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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.19 No.3 pp.704-715
DOI : https://doi.org/10.7232/iems.2020.19.3.704

# Decision Model Development under Different Scenarios for New Product Development

Thanyatorn Fongsatitkul*, Yasutaka Kainuma
Department of Electrical Engineering and Computer Science, Graduate School of Systems Design, Tokyo Metropolitan University, Hino, Japan
Department of Electrical Engineering and Computer Science, Graduate School of Systems Design, Tokyo Metropolitan University, Hino, Japan
*Corresponding Author, E-mail: thanyatorn_f@hotmail.com
January 9, 2020 June 1, 2020 June 2, 2020

## ABSTRACT

Under a highly competitive market, companies have to develop a new product as an effective strategy to maintain or even enhance their market shares. New product development (NPD) with an involvement of environmental dimension, nowadays, is one of the most crucial factors for business success. A feasibility study and a milestone of the NPD project have to be systematically established and subsequently evaluated. A Bayesian decision analysis was then employed to deal with three uncertainties of the future market shares with or without an environmental-friendly component and the competitors’ responses, producing expected values and variances for three uncertainties. An application of a decision model using MATLAB can be an effective tool to identify whether or not the NPD project under different scenarios should be continued in terms of future expected profits. Four scenarios were explored: Business as usual (BAU), improvements with or without an involvement of environmental aspects, and project termination. Moreover, three uncertainties were also considered: market status (future conventional market share and environmentallyfriendly market share), and competitors’ reactions. Sensitivity analysis of the selected scenario/model under three uncertainties was finally established to identify the effects of change in the uncertainties as the input parameters with respect to the output profit.

## 1. INTRODUCTION

Two different approaches, operation and marketing, are generally followed regarding a new product development (NPD). Operation is an internal management and control method using the Lean manufacturing technique which emphasizes the core-designed team, project management and planning, product specifications and prototyping, performance control, and other matters within manufacturing. The marketing approach engages external management to influence the new product development which covers customers’ needs, marketing competitive responses, and a sale forecasting. Investment of the new product has to be evaluated and justified whether or not it is worth the expenses on the design-build-test-andoperation. Such decisions should be carefully evaluated in terms of effectiveness and the risk involving the money spent at each step of the process. Potential profits are expected for a successful new product, but in the case of failure, it can cause tremendous financial losses. It is, therefore, necessary to develop a boarder comprehensive and effective evaluation system to help managers to deal with the marketing uncertainties and the successful potential of a new product whether it is worth or not to be carried on as a NPD project.

Green manufacturing, relating to environmental issues, is nowadays growing and spreading into many activities of the industry. Environmentally-friendly new product development (EF-NPD) has become one of the most important issues for the manufacturing industry, forcing the industry to increase its awareness towards the environment and produce products which meet both the customers’ and environmental requirements. NPD ultimately needs to be shifted from the transitional stage to the sustainable products and technologies domain, focusing on reengineering, clean technologies, products purchasing, use and disposal. This would encourage closer teamwork in the future among manufacturing managers who are in charge of product development, marketing, and environmental protection and control. Uncertainties of marketing status with or without an environmentallyfriendly component and competitors’ reactions have then played important roles in the product development process. By using the go/kill decision approach in conjunction with Bayesian decision analysis which is extensively recognized as an effective quantitative technique, a decision model development for EF-NPD can be effectively initiated. Generally, one of the limitations of the NPD process is the insufficiency and unavailability of information on new products; especially, regarding environmentally- friendly product development (EF-NPD).

This research aims to develop an appropriate and effective decision model in combination with the go/kill decision approach and Bayesian decision analysis using both expert knowledge/experience and other sources of information (survey data). The major advantage of implementing a Bayesian decision analysis is that the experts’ knowledge and the sampling data can both be considered and taken into account in making a decision. An expansion and modification of the scenarios proposed by Huang et al. (2015) was made to include an environmental component for a NPD plan; especially for EF-NPD, using Bayesian decision analysis to evaluate the go/kill procedure regarding potential project investment profits. The following four scenarios were explored: Business as usual (BAU), improvements with or without an involvement of environmental aspects, and project termination. Moreover, three uncertainties were considered: market status (future conventional market share and environmentally- friendly market share), and competitors’ reactions. An application of a decision model using MATLAB can finally be evaluated in terms of future expected profits to identify whether or not the NPD project should be continued with or without an involvement of environmental aspects under different scenarios. The rest of this paper is organized as follows: a brief literature review as well as the rational for this research are included in Section 2; materials and methods including the steps and approach of the decision model for NPD are summarized in Section 3 including decision model development (profits) under different scenarios with an application of Bayesian decision analysis (prior and posterior analysis), decision analysis (process and expected profits); results and discussion are delineated in Section 4 covering decision model application (MATLAB) and sensitivity analysis as shown in Section 4.1, 4.2, respectively; and finally, conclusions and suggestions for future research are included in Section 5.

## 2. LITERATURE REVIEW

The NPD process has been extensively studied and reported in the literature, including initial product selection and development, commercialized evaluation, and product manufacturing and marketing (Urban and Hauser, 1993;Bigliard et al., 2013). Metikurke and Shekar (2011) suggested using seven dimensions strategy, process, research, project climate, company culture, metrics, and commercialization for analyzing the NPD of small and medium enterprises in New Zealand. Wu and Pagell (2011) indicated that a shift towards green products and production processes which considered environmental factors may become the norm in the near future regarding manufacturing. To maintain such a platform, manufacturing needed to produce environmentally-friendly products with a minimal usage of non-renewable resources, climate- change free emissions, and sustainable disposal systems (Wolf and Seuring, 2010). Williams et al. (2017) indicated that sustainable supply chain management (SSCM) appeared to be an effective strategy to survive in the future global market. Nowadays, industries across the world have effectively integrated SSCM into their allinclusive systems (Hassini et al., 2012). SSCM practices, such as environmentally supportive packaging, 3R (reuserecycling- recovery) of the already-consumed products to the manufacturer, and an effective disposal system could encourage society to move towards sustainability (Lin and Tseng, 2016). Keoleian et al. (1995) indicated that Design-for-X represented the design for the product properties which are on the top of basic requirements such as ease of use, quality, and safety. Subsequently, it has been further transformed into the design-for-environment, representing an environmentally-friendly practice incorporated into the product and the procedures of process engineering design. However, Porter and van der Linde (1995) have proposed “win–win” logic, serving as a simultaneously “green and competitive” one. A few studies have empirically evaluated the impacts and/or the operations of the companies’ environmentally-friendly products (Prothero and McDonagh, 1992). Up till now, it has been frequently quoted using subjective evidence (i.e. not independently or scientifically verified) the successful marketing for green-products such as Body Shop’s range and ARCO’s environmentally-reformulated gasoline. This has encouraged several individuals as well as public and private agencies to advocate their commercialized products for “going green”. The government has recently been the leader of these initiatives; the industrial sector, however, appears to face pressure not only from competitors but also from the end users to convert a conventional supply chain into a sustainable one (Xie, 2016).

The majority of existing literature on decision making in product lifecycle management focuses on the new product development phase before it enters the market, and the methodology used in decision making is mainly from a conceptual perspective. Ali et al. (1995) defined product lifecycle time to be the elapsed time from the beginning of the idea to the end of product launch and did not consider the decision making after the products were released into the competitive market. Olson et al. (1995), Srinivasan et al. (1997), and Salhieh (2018) discussed methodologies that incorporated the product marketing information into new product development. Day (1981) and Ameri and Dutta (2005) discussed the factors that determine the progress of the product through the stages of the lifecycle and the role of the product lifecycle concept in the formulation of competitive strategy. However, these were all qualitatively focused. When new product investments are financially evaluated, the most common questions are whether projects are worth investing in and how all uncertainties can be factored into the evaluation, including the uncertainty in the temporal variation of the product value after launch. The NPD process is a longterm decision-making process at the strategic level. The perceptions and preferences of decision-makers regarding uncertainties and values of alternatives should be incorporated. The go/kill decision regarding NPD project is generally required to allocate the limited resources and to take advantage of the market opportunities. Several stages of the stage-gate approach were descripted and assessed using a certain preset of thresholds (Kumar et al., 1996;Carbonara and Scozzi, 2006). In addition to operational quantitative models, qualitative methods are necessary to comprehend strategic analysis results. Two different approaches, operation (internal management) and marketing (external management), are principally used for a new product development (NPD). Decision making models for NPD frequently include dynamic programming, decision tree, and Bayesian analysis. Hu and Bidanda (2009) concentrated on developing and validating mathematical models (Stochastic Dynamic Programming method) within the framework of the sustainable product decision support systems. There were mainly four interrelated parts of this research: waste management in manufacturing, green product manufacturing strategy, product upgrade strategy and reverse logistics. Wul et al. (2015) initiated an integration of scenario planning and decision tree analysis for NPD evaluation in such a way that proposed scenarios for modeling uncertainties can be generated systematically by using a case study of a Taiwanese original equipment manufacturing company for validating the proposed model. Jackson (1983) used a decision tree approach to formulate the NPD problem, and obtained an optimal budget supporting alternative with the highest expected utility. Bayesian approach has been another powerful tool for risk decision-making due to its convenience and easiness, this approach was applying in many fields (Richard, 2007). Venter and Van Waveren (2009) used the Bayesian Decision technology to support new product development management. Chin et al. (2009) applied the Bayesian network method to the risk evaluation in new product R&D. Reynolds and Lancaster (2007) proposed a Bayesian solution for enterprises predicting the strategic marketing management decision. Chen et al. (2010) built a Bayesian model to achieve dynamic knowledge update, in order to deal with the supply uncertainties and risks. Guo (2012) explored the effective quantitative risk decisionmaking method, in order to help enterprise managers to achieve effective innovation risk management. Furthermore, by merging Bayesian analysis (prior and post analysis) and decision theory, Ferre (2020) highlighted that such an approach can lead to reduction of uncertainties and improvement in decision making in the field of hydrology.

In practice, one of the limitations of the NPD process is the insufficiency and unavailability of information on new products, potential customers, the market, competitors and technology. Howell and Sheab (2001) listed several sources of information such as original documents, journals, books, training documents, meetings and conferences, suppliers and competitors, and so on. Cooper et al. (2000) also specified that NPD projects normally required accurate information to help managers to make the right and reasonable decisions using the stage-gate approach. A related previous research, Huang et al. (2015) employed the approach of Bayesian decision analysis to deal with the two crucial uncertainties for NPD, such as the future market share and the responses of competitors; however, it did not include an environmental aspect in the model. The chief merits of the Bayesian decision model is to integrate the subjective knowledge of the decision makers and the objective survey results of marketing research to deal with these market uncertainties; this would thus turn out to be a more convincing and reliable decision making process to enhance the quality of decision making. Scenario planning is a qualitative method for managing strategies by generating a set of scenarios that comprehend the understandings of future uncertain states, whereas R&D strategy refers to one of the most critical alternative strategies to be formulated (Goodwin and Wright, 2001).

Based on the above literature review it is apparent that insufficient and/or limited information on envi-ronmentally-friendly product development (EF-NPD) exists, which indicates a research gap in this area since very few studies have been focused on decision analysis using a marketing approach incorporating Bayesian analysis to deal with the EF-NPD. Therefore, a decision model analysis using a marketing approach along with Bayesian prior and post analysis has been then em-ployed in this study to evaluate the NPD; especially, EF-NPD under different scenarios focusing on maximizing company profit with a consideration of three uncertain-ties including the conventional market, the potential of the environmentally-friendly market and the competi-tors’ responses.

## 3. MATERIALS AND METHODS

The research has been designed step-by-step fol-lowing the decision model of a NPD strategy as present-ed in Figure 1. The procedure begins with the identifica-tion of decision problems relating to EF-NPD under three uncertainties: future conventional market share (θ), environmentally-friendly market share (ϕ) and competitors’ response (ρ). This was followed by deci-sion model development focusing on new product profit equations with a combination of Product Revenues (PR), Production and Marketing Cost (PMC), Product Development Cost (PDC) and Environmental Cost (EC) under four scenarios. Each scenario represents for alter-native action as: (1) maintaining the status quo (a1) (Business as usual, BAU); (2) improvement without incorporating environmental issues (Iw/oE) (a2); (3) improvement with incorporating environmental issues (IE) (a3) and (4) termination of the project (TP). Sub-sequently, a Bayesian decision analysis was employed to associate with these three uncertainties for EF-NPD as $θ , ϕ and ρ$ to help estimating the expected profits (prior and posterior analysis). A decision model applica-tion using MATLAB was eventually developed.

### 3.1 Decision Model Development: Profit Functions

Demeke et al. (2018) has initiated the green profit for a single unit of paper towel basing on the following equations as: (1) Green Profit = Unit Price - Full Cost; (2) Full Cost = Total Financial Cost + TotalXCost; and (3) TotalXCost = Externality Costs (ExternalCostPM2.5 + ExternalCostCO2). Therefore, the Green Profit could be summarized as:

Green Profit = Unit Price - Total Financial Cost - Externality Costs

Accordingly, the ultimate objective of this study has then been to develop a profit function model for an environmentally- friendly scenario and evaluate whether or not the NPD project should be continued based on future expected profits, which can be modified and summarized as follows:

• Green Product Profits (GPP) = Product Revenues (PR)

• – Product Development Cost (PDC)

• – Production and Marketing Cost

• (PMC) – Environmental Cost (EC)

In addition, the expected profits could be extensively influenced by the potential market shares (future conventional and environmentally-friendly market shares) and competitors’ responses to the NPD. All notations and descriptions are stated in Table 1.

A basic assumption using Bayesian decision analysis (prior and posterior analysis) for the go/kill decision of the NPD project was applied using the following elements:

• (1) State boundary: $Θ = { θ ¯ | 0 ≤ θ ¯ ≤ 1 , θ ¯ = θ + ϕ }$, where θ, φ are the future conventional market share and the environmentally-friendly market share of the new product, respectively. Hence, the total market share (θ) is a combination of θ and φ, which its value is less than or equal one.

• (2) Scenarios regarding space A: ${ a 1 , a 2 , a 3 , a 4 }$ where a1 refers to maintaining the status quo (Business as usual, BAU), a2 denotes improvement without incorporating environmental issues (Iw/oE), a3 signifies improvement with incorporating environmental issues (IE) and a4 indicates termination of the project (TP).

• (3) Profit function: it is defined as $π ( θ ¯ , a i | i = 1 , 2 , 3 , 4 )$ under uncertain market shares θ, φ and competitor’s reactions ρ.

Considering the profit functions under the assumed uncertainties θ, φ and ρ. The four scenarios mentioned above can be quantified as:

• Scenario a1 : Maintaining the status quo (Business as usual, BAU)

$π ( θ ¯ , a 1 ) = p 1 Q θ ( 1 − ρ ) ︸ (I) − ( Q y l + Q f q + c 1 + Q w 1 ) θ ︸ (II) − V 1$
(1)

The first term (I) in Equation (1) represents for the Product Revenues (PR) can be defined as $P R = p 1 Q θ ( 1 − ρ )$ and the second term (II) represents for the Production and Marketing Cost (PMC) with $γ = γ 1 = 0$. For this case, the adjusting factor of market share is not considered.

• Scenario a2: Improvement without an involvement of environmental aspects (Iw/oE)

$π ( θ ¯ , a 2 ) = p 2 Q ( γ + ( 1 − γ ) θ ) ( 1 − ρ ) ︸ (III) − [ ( Q y l + Q f q + c 2 + Q w 2 ) ( γ + ( 1 − γ ) θ ) ] ︸ (IV) − V 2$
(2)

In this scenario, an adjustment of the current NPD project is required. The adjusting factor 0≤γ≤1 is made in the revenue term (III) and the PMC in term (IV) to adjust the market share. For the case that γ = 0, it means that there is no improvements in the products, resulting in the terms (III) and (IV) became the same as those in the terms (I) and (II) as illustrated in the Scenario a1, respectively. For the case that γ = 1 , the Scenario 2 a is fully developed. The related cost analysis indicated that the corresponding costs are the term (IV) and PDC = V2.

• Scenario a3: Improvement with an involvement of environmental aspects (IE)

$π ( θ ¯ , a 3 ) = p 3 Q { γ + ( 1 − γ ) ( θ + γ 1 ϕ ) } ( 1 − ρ ) − ( Q y l + Q f q + c 3 + Q w 3 ) { γ + ( 1 − γ ) ( θ + γ 1 ϕ ) } − V 3 − V 4$
(3)

The Equation (3) shows the profit function of this case, in which each term is described in the foregoing section. To formulate the Equation (3), consider the term $γ + ( 1 − γ ) ( θ + γ 1 ϕ )$ as “proportional market share”, which depends on two adjusting factors (γ and γ1) as shown in the following cases:

• Case 1: No improvement in any adjusting factors of market share $( γ = γ 1 = 0 ) ,$ resulting in $γ + ( 1 − γ ) + γ 1 ϕ ) ⇒ θ$ i.e., it appears only on a conventional market share.

• Case 2: Full-improvements $( γ = γ 1 = 1 ) ,$, so that $γ + ( 1 − γ ) ( θ + γ 1 ϕ ) ⇒ 1$ i.e., it means all the market shares of the new product are occupied.

• Case 3: No improvement on the adjusting factor of conventional market share (γ = 0) , so that $γ + ( 1 − γ ) ( θ + γ 1 ϕ ) ⇒ θ + γ 1 ϕ$ i.e., the proportional market share depends on how much the environmental adjusting factor has improved.

• Case 4: No improvement on the adjusting factor of environmental market share $( γ 1 = 0 )$, so that $γ + ( 1 − γ ) ( θ + γ 1 ϕ ) ⇒ γ + ( 1 − γ ) θ$ i.e., it appears only on the case that the conventional market share being adjusted by the adjusting factor of conventional market share (γ).

• Scenario a4: Terminating the project (TP)

If the NPD project is terminated, the residual resources can then be reinvested. The expected profit of the reinvestments (Huang, 2015) can be defined as:

$π ( θ ¯ , a 4 ) = M$
(4)

### 3.2 The Decision Analysis Process

The Bayesian decision analysis was employed to estimate the uncertainties θ, φ, ρ and resulting in the expected profits for EF-NPD. Beta distribution can be utilized to model the uncertainty about the total market s h a r e s $θ ¯ = θ + ϕ , θ ∼ m ( θ | θ ¯ ) ≡ b e t a ( α θ ¯ , β θ ¯ ) , ≡ b e t a ( α θ ¯ , β θ ¯ ) ,$ and $ρ ∼ g ( ρ | θ ¯ ) ≡ b e t a ( α θ ¯ , β θ ¯ ) ,$, a beta distribution with parameter (α,β) can be used as $θ ¯ ∼ f ( θ ¯ ) ≡ b e t a ( α , β )$. In addition, we suppose that a conditional probability of competitors’ reaction (ρ) which also follow a beta distribution. If a marketing survey is already available, a possible market share of the new product development can be expressed as $f ( θ ¯ ) = Γ ( α + β ) Γ ( α ) Γ ( β ) θ ¯ α − 1 ( 1 − θ ¯ ) β − 1$. Consequently, a conditional probability of competitors’ reaction (ρ) which also follow a beta distribution can be expressed as $g ( ρ | θ ¯ ) = Γ ( α θ ¯ + β θ ¯ ) Γ ( α θ ¯ ) Γ ( β θ ¯ ) ρ α θ ¯ − 1 ( 1 − ρ ) β θ ¯ − 1 ,$, where $α θ ¯ = b θ ¯$ and $β θ ¯ = a − b θ ¯ .$. In a similar way, the parameters of $α θ ¯$ and $β θ ¯$ are set as $α θ ¯ = d θ ¯$ and $β θ ¯ = c − d θ ¯$ for environmentally-friendly market share (φ), the parameters of $α θ ¯ = k θ ¯$ and $β θ ¯ = j − k θ ¯$ for the future conventional market share (θ).

### 3.3 Decision Analysis: Expected Profits

Since both the market share uncertainties and the profit decreasing factors have been included, the expected profits of the four scenarios corresponding to the Equations (1)-(4) can be derived as follows:

$E { π ( θ ¯ ; a 1 ) } = ( p 1 Q − Q y l − Q f q − c 1 − Q w 1 ) E { θ ¯ } − p 1 Q b a E 2 { θ ¯ } − p 1 Q b a V a r { θ ¯ } − V 1$
(5)

$E { π ( θ ¯ ; a 2 ) } = p 2 Q b a ( γ − 1 ) E 2 { θ ¯ } + [ p 2 Q ( 1 − b a γ − γ ) − ( Q y l + Q f q + c 2 + Q w 2 ) ( 1 − γ ) ] E { θ ¯ }$
(6)

$E { π ( θ ¯ ; a 3 ) } = p 3 Q ( γ − 1 ) ( γ 1 d c + k j ) b a E 2 { θ ¯ } + { ( 1 − γ ) ( γ 1 d c + k j ) ( p 3 Q − ( Q y l + Q f q + c 3 + Q w 3 ) ) − p 3 Q γ b a } E { θ ¯ } + p 3 Q ( γ − 1 ) ( γ 1 d c + k j ) b a V a r { θ ¯ } + ( p 3 Q − ( Q y l + Q f q + c 3 + Q w 3 ) ) γ − V 3 − V 4$
(7)

$E { π ( θ ¯ ; a 4 ) } = M$
(8)

where $E { θ ¯ } = α α + β$ and $V a r { θ ¯ } = α β ( α + β ) 2 ( α + β + 1 )$. Four possible scenarios were evaluated in terms of economic feasibility and the maximal expected profit generated from each scenario was selected according to the $max i { E [ π ( θ ¯ , a i ) ] | i = 1 , 2 , 3 , 4 }$.

Decision rules can be alternatively generated by using the Equations (5)-(8). Subsequently, multiple comparisons can be carried out to revise any decision rule, as follows:

${ If Q > A 0 E { θ ¯ } − c 2 γ + V 1 − V 2 A 1 ( E 2 { θ ¯ } + V a r { θ ¯ } ) + A 2 E { θ ¯ } − A 3 , then a 1 is optimal else if C 0 E { θ ¯ } + ( c 2 − c 3 ) γ + V 2 − V 3 − V 4 C 1 ( E 2 { θ ¯ } + V a r { θ ¯ } ) + C 2 E { θ ¯ } + C 3 ≤ Q < A 0 E { θ ¯ } − c 2 γ + V 1 − V 2 A 1 ( E 2 { θ ¯ } + V a r { θ ¯ } ) + A 2 E { θ ¯ } − A 3 , then a 2 is optimal else if B 0 E { θ ¯ } + γ c 3 + V 3 + V 4 + M B 1 ( E 2 { θ ¯ } + V a r { θ ¯ } ) + B 2 E { θ ¯ } + B 3 ≤ Q < C 0 E { θ ¯ } + ( c 2 − c 3 ) γ + V 2 − V 3 − V 4 C 1 ( E 2 { θ ¯ } + V a r { θ ¯ } ) + C 2 E { θ ¯ } + C 3 , then a 3 is optimal else Q ≤ B 0 E { θ ¯ } + γ c 3 + V 3 + V 4 + M B 1 ( E 2 { θ ¯ } + V a r { θ ¯ } ) + B 2 E { θ ¯ } + B 3 , then a 4 is optimal$
(9)

where

$A 0 = c 1 − c 2 ( 1 − γ ) , A 1 = b a { p 2 ( 1 − γ ) − p 1 } , A 2 = p 1 + ( ( 1 + b / a ) γ − 1 ) p 2 − γ Ψ 2 + w 2 − w 1 , A 3 = p 2 − γ Ψ 2 , B 0 = ( 1 − γ ) ( γ 1 d / c + k / j ) c 3 , B 1 = p 3 ( γ − 1 ) ( γ 1 d / c + k / j ) ( b / a ) , B 2 = ( p 3 − Ψ 3 ) ( 1 − γ ) ( γ 1 d / c + k / j ) − p 3 γ b / a , B 3 = γ ( p 3 − Ψ 3 ) , C 0 = ( 1 − γ ) { c 2 − c 3 ( γ 1 d / c + k / j ) } , C 1 = ( γ − 1 ) ( p 2 − p 3 ( γ 1 d / c + k / j ) ) , C 2 = p 2 ( 1 − γ b / a − γ ) + ( 1 − γ ) [ ( γ 1 d / c + k / j ) ( Ψ 3 − p 3 ) − Ψ 2 ] + p 3 γ b / a , C 3 = γ { p 2 − p 3 − Ψ 2 + Ψ 3 } , Ψ 2 = y / l + f / q + w 2 and Ψ 3 = y / l + f / q + w 3 .$

The major advantage of implementing such an analytical tool is the utilization of not only the experts’ knowledge/ experience but also of the survey’s data prior to making a decision. Prior analysis of both $E { θ ¯ }$ and $V a r { θ ¯ }$ can be evaluated by using the experts’ experience and knowledge to formulate the uncertainties of θ as a beta prior distribution $f ( θ ¯ )$. Such information on $E ( θ ¯ )$ and $V a r { θ ¯ }$ is subsequently applied regarding the decision rules as shown in Equation (9). The posterior analysis is further performed basing on the sampling survey data.

## 4. RESULTS AND DISCUSSION

### 4.1 Decision Model Application: MATLAB

The derivative procedure for the EF-NPD decision model incorporating Bayesian analysis using MATLAB under different scenarios and uncertainties as shown in Figure 2, can be described as follows:

• A. Prior analysis: (1) Assign Q, α and β of beta distribution for θ, including a set $α θ ¯$ and $β θ ¯$ of beta distribution for $ρ , ϕ , θ$; (2) Assign $p i , l , y , q , f , c i , V i , γ$ and M (The parameters are assessed based on the experts’ prior experience and knowledge); (3) Compute $E { θ ¯ } , V a r { θ ¯ }$ and identify the optimal prior decision with the maximum expected profit using Equation (9).

• B. Posterior analysis: (4) Allocate the number of people (x) intending to purchase the new product out of the total respondents (n) and calculate $E ′ { θ ¯ } = α + x α + β + n$ and $V a r ′ { θ ¯ } = ( α + x ) ( β + n − x ) ( α + β + n ) 2 ( α + β + n + 1 )$. Identify the optimal posterior decision with the maximum expected profit using Equation (9) by substituting $E { θ ¯ } , V a r { θ ¯ }$ with $E ′ { θ ¯ } , V a r ′ { θ ¯ }$, respectively. Therefore,

• C. Decision Model Application (MATLAB): (5) Based on the experts’ prior experience and knowledge, the market potential of the new product (EF-NPD) is calculated to be 300,000 units (Q = 300,000), while its market shares, environmental involvement (IE) and conventional (I w/o E), are estimated within the range of 15% to 20% and 20% to 25%. The environmental cost is set to be \$225000 (V4 = 225,000). The parameters α , and β of the beta distribution for the market share are assigned to be 4 and 6, respectively. The values of each parameter under different scenarios (a1, a2, a3) are illustrated in Table 2. The profit decreasing factor is influenced by the market shares (conventional (I w/o E) and environmental involvement (IE)). It appears to follow the beta distribution for ρ with parameters $α θ ¯ = 9 θ ¯$ and $β θ ¯ = 12 − 9 θ ¯$ (i.e. a=12, b=9) and the beta distribution for θ and φ with parameters are shown in Table 2.

For Scenarios a2 and a3 (conventional (I w/o E) and environmental involvement (IE)), the adjusting factors are expected to be better, and were assigned as γ = 0.15 and 0.20 respectively. Regarding the Scenario a4 (terminating the project (TP) and investing elsewhere), the expected profit is about ¥40,000,000 (M = 40,000,000). Two prior moments for θ are derived as E{θ} = 0.4 and $V a r { θ ¯ }$ = 0.0218 , respectively, in accordance with the decision rule indicated in Equation (9). Scenario a1 can then be selected as the optimal choice with a maximum expected profit of ¥53,543,000. The sample size of the survey can be calculated as n = 309 ($n = Z α / 2 2 p q / d 2$; where Z0.025 = 1.96, p = 0.28, d = 0.05 ). Based on the additional survey, only 87 out of the 309 target customers intend to buy a new product if it is available on the market. Combining the marketing survey and the previous experts’ knowledge and experience by using Bayesian decision analysis, two posterior moments for θ can then be derived as 0.2853 and $V a r ′ { θ } = 0.001$, respectively. The posterior analysis can finally be implemented using Equation (3.9) by substituting the two prior moments with the two posterior moments. This generates a different outcome, suggesting that Scenario a3 (environmental involvement (IE)) is the optimal decision with the expected profit of about ¥63,176,000.

### 4.2 Sensitivity Analysis: Derivative-based Approach

An effective tool to analyze sensitivity is come from the concept of partial derivative of functions so-called the derivative-based approach. Sensitivity analysis can be used as a tool to measure the changes in output variables compared with those changes in input variables (Saltelli and Ratto, 2008;Loucks and Beek, 2017). Regarding to the profit functions under different scenarios and uncertainties in this study, it is then highly appropriate and effective to establish the sensitivity analysis using the partial derivative. The results from the sensitivity analysis indicate the importance and priority of each variable affecting the profit and needed to be improved.

In this study, Scenario a3 was selected from the posterior step and the input independent variables for determining the sensitivity of the model were θ, φ, ρ for Scenario a3 while other constant parameters are given in Table 1. Let us consider the profit functions for Scenario a3 as in Equation (3). The partial derivatives with respect to θ, φ, ρ are given by

$∂ π ( θ ¯ , a 3 ) ∂ θ = ( 1 − γ ) { p 3 Q ( 1 − ρ ) − ( Q y l + Q f q + c 3 + Q w 3 ) }$
(10)

$∂ π ( θ ¯ , a 3 ) ∂ ϕ = γ 1 ( 1 − γ ) { p 3 Q ( 1 − ρ ) − ( Q y l + Q f q + c 3 + Q w 3 ) = γ 1 ∂ π ( θ ¯ , a 3 ) ∂ θ$
(11)

and

$∂ π ( θ ¯ , a 3 ) ∂ ρ = − p 3 Q { γ + ( 1 − γ ) ( θ + γ 1 ϕ ) }$
(12)

The numerical simulation in this case was established by using the parameters given in Table 2 with the posterior parameters θ = 0.1712, φ = 0.1141 and ρ = 0.2139 Consequently, the sensitivity outcomes from Equation (10)-(12) were given by $∂ π ( θ ¯ , a 3 ) / ∂ θ = 1.8 × 10 8 ,$ $∂ π ( θ ¯ , a 3 ) / ∂ ϕ = 3.6 × 10 7$ and $∂ π ( θ ¯ , a 3 ) / ∂ ρ = − 2.173 × 10 8$, respectively. Considering the changes of these variables (θ, φ, and ρ) affecting those of profit function in terms of percentage, it can be seen that these changes are as 50.2%, 41.5%, and 8.3%, respectively. The graphical representation for the profit function $π ( θ ¯ , a 3 )$ was shown in Figure 3-5 plotted versus θ - ρ, φ - ρ and θ - φ, respectively. As shown in the slope of the dash line of Figure 3, the market share θ and competitor's reactions ρ have equal effect on the profit function. Every increasing of the market share θ will increase the profit function $π ( θ ¯ , a 1 )$ of about 1.8×108 (¥) times and every unit reduction of competitor’s reactions (negative sign) will increase the profit function $π ( θ ¯ , a 3 )$ of about 2.76 × 108 ( ¥ ) times. Similarly, as shown in Figure 4, increasing of the market share φ will affect the profit functions $π ( θ ¯ , a 3 )$ of about 3.6×107 ( ¥ ) less than that of competitor’s reactions ρ and it actually depends on the adjusting factor γ1. Finally, as illustrated in Figure 5, it is can be seen that the profit function $π ( θ ¯ , a 1 )$ increases according to the increasing of both market share θ and φ. However, the change of the market share θ have more significantly effects than that of the market share φ. In conclusion, the improvement with environmental involvement in the Scenario 3 a can be done through the increasing of θ which will induce the increasing of profit much more than that of the reduction of ρ while the increasing of φ will result in minimal profit.

In conclusion, it can be stated that Bayesian decision analysis (prior and posterior analysis) under different scenarios is a reliable, effective, and worthy marketing approach, derived especially for EF-NPD to deal with three uncertainties. The proposed decision model is also practical and easy to be used in cases of insufficient and/or unavailable information and data; especially regarding the EFNPD and the decision model application using MATLAB.

## 5. CONCLUSION AND FUTURE WORK

This study reveals that Bayesian decision analysis integrated with the knowledge and experience of the experts, information from various sources (i.e. initial documents, journals, training documents, meetings and conferences, as well as task forces) combined with objective survey results from marketing research can provide a better approach to deal with market uncertainties. This can lead to a more reliable and trustworthy procedure to improve decision-making. The proposed decision model using MATLAB was developed and implemented.

• 1. The related costs estimated for the unit production variable cost in improvement with incorporating environmental issues (IE), for example, recycling materials cost, could affect the unit production variable cost

• 2. Another crucial point is that the variance value are lower in posterior moment than the prior moment which leads to more reliable results.

• 3. The prior analysis indicated that Scenario a1 was optimal with an expected profit of ¥53,543,000. In contrast, posterior analysis suggested that Scenario a3 was optimal with an expected profit of ¥63,176,000.

• 4. The sensitivity analysis specified that the changes of variables (conventional market share θ, competitor’s reactions ρ, and environmentally-friendly market share φ) could affect the profit by 50.2%, 41.5%, and 8.3%, respectively.

Overall, the proposed Bayesian decision analysis approach can be an effective tool to enhance the quality of decision-making. The proposed model can be used to enhance business success in the future by assisting managers to effectively address any EF-NPD issues under a competitive market. Based on the findings, the following agenda for future research using two different approaches, (operation and marketing) are recommended. Regarding to the operation approach, the theme of the research is in the area of green manufacturing product packaging; for example, food green packaging etc. A prototype of the designed device can be initiated using Solid Works Software and 3-D printer. For the marketing approach, a combination of information from both internal and external approaches as mentioned above will be used as an input for the decision model development under different scenarios for new product development (NPD); for example, food green packaging.

## ACKNOWLEDGEMENT

The authors would like to thank all staff and members of Kainuma Research’s laboratory, Faculty of Systems Design, Tokyo Metropolitan University, Japan, for their support while developing this publication. Special thanks are also due to the Tokyo Human Resources Fund for City Diplomacy for the financial support.

## Figure

Steps and approach of the decision model for new product development.

Flow chart of decision model application: MATLAB using Bayesian Analysis under Different Scenarios and Uncertainties.

Surface plot of the profit function π(θ¯,a3) versus θ and ρ.

Surface plot of the profit function π(θ¯,a3) versus ϕ and ρ.

Surface plot of the profit function π(θ¯,a3) versus θ and ϕ.

## Table

The notations and descriptions used

Estimated parameter values under different scenarios (a1, a2, a3)

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