance metric weights analysisThe first step in the PGP model building process is to calculate the prioritised weights of performance metrics. For

this, the priority of a given performance metric with respect to a given measure needs to be identified. A pair-wise

comparison using the collective judgements obtained from the case organisation, similar to the AHP process,

Table 6. Weight of attributes.

Sub-criteria

Weight ofsub-criteriaLevel III

Criterialevel II PAM SCR PVF QFM DAM DPA PSM LVS

OPD (PRD) 0.090 0.358 0.082 0.129 0.021 0.064 0.127 0.127 0.022 0.427WTG (PRD) 0.047 0.358 0.271 0.271 0.067 0.028 0.106 0.106 0.026 0.124TRN (PRD) 0.026 0.358 0.405 0.058 0.037 0.033 0.033 0.071 0.199 0.163OPR (PRD) 0.179 0.358 0.392 0.042 0.221 0.109 0.042 0.109 0.042 0.042INV (PRD) 0.125 0.358 0.074 0.183 0.080 0.022 0.183 0.086 0.040 0.333MOT (PRD) 0.139 0.358 0.412 0.142 0.051 0.049 0.049 0.049 0.049 0.199DEF (PRD) 0.394 0.358 0.162 0.049 0.049 0.427 0.050 0.050 0.049 0.165OPD (QUA) 0.141 0.329 0.082 0.129 0.021 0.064 0.127 0.127 0.022 0.427WTG (QUA) 0.069 0.329 0.271 0.271 0.067 0.028 0.106 0.106 0.026 0.124TRN (QUA) 0.090 0.329 0.405 0.058 0.037 0.033 0.033 0.071 0.199 0.163OPR (QUA) 0.027 0.329 0.392 0.042 0.221 0.109 0.042 0.109 0.042 0.042INV (QUA) 0.215 0.329 0.074 0.183 0.080 0.022 0.183 0.086 0.040 0.333MOT (QUA) 0.058 0.329 0.412 0.142 0.051 0.049 0.049 0.049 0.049 0.199DEF (QUA) 0.400 0.329 0.162 0.049 0.049 0.427 0.050 0.050 0.049 0.165OPD (COS) 0.103 0.038 0.082 0.129 0.021 0.064 0.127 0.127 0.022 0.427WTG (COS) 0.042 0.038 0.271 0.271 0.067 0.028 0.106 0.106 0.026 0.124TRN (COS) 0.065 0.038 0.405 0.058 0.037 0.033 0.033 0.071 0.199 0.163OPR (COS) 0.129 0.038 0.392 0.042 0.221 0.109 0.042 0.109 0.042 0.042INV (COS) 0.228 0.038 0.074 0.183 0.080 0.022 0.183 0.086 0.040 0.333MOT (COS) 0.029 0.038 0.412 0.142 0.051 0.049 0.049 0.049 0.049 0.199DEF (COS) 0.403 0.038 0.162 0.049 0.049 0.427 0.050 0.050 0.049 0.165OPD (DLV) 0.059 0.052 0.082 0.129 0.021 0.064 0.127 0.127 0.022 0.427WTG (DLV) 0.123 0.052 0.271 0.271 0.067 0.028 0.106 0.106 0.026 0.124TRN (DLV) 0.065 0.052 0.405 0.058 0.037 0.033 0.033 0.071 0.199 0.163OPR (DLV) 0.145 0.052 0.392 0.042 0.221 0.109 0.042 0.109 0.042 0.042INV (DLV) 0.221 0.052 0.074 0.183 0.080 0.022 0.183 0.086 0.040 0.333MOT (DLV) 0.026 0.052 0.412 0.142 0.051 0.049 0.049 0.049 0.049 0.199DEF (DLV) 0.362 0.052 0.162 0.049 0.049 0.427 0.050 0.050 0.049 0.165OPD (SFT) 0.061 0.105 0.082 0.129 0.021 0.064 0.127 0.127 0.022 0.427WTG (SFT) 0.031 0.105 0.271 0.271 0.067 0.028 0.106 0.106 0.026 0.124TRN (SFT) 0.363 0.105 0.405 0.058 0.037 0.033 0.033 0.071 0.199 0.163OPR (SFT) 0.031 0.105 0.392 0.042 0.221 0.109 0.042 0.109 0.042 0.042INV (SFT) 0.081 0.105 0.074 0.183 0.080 0.022 0.183 0.086 0.040 0.333MOT (SFT) 0.290 0.105 0.412 0.142 0.051 0.049 0.049 0.049 0.049 0.199DEF (SFT) 0.142 0.105 0.162 0.049 0.049 0.427 0.050 0.050 0.049 0.165OPD (MRL) 0.044 0.119 0.082 0.129 0.021 0.064 0.127 0.127 0.022 0.427WTG (MRL) 0.182 0.119 0.271 0.271 0.067 0.028 0.106 0.106 0.026 0.124TRN(MRL) 0.067 0.119 0.405 0.058 0.037 0.033 0.033 0.071 0.199 0.163OPR (MRL) 0.029 0.119 0.392 0.042 0.221 0.109 0.042 0.109 0.042 0.042INV (MRL) 0.095 0.119 0.074 0.183 0.080 0.022 0.183 0.086 0.040 0.333MOT (MRL) 0.340 0.119 0.412 0.142 0.051 0.049 0.049 0.049 0.049 0.199DEF (MRL) 0.243 0.119 0.162 0.049 0.049 0.427 0.050 0.050 0.049 0.165


is adopted here.

(1) In this step, each 29 performance metrics undergoes a pair-wise comparison depending on its relative effect

on the corresponding performance measure. A pair-wise comparison matrix similar to the approach

described in the AHP process and the principal vector for each of the performance metrics was recorded as

the weight. This analysis was performed on the performance metrics for each PM of lean manufacturing.

Table 7. Data summary.

Sub-criteria hPAMi hSCRi hPVFi hQFMi hDAMi hDPAi hPSMi hLVSi

OPD (PRD) 0.003 0.004 0.001 0.002 0.004 0.004 0.001 0.014WTG (PRD) 0.005 0.005 0.001 0 0.002 0.002 0 0.002TRN (PRD) 0.004 0.001 0 0 0 0.001 0.002 0.002OPR (PRD) 0.025 0.003 0.014 0.007 0.003 0.007 0.003 0.003INV (PRD) 0.003 0.008 0.004 0.001 0.008 0.004 0.002 0.015MOT (PRD) 0.021 0.007 0.003 0.002 0.002 0.002 0.002 0.01DEF (PRD) 0.023 0.007 0.007 0.06 0.007 0.007 0.007 0.023OPD (QUA) 0.004 0.006 0.001 0.003 0.006 0.006 0.001 0.02WTG (QUA) 0.006 0.006 0.002 0.001 0.002 0.002 0.001 0.003TRN (QUA) 0.012 0.002 0.001 0.001 0.001 0.002 0.006 0.005OPR (QUA) 0.004 0 0.002 0.001 0 0.001 0 0INV (QUA) 0.005 0.013 0.006 0.002 0.013 0.006 0.003 0.024MOT (QUA) 0.008 0.003 0.001 0.001 0.001 0.001 0.001 0.004DEF (QUA) 0.021 0.006 0.006 0.056 0.007 0.007 0.006 0.022OPD (DEF) 0 0.001 0 0 0 0 0 0.002WTG (DEF) 0 0 0 0 0 0 0 0TRN (DEF) 0.001 0 0 0 0 0 0 0OPR (DEF) 0.002 0 0.001 0.001 0 0.001 0 0INV (DEF) 0.001 0.002 0.001 0 0.002 0.001 0 0.003MOT (DEF) 0 0 0 0 0 0 0 0DEF (DEF) 0.002 0.001 0.001 0.007 0.001 0.001 0.001 0.003OPD (DLV) 0 0 0 0 0 0 0 0.001WTG (DLV) 0.002 0.002 0 0 0.001 0.001 0 0.001TRN (DLV) 0.001 0 0 0 0 0 0.001 0.001OPR (DLV) 0.003 0 0.002 0.001 0 0.001 0 0INV (DLV) 0.001 0.002 0.001 0 0.002 0.001 0 0.004MOT (DLV) 0.001 0 0 0 0 0 0 0DEF (DLV) 0.003 0.001 0.001 0.008 0.001 0.001 0.001 0.003OPD (SFT) 0.001 0.001 0 0 0.001 0.001 0 0.003WTG (SFT) 0.001 0.001 0 0 0 0 0 0TRN (SFT) 0.015 0.002 0.001 0.001 0.001 0.003 0.008 0.006OPR (SFT) 0.001 0 0.001 0 0 0 0 0INV (SFT) 0.001 0.002 0.001 0 0.002 0.001 0 0.003MOT (SFT) 0.013 0.004 0.002 0.001 0.001 0.001 0.001 0.006DEF (SFT) 0.002 0.001 0.001 0.006 0.001 0.001 0.001 0.002OPD (MRL) 0 0.001 0 0 0.001 0.001 0 0.002WTG (MRL) 0.006 0.006 0.001 0.001 0.002 0.002 0.001 0.003TRN (MRL) 0.003 0 0 0 0 0.001 0.002 0.001OPR (MRL) 0.001 0 0.001 0 0 0 0 0INV (MRL) 0.001 0.002 0.001 0 0.002 0.001 0 0.004MOT (MRL) 0.017 0.006 0.002 0.002 0.002 0.002 0.002 0.008DEF (MRL) 0.005 0.001 0.001 0.012 0.001 0.001 0.001 0.005

Table 8. Decision index for the desirability of each alternative.

VSM Tool PAM SCR PVF QFM DAM DPA PSM LVS

Decision index 0.2272 0.107 0.0674 0.1811 0.0799 0.0744 0.0562 0.2068


(2) In the next step, a pair-wise alternative analysis for each of the 29 performance metrics was carried out toevaluate the impact of each mapping tool in improving individual performance metrics. The results for eachcomplete performance metric and alternative analysis are given in Table 9.

The weights calculated after the pair-wise comparison are on a scale of 0 to 1 (and the sum of all the weights isequal to 1). This can also be considered as indicating a metric’s relative importance or its relative percentagecontribution in the overall PM. This relative percentage contribution is integrated with the optimisation method, sothat the optimal level of each considered performance indicator can be identified.

Description of the modelThe purpose of the approach is to aid the decision maker in choosing when and in what sequence a new mappingtool should be introduced to produce the maximum improvement with the least expenditure of time and energy.Each subsequent mapping tool incrementally builds on the benefits of the previously applied mapping tool. ThePGP guarantees to maximise each performance measure under given constraints.

Elements of PGPFor mathematical modelling of the PGP, first the decision variable must be defined, followed by the objectivefunction (goal) and constraints in terms of the decision variable.

Decision variableHere, the objective is to find the best sequence for the application of the VSM tools, such that the performancemetrics are optimised while simultaneously maximising each of the performance measures in the long term.Therefore, the performance metrics identified for the performance measures and prioritised through performance

Table 9. Results of performance metric and alternative analysis.

Mapping tool weightage for the metrics

Performance Metric Weightage hPAMi hSCRi hPVFi hQFMi hDAMi hDPAi hPSMi hLVSi

WKT 0.030 0.032 0.237 0.072 0.032 0.157 0.125 0.069 0.275PLH 0.151 0.275 0.062 0.062 0.062 0.062 0.062 0.062 0.356TPP 0.091 0.275 0.062 0.062 0.062 0.062 0.062 0.062 0.356LST 0.178 0.177 0.096 0.043 0.240 0.043 0.043 0.043 0.318EDT 0.138 0.083 0.083 0.083 0.417 0.083 0.083 0.083 0.083SSP 0.054 0.142 0.054 0.054 0.334 0.054 0.054 0.054 0.256SCP 0.054 0.142 0.054 0.054 0.334 0.054 0.054 0.054 0.256C/T 0.305 0.330 0.050 0.050 0.050 0.050 0.203 0.052 0.217MDC 0.143 0.257 0.048 0.048 0.048 0.048 0.212 0.051 0.288QRC 0.429 0.039 0.165 0.045 0.045 0.380 0.074 0.039 0.212DRL 0.429 0.061 0.355 0.061 0.061 0.170 0.170 0.061 0.061SCC 0.625 0.064 0.064 0.106 0.479 0.072 0.072 0.072 0.072TIN 0.125 0.044 0.195 0.062 0.027 0.119 0.080 0.119 0.354LCN 0.125 0.099 0.031 0.067 0.083 0.203 0.109 0.037 0.370RMV 0.125 0.048 0.048 0.403 0.233 0.048 0.048 0.124 0.048CUS 0.501 0.169 0.070 0.080 0.399 0.070 0.070 0.070 0.070DEF 0.077 0.071 0.071 0.071 0.500 0.071 0.071 0.071 0.071YLD 0.159 0.097 0.039 0.157 0.402 0.041 0.041 0.041 0.181SCR 0.263 0.140 0.101 0.140 0.435 0.046 0.046 0.046 0.046INJ 0.273 0.467 0.061 0.061 0.061 0.061 0.061 0.061 0.168LWD 0.533 0.467 0.061 0.061 0.061 0.061 0.061 0.061 0.168MDV 0.128 0.467 0.061 0.061 0.061 0.061 0.061 0.061 0.168WRR 0.067 0.421 0.055 0.055 0.055 0.055 0.055 0.055 0.251EMS 0.221 0.028 0.115 0.047 0.345 0.096 0.096 0.096 0.175ETD 0.069 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125A/R 0.049 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125EMI 0.221 0.285 0.054 0.054 0.136 0.054 0.054 0.054 0.309CUL 0.221 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125GOV 0.221 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125


metrics and alternative analysese will be considered as the decision variables. The objective functions and constraints

need to be further defined in terms of the performance metrics, i.e. the decision variables.In the goal programming model, the decision variables are different performance metrics, which are represented

by Xk (where k varies from 1 to 29, from 1 to 8 for productivity performance metrics, 9 to 12 for quality metrics, 13

to 16 for cost metrics, 17 to 19 for delivery metrics, 20 to 23 for safety metrics and 24 to 29 for metrics of morale).

Objective functionsThe idea of the PGP is to set objectives in order of priority (Ghodsypour and O’Brien 2001; Bhagwat and Sharma

2009). In this case, the objective is to maximise the six performance measures, i.e. productivity, quality, cost,

delivery, safety and morale, in the order as prioritised. The six objective functions in order of their priority are:

(1) Maximise productivity (consisting of performance metrics 1 to 8)(2) Maximise quality (consisting of performance metrics 9 to 12)(3) Maximise morale (consisting of performance metrics 24 to 29)(4) Maximise safety (consisting of performance metrics 20 to 23)(5) Maximise delivery (consisting of performance metrics 17 to 19)(6) Maximise cost (consisting of performance metrics 13 to 16)

The goals of the problem can be restated as:

maximize Pi ¼X

WikXk such that k 2 i,

where, Pi¼Objective functions and i¼ 1 to 6 (i¼ 1 for productivity, i¼ 2 for quality, i¼ 3 for morale, i¼ 4 for

safety, i¼ 5 for delivery and i¼ 6 for cost) k ¼ 1, 2, 3, . . . , n (n¼ number of performance metrics). (In the present

study n¼ 29, and k¼ 1, 2, 3, 4, 5, 6, 7, 8 2 (i¼ 1), k¼ 9, 10, 11, 12 2 (i¼ 2), k¼ 13, 14, 15, 16 2 (i¼ 6), k¼ 17, 18, 19 2

(i¼ 5), k¼ 20, 21, 22, 23 2 (i¼ 4) and k¼ 24, 25, 26, 27, 28, 29 2 (i¼ 3).) Wik¼Performance metric analysis weight

for the kth performance metric of the ith level (see Table 9, Column 2).Mathematically, the objectives are given as:

maximise P1 ¼X

W1kXk such that k 2 i ¼ 1, ðProductivityÞ ð2Þ

maximise P2 ¼X

W2kXk such that k 2 i ¼ 2, ðQualityÞ ð3Þ

maximise P3 ¼X

W3kXk such that k 2 i ¼ 3, ðMoraleÞ ð4Þ

maximise P4 ¼X

W4kXk such that k 2 i ¼ 4, ðSafetyÞ ð5Þ

maximise P5 ¼X

W5kXk such that k 2 i ¼ 5, ðDeliveryÞ ð6Þ

maximise P6 ¼X

W6kXk such that k 2 i ¼ 6, ðCostÞ ð7Þ

Constraints. In practice, the constraints are on the availability of manpower, time, energy and the ability of the

decision maker to keep the employees motivated in the improvement process. Mathematically, these constraints

have been modelled as a function of the various VSM tools. There are eight VSM tools: PAM, SCR, PVF, QFM,

DAM, DPA, PSM and LVS. As the tools have been evaluated under different performance metrics (Table 9), these

have been considered as constraints in this model. Thus the constraints on the goal programming are the different

VSM tools (Equation (8)) and the different performance metrics (Equation (9)).

XWikXk �Min:

XWikðk2iÞ,

XWlk

n oð8Þ

k ¼ 1, 2, 3, 4 . . . n ðn ¼ 29Þ

l ¼ 1, 2, 3, 4, 5, 6, 7, 8 ðfor eight VSM toolsÞ

0 � Xk � 1

ð9Þ


In Equation (8), l represents the eight VSM tools hence, there will be eight constraints for the optimisation ofpriority 1, i.e. productivity.

PGP methodologyUsing TORA (optimisation software), sequential programming was initiated with the optimisation of the firstpriority, i.e. productivity and nine constraints (eight for VSM tools and one on Xk).The iteration counter was set toq¼ 0 and initialise "¼ 0.01. The algorithm for sequential optimisation is as follows:

Step 1: Optimise ith Priority (Pi) under the given constraints. Obtain the best performance levels for Xk (k 2 i). Setiteration counter q¼ qþ 1

Step 2: Substitute the optimum values of Xk (k 2 i) into the qth iteration constraints to calculate the constraints forthe next priority (i¼ iþ 1). Let the R.H.S. for the lth constraint of the qth iteration be R:H:S:ql

(a) If the R.H.S. for any of the constraints for the (qþ 1)th iteration falls below " i.e. R:H:S:ðqþ1Þl � " (l¼ 1, 2, 3,4, 5, 6, 7, 8) eliminate the constraint from further iterations.

(b) If the R.H.S. for all the constraints is � " i.e. R:H:S:ðqþ1Þl � " proceed to Step 3.

Step 3: Record the difference between the R.H.S. for the lth constraint (l¼ 1, 2, 3, 4, 5, 6, 7, 8) of the qth iterationand the lth constraint (l¼ 1, 2, 3, 4, 5, 6, 7, 8) of the (qþ 1)th iteration. Let the difference be Dl for the lth constraint.

fD½ �½ �l¼ R:H:S:½ �½ �l� �� q

� R:H:S:½ �½ �l� �� ððqþ1ÞÞ

g ð10Þ

Step 4: Calculate Dmax ¼MaxfDlg (l¼ 1, 2, 3, 4, 5, 6, 7, 8; ignore the eliminated constraints. Record l correspondingto Dmax.

(a) If the Dmax maps to more than one l, l has the same maximum value for any iteration. Any one of the toolsmay be chosen depending on the results of the subsequent iteration.

Step 5: For the qth iteration, the VSM tool corresponding to l obtained in Step 4 is the best suited VSM tool tomaximise the ith priority (Pi).

Step 6: If q¼ 6 TERMINATE. Or, if i¼ iþ 1 go to Step 1.

The algorithm was implemented for the case manufacturing organisation to identify the optimum levels ofoperation of the performance metrics and also to find the best sequence of VSM tool that will maximise the PMs.Table 10 tabulates the results at the end of the first iteration of the model.

In addition to the best sequence of VSM selection, the results of PGP will provide the values of the performancemetrics to maximise overall performance (Table 11). These optimised values of the performance indicator will helpthe decision maker to identify and focus on performance metrics that are crucial for overall PM of the system. ThePGP will identify the required optimised values of the performance indicators as a benchmark. The decision makerhas to ensure that the actual values of the metrics never fall below the values obtained by PGP optimisation. Thisshould be achieved through adequate mapping efforts. Once the performance metrics for a particular performancemeasure stabilise around the value identified by the PGP optimisation, the decision maker must now focus theirattention on the next priority and channel the organisation’s energy to implement the mapping tool correspondingto that priority as proposed by the model.

Results of PGPFrom Table 10 it can be seen that Dl is at a maximum for l¼ 1 and for l¼ 8, i.e. performance activity mapping(PAM) and lean value stream mapping (LVS). This observation also supports the result obtained from the previousAHP model. Hence, the case organisation must focus on improving its productivity by first mapping the processesusing PAM and subsequently adopting LVS. Continuing with the PGP methodology, the complete sequence ofVSM tool application was found. This is illustrated as a flowchart in Figure 3.

The optimum values for Xk (k2 I¼ 1) are X1 ¼ 0:09, X2 ¼ 1, X3 ¼ 0:45, X4 ¼ 1, X5 ¼ 1;X6 ¼ 0;X7 ¼ 0; X8 ¼ 0. According to the result, the metrics stopping supplier process ½½ðX��6Þ and shorting customerprocess (½½X��7) have no impact on the optimisation of productivity. It shows that only six out of the eight metricscontribute to the maximisation of priority 1 (P1). Further, three metrics – parts per labour hour (½½X��2), line stop time(½½X��4) and changeover time (½½X��8) – are the most critical as far as productivity is concerned and the target must be tomaintain them at as high a level as possible. Refer to Table 11 for optimum performance values of all 29 metrics.


Table

10.Objectivefunction(row

3)andconstraints

(Rows4to

row

11)forP2-quality.

X9

X10

X11

X12

X13

X14

X15

X16

X17

X18

X19

X20

X21

X22

X23

X24

X25

X26

X27

X28

X29

CUS

DEF

YLD

SCR

SCC

TIN

LCN

RMV

MDC

QRC

DRL

INJ

LWD

MDV

WRR

EMS

ETD

A/R

EMI

CUL

GOV

R.H

.SD

l

Obj.

0.501

0.077

0.159

0.263

00

00

00

00

00

00

00

00

0PAM

0.17

0.07

0.1

0.14

0.06

0.04

0.1

0.05

0.26

0.04

0.06

0.47

0.47

0.47

0.42

0.03

0.13

0.13

0.29

0.13

0.13

0.01

0.99

SCR

0.07

0.07

0.04

0.1

0.06

0.2

0.03

0.05

0.05

0.17

0.36

0.06

0.06

0.06

0.06

0.12

0.13

0.13

0.05

0.13

0.13

0.66

0.34

PVF

0.08

0.07

0.16

0.14

0.11

0.06

0.07

0.4

0.05

0.05

0.06

0.06

0.06

0.06

0.06

0.05

0.13

0.13

0.05

0.13

0.13

0.73

0.27

QFM

0.4

0.5

0.4

0.44

0.48

0.03

0.08

0.23

0.05

0.05

0.06

0.06

0.06

0.06

0.06

0.35

0.13

0.13

0.14

0.13

0.13

0.2

0.799

DAM

0.07

0.07

0.04

0.05

0.07

0.12

0.2

0.05

0.05

0.38

0.17

0.06

0.06

0.06

0.06

0.1

0.13

0.13

0.05

0.13

0.13

0.72

0.28

DPA

0.07

0.07

0.04

0.05

0.07

0.08

0.11

0.05

0.21

0.07

0.17

0.06

0.06

0.06

0.06

0.1

0.13

0.13

0.05

0.13

0.13

0.57

0.43

PSM

0.07

0.07

0.04

0.05

0.07

0.12

0.04

0.12

0.05

0.04

0.06

0.06

0.06

0.06

0.06

0.1

0.13

0.13

0.05

0.13

0.13

0.73

0.27

LVS

0.07

0.07

0.18

0.05

0.07

0.35

0.37

0.05

0.29

0.21

0.06

0.17

0.17

0.17

0.25

0.18

0.13

0.13

0.31

0.13

0.13�0.2

1.15

Table

11.Optimum

perform

ance

levelsusingPGP.

Perf.metric

WKT

PLH

TPP

LST

EDT

SSP

SCP

C/T

CUSDEF

YLD

SCR

SCC

TIN

LCN

RMV

MDC

QRC

DRL

INJLWD

MDV

WRR

EMSETD

A/R

EMICUL

GOV

Optimum

perform

ance

0.1

10.45

11

00

10.5

00

00.86

00

01

0.12

00

0.33

00

10.9

01

11


The final inference from iteration one of the PGP model is that PAM followed by LVS mapping must beimplemented in the organisation, with the objective of improving productivity. Efforts must be sustained until therequired optimum performance of the metrics as given by PGP is achieved.

4. Results and conclusion

On a practical front, the novelty of the proposed decision framework lies in its ability to simultaneously considerboth the current state and the future state of a system through an innovative formulation of the integrated AHP-PGP approach. This allows the framework to guide the user in the selection of the best sequence of the VSM tool toeliminate all possible forms of waste within the shortest timeframe. Additionally, the theoretical contribution of theapproach lies in the iterative PGP strategy which allows the user to accurately determine the optimum values of eachperformance metric that maximises overall performance. Together, the decision framework successfully bridges thegap identified in the methods known at present for selecting VSM tools.

For the present model, AHP is used to select the best VSM tool that will give the highest rate of improvement forthe case study. For the considered case, productivity (PRD) was found to be of the highest importance and, hence,using AHP, process activity mapping (PAM) has been identified as the most suitable tool to achieve rapidimprovements in productivity on the shopfloor and to maximise the return on the mapping effort.

The best VSM tool selected via the AHP model only guarantees the quickest method for removal of waste in anorganisation depending on the current organisational preferences and goals. According to the lean philosophy, oncethe tool has been applied and the relevant waste(s) reduced, the priorities of the organisation should then rapidlyshift to focus on another PM and, hence, in the long term, focus on removing all forms of waste and becoming trulylean. This is the mantra for continuous improvement as proposed by the model.

Hence, the overall approach suggested by the decision framework is to use AHP to kick-start value streammapping techniques in the case organisation and also build momentum for the waste-removal process. Once that hasbeen achieved, the best sequence of mapping tools, based on the results of PGP, must be used to sustain interest inwaste identification and removal and also to meet the objective of kaizen or continuous improvement in thelong term.

For the present case, PAM should be sequentially followed by LVS. Once the performance metrics following theshopfloor restructuring suggested by PAM stabilise, efforts must be diverted to improving the plant using thecurrent state–future state VSM technique, as originally suggested by Toyota (LVS). The target of this effort shouldbe to achieve 100% of the targeted parts per labour hour (PLH), line stop time (LST), equipment down time (EDT)and changeover time (C/T), since these metrics have the highest impact on productivity, which is our primary goal.Quality is the next on our checklist; for this, PGP suggests using quality filter mapping (QFM) to achieve at least50% of targeted customer satisfaction (CUS). The other priorities follow in sequence and the appropriate tool asgiven by PGP may be used to achieve them. Target performance must be to achieve 100% of the missed deliverycycles (MDC), employment security (EMS), employee involvement (EMI), culture (CUL) and governance (GOV)metrics because these have the highest impact on maximising their respective PMs.

In the present research paper, the solution to the problem has been modelled as a multi-criteria decision-making(MCDM) approach. Since data in MCDM problems are imprecise and changeable (Triantaphyllou and Sanchez1997), a natural extension of the present research is to include sensitivity analysis. As Dantzig (1963, p. 32) stated:‘Sensitivity analysis is a fundamental concept in the effective use and implementation of quantitative decisionmodels, whose purpose is to assess the stability of an optimal solution under changes in the parameters.’ For thegiven problem, as proposed by Triantaphyllou et al. (2007), this can be carried out to study the impact of changes inthe weights assigned to the criteria and sub-criteria on the selection of the VSM tool. By knowing which data is morecritical, the decision maker can more effectively focus their attention on the most critical parts of the problem.Alternatively, sensitivity analysis can also be applied in the data-gathering phase to calculate, with higher accuracy,the weights that are more critical in the interest of a constrained budget.

Figure 3. Flowchart for VSM tool application.


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A Decision Framework for Maximising Lean Manufacturing Performance

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