Determining the Influencing Factors of Procurement Outsourcing Decision Making

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University of Groningen

Faculty of Economics and Business

MSc Technology & Operations Management

Master’s Thesis

Determining the Influencing Factors of

Procurement Outsourcing Decision

Making

Under Supervision of

Dr. Stuart Xiang Zhu

Co-assessor

Dr. Stefano Fazi

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Abstract

Manufacturing outsourcing is a common practice for a company. The aim is to reduce the labor cost and production cost. In practice, the material is provided by the company to its contracted manufacturer in order to ensure the material quality. However, this practice may result in higher overhead cost and longer lead time. Procurement outsourcing is considered to reduce this risk. It enables the contracted manufacturer to choose the material for manufacturing purpose. The drawback is the contracted manufacturer may choose the optimal material for its best interest without concerning the company’s interest. Low quality material may result in defective product which can damage the brand of the company. This damage can be considered as quality related cost which influences the company’s profit. Procurement outsourcing decision making is based on the profit for the company. However, the profit is influenced by many parameters including the material quality and the quality related cost. Therefore, procurement outsourcing decision must be made after a careful and thorough consideration. In addition, the previous study about the investment to improve material quality motivates the Author to observe the effect of the investment application to the procurement outsourcing decision. The aim of this paper is to identify the influencing factors regarding procurement outsourcing decision and to find the best condition when procurement outsourcing gives the most benefit to the company. The results can be used as consideration for the procurement outsourcing decision. Analytical quantitative research method is used to describe the behaviour of profit function. Moreover, sensitivity analysis is performed for each parameter which influences the profit function in order to find the best decision regarding procurement scenario in certain condition. The results show that procurement outsourcing makes the company has less profit. However, the sensitivity analysis is performed to determine the condition when the company suffers the least disadvantage of procurement outsourcing when the company is obliged to outsource its procurement activities.

Keywords: Outsourcing, procurement outsourcing, outsourcing decision, material quality

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Acknowledgements

This thesis is written as a graduation requirement of Master of Science degree in the program Technology and Operations Management at the University of Groningen.

In writing this thesis, I had to take some help and guidelines of some respected persons. In this opportunity, I would like to show my gratitude to Dr. Stuart Xiang Zhu for being my supervisor. His continuous guidance, valuable feedback, and broad knowledge have inspired me in during the writing of this thesis. In addition, a thank you for Dr. Stefano Fazi for being my second supervisor which has spent his precious time in reviewing my thesis.

Additionally, thank you to LPDP scholarship for making this happen. Many people, especially my family and my friends, have supported me during the writing of this thesis which gave me the motivation and inspiration for my thesis. I thank all the people for their help in making this the thesis possible. Last but not least, special thanks to my beloved Litha Nathania who always gives her love, care, and making sure this thesis is finished on time.

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Table of Tables

Table 3.1 Components of the Model... 8

Table of Figures

Figure 5.1 The Impact of The Quality Related Cost on the OEM’s Profit Gap ... 16

Figure 5.2 The Impact of The Quality Related Cost on the Material Quality Selection ... 16

Figure 5.3 The Impact of The Quality Related Cost on the Selling Price ... 17

Figure 5.4 The Impact of The Rework Cost on the OEM's Profit Gap ... 18

Figure 5.5 The Impact of The Rework Cost on the Material Quality Selection ... 18

Figure 5.6 The Impact of Initial Demand on The OEM's Profit Gap ... 19

Figure 5.7 The Impact of Price Sensitivity on The OEM's Profit Gap ... 19

Figure 5.8 The Impact of The Material Cost on The OEM's Profit Gap ... 20

Figure 5.9 The Impact of The Material Cost on The Material Quality Selection Behaviour ... 21

Figure 5.10 The Impact of The Compensation on The OEM's Profit Gap ... 21

Figure 5.11 The Impact of The Investment Cost on The OEM's Profit Gap ... 22

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1. Introduction

Manufacturing outsourcing is a common practice by most companies. According to Yang, Zhang, and Zhu (2016), outsourcing manufacturing is usually practiced by a brand name manufacturer to its contracted manufacturer which is often located in developing countries. Furthermore, the authors explain that lower labor and material cost drive this behavior. However, outsourcing is not always beneficial for the company. Outsourcing may lead into a disaster if it is not properly managed. The example of outsourcing goes wrong is Boeing’s Dreamliner case (Rushe, 2017) when Boeing outsourced the manufacture of Boeing 787 which turned out to be a massive disaster for the company. It was initiated by Boeing’s decision to outsource the part manufacturing from many contractors. The result was not satisfying. Many parts did not fit properly and many aircrafts needed to be reworked. At that time, Boeing had to bear major loss from this project since it was late and over budget.

According to Yang et al. (2016), in common manufacture outsourcing practice, brand name companies procure their material to the contracted manufacturer in order to ensure quality input to the contracted manufacturer. By procuring the material by itself, the company will have more control regarding material quality which will affect the product quality. However, the company will have more overhead cost if they choose to do so. Since often most manufacturers are located far away from the company which may create risk in material procurement especially in the delivery time and cost.

Regarding material procurement, the company may consider to outsource its procurement to a contracted manufacturer. In this case, the company offers a contract to a contracted manufacturer for procuring material which may reduce the company’s overhead cost and make the company be more focused on its core competencies (Heikkilä and Cordon, 2002). However, procurement outsourcing may arise quality issues which will increase the number of defective products. In addition, product quality depends heavily on the quality of incoming material (Tagaras and Lee, 1996). Customers which are dissatisfied by low quality products that are produced by manufacturers may be harmful for the companies’ brand name and market share since the customers will look for products from competitors (Yang et al., 2016). Therefore, procurement outsourcing should get more attention to reduce these risks. This paper will be focused on quality issues that may arise from the nonconformance material.

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4 Regarding material selection, the company may desire a high quality material to decrease the risk of having defective product. Battigali, Fumagalli, and Polo (2007) have investigated that buyer power influences the incentive to the supplier in order to improve the quality of material. Motivated by the incentive to improve the material quality, it is interesting to find how the investment relate to the material choosing and procurement outsourcing decision. By having high quality material, the material cost and the investment cost will increase. However, it may be beneficial for the company since the risk of rework and quality related issue cost will decrease. In addition, it will influence on how the company set the selling price and the compensation to the contracted manufacturer which will impact on procurement outsourcing decision. This leads to following research question:

1. What are the influencing factors for the procurement outsourcing decision? 2. When should a company outsource its procurement activities?

Using analytical quantitative method, this thesis aims to find the influencing factors of procurement outsourcing decision and to find the condition when the procurement outsourcing is beneficial for the company. In order to solve the problem, a model to determine procurement outsourcing decision is developed. This paper proposes an extension of procurement outsourcing model which is developed by Yang et al. (2016) by adding investment variable which may affect material selection. The procurement outsourcing decision will be based on which scenario gives more profit for the company. It is important to find the influencing factors in the procurement outsourcing decision to avoid mistakes in the decision making.

This thesis is structured as follow: Section 2 will discuss about related theory regarding outsourcing decision and investment in order to improve material selection. In Section 3, the basic model and its extension will be introduced. In section 4, the extended model and its optimal solution for each scenario will be identified. The numerical study will be performed and discussed in section 5. The last section will conclude all the findings of this research and the limitations of this thesis will be addressed.

2. Theoretical Background

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5 risk of outsourcing, the decision should have been a thorough consideration. There are some approaches in determining when should a company outsource its activities. The common approaches are core competencies, resource based view, and transaction cost economics (Vaxevanou and Konstantopoulos, 2015). Core competencies approach suggests that company should outsource its non-core competencies while keeping the core competencies in-house (Quinn and Hilmer, 1994; Heikkilä and Cordon, 2002; Yang, et al. 2016). Core competencies can be described as skills or knowledge sets that allows company to perform an activity better than its competitor and increase its competitiveness as the market evolve (Quinn and Hilmer, 1994). By outsourcing its non-core activities, a company can free up its capital and resources to be more focused on its core-competencies (Demirtas, 2013). Resource Based View (RBV) is an approach that concerns the resources and capabilities of the company that is used in order to gain competitive advantage (McIvor, 2009). Resources and capabilities may be outsourced when a company lacks of the resources and capabilities which are needed in order to gain a competitive advantage (McIvor, 2009). Transaction Cost Economics (TCE) is an approach for outsourcing decision that considers of how the activities are conducted, in-house or outsourced (Brewer et al., 2014). TCE possesses two major attributes: behavior and transaction. Behavior attributes of TCE are bounded rationality, opportunism, small numbers bargaining, and information impactedness (McIvor, 2009). This paper will be focused on outsource the procurement of raw material which is beneficial since the material quality will determine the quality of the product. The assumption that is used in this model is the procurement of raw material is not the company core competencies and the governance of purchasing process is not significantly related to the product quality. Thus, procurement outsourcing may be an option for the company. However, it needs to be investigated whether procurement outsourcing is really beneficial for the company.

Delegating procurement activities from companies to their contracted manufacturers has been practiced by some companies. Procurement outsourcing can improve the quality of the procured material and supply chain efficiency benefiting both company, the manufacturer, and customer (Yang et al., 2016). In addition, procurement outsourcing can reduce cost, improve service level, shorten delivery lead time, reduce cashflow pressure, and fewer environmental footprint (Shi, Zhang, Arthanari, Liu, and Cheng, 2014). There is a specific approach in deciding procurement outsourcing. Yang et al. (2016) have developed a model for procurement outsourcing decision based on bargaining power of the company and bargaining power of contracted manufacturer. In general, this model suggests that procurement should be outsourced to contracted manufacturer when both parties achieve lower cost in procuring material. The bargaining power in this model has a role to determine the material price from the supplier which is also related with material quality selection. Furthermore, material quality influences the rework cost and quality related cost which directly affect total procurement cost.

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6 accommodate demand from large supplier. Nonetheless, Inderst and Wey (2007) and Battigali et al. (2007) agreed that profit of the industry is also contributed by the margin of the supplier. This paper will be focused on the initiative of supplier, in this case the supplier of material, to improve quality based on incentives from buyer despite of its buyer power. Specifically, this thesis will analyze the influence of supplier initiative to invest on its material selection in order to get more profit from procurement outsourcing scenario.

The relationship between incentive and investment in quality improvement in supply chain has been investigated by Zhu, Zhang, and Tsung (2007). The incentive to improve quality by both parties significantly affects profit for both parties. In their paper, the quality of production process is indicated by how often the process is in out-of-control state in which more likely to produce nonconforming product. The investment in quality improvement is meant to reduce the mean time of the process to be in its out-of-control state by buying more advanced technology. Quality improvement can also be done by reducing the probability of making nonconforming product by improving the manufacturability of the product (Zhu et al., 2007). Tagaras and Lee (1996) indicated that the quality of the product relies on the interaction of supplier’s input quality and buyer’s manufacturing reliability and quality control. Moreover, based on Zhu et al. (2007), the investment in quality improvement can be done by both sides – buyer and supplier. However, there are conditions when buyer or supplier is the one who holds significant role in maximizing profit for both parties based on how they share the quality cost.

This paper will adopt procurement outsourcing to the contracted manufacturer model by Yang et al. (2016). Thus, we will take into account most of elements that is used for procurement outsourcing decision making with some adjustments in its objective functions and its cost elements. Procurement outsourcing is beneficial for the company, the manufacturer, and the customers (Yang et al. 2016). Customers are willing to pay more for high quality product (Battigali et al., 2007). Since customer hold a role in procurement outsourcing, therefore, the demand will be taken into account. Thus, profit will be used as objective function instead of procurement cost since demand is influenced by selling price and material quality as result of procurement outsourcing. The extension will be adding investment of contracted manufacturer in order to improve quality of material selection. Therefore, investment will be considered as cost for contracted manufacturer in procurement outsourcing scenario.

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7 model is replaced by the material cost which is the function of material quality. The motivation of this replacement is to simplify the model since if bargaining power is considered, then the material cost will depend on the bargaining power which may be different for each party and difficult to measure.

3. Model Description

For this model, there will be two parties involved in the outsourcing contract: the Original Equipment Manufacturer (OEM) and the Contracted Manufacturer (CM). The OEM is brand name manufacturer who gives contract to the CM. For the sake of easiness, the OEM and the CM will be addressed as she and he respectively for the rest of this paper.

By default, the OEM does the procurement activities by herself. Procurement activities in this case is a series of activities starting from choosing material quality, selecting supplier, negotiating, and delivering materials. This scenario is called in-house procurement scenario. On the other hand, the OEM can also cede the procurement activities to the CM, which is called procurement outsourcing scenario. Regardless of which procurement scenario is chosen, the aims of both the OEM and CM are profit maximization.

The profit is determined by two elements: revenue and cost. Revenue is obtained by selling the product with certain price in certain quantity. Assuming that demand is always fulfilled, thus the quantity can be replaced by the demand of the customers. Furthermore, the selling price which is determined by the OEM, has negative influence to the demand according to the law of demand and supply. The higher the price, the lower the demand. Let 𝐷₀ as initial demand and 𝛽 as the price sensitivity. Thus, the actual demand can be formulated as:

𝐷 = 𝐷₀− 𝛽𝑃.

On the other hand, Yang et al. (2016), indicate the costs elements that are taken in to account are material cost, quality related cost, rework cost, and material quality influence procurement cost. Since this paper considers the profit from selling the product, thus all elements in the profit function are measured as unit cost instead of total cost. Assuming the material is contractible, then the material quality can be easily identified. Let α represents the material quality which can be regarded as nonconformance rate of material where 0 < 𝛼 < 1. Low quality material is represented with high value of 𝛼 and most likely will result a defect product. Having a defect product, both the OEM or the CM will suffer from quality related cost which are denoted as 𝑅_𝑂𝐸𝑀 and 𝑅_𝐶𝑀 for the OEM and the CM respectively. In addition, there will be rework cost incurred which is denoted as 𝑟. Rework cost will be paid by either the OEM or CM depends on who procures the material. The OEM will pay the rework cost under in-house procurement scenario, otherwise, the CM will pay the rework cost under procurement outsourcing scenario. Since 𝑅𝑂𝐸𝑀, 𝑅𝐶𝑀, and 𝑟

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8 is decreasing convex in 𝛼. In this case, a linear function is used to represent cost function to generalize decreasing convex function.

The basic assumption that are used in this thesis are: First, procurement activities is not the OEM’s core competency, thus the OEM can outsource her procurement activity without any significant consideration. The second assumption is the material is contractible, which means the material quality can be identified easily, in example by the material quality certification. The third assumption is the material is public information, thus the OEM shall not pay the compensation lower than the highest material cost. The fourth assumption is all elements for profit function calculation are measured in unit. The fifth assumption is the demand is affected by the selling price of the product due to price sensitivity and the demand is always fulfilled by the OEM. Therefore, the demand must not be zero. The sixth assumption is the quality related cost functions and rework cost function are increasing convex in material quality while the material cost function is decreasing convex in material quality. The last assumption is the investment is always succeeded, which means it will always improve the material quality from initial quality to the desired quality. To summarize, the components in the model are represented in Table 3.1 below:

Table 3.1 Components of the Model

Components of the Model Notation Definition Objective Functions

• Maximize Profit of the OEM 𝜋_𝑂𝐸𝑀𝐼 & 𝜋_𝑂𝐸𝑀𝑆 Profit of the OEM under in-house procurement scenario & procurement outsourcing scenario • Maximize Profit of the CM 𝜋_𝐶𝑀𝑆 Profit of the CM under

procurement outsourcing scenario

Decision Variables

• Selling price of the product 𝑃 Selling price which is set by the OEM

• Compensation for material cost

• Material quality which is chosen by the OEM

𝑊

𝛼

Compensation which is paid by the OEM to the CM

The material’s nonconformance rate that is chosen by the OEM in in-house procurement scenario • Desired material quality of the

CM based on investment

𝛼𝑆 Nonconformance rate of desired

material quality by the CM

Parameters

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• Price Sensitivity 𝛽 Price sensitivity of the product

• Quality Related Cost Function 𝑅𝑂𝐸𝑀(𝛼) = 𝜇𝛼2

𝑅_𝐶𝑀(𝛼) = 𝜏𝛼2

Quality related cost for the OEM and the CM

• Material Cost Function

𝑐(𝛼) = 𝑐0(1 − 𝛼)

Cost of the material of certain quality

• Rework Cost Function 𝑟(𝛼) = 𝜃𝛼2 Cost to rework the defect product

• Initial material cost 𝛼0 Initial nonconformance rate

• Material quality improvement

cost 𝐾𝛼

Constraints

• Nonconformance rate of

improved material is lower than initial material

• Nonconformance rate is between 0 and 1

• Quality related cost, material cost, and rework cost multiplier are greater than 0

• Compensation must be higher than material cost

• Selling price must be higher than material cost

• The function of demand

reduction cannot be higher than initial demand 𝛼_𝑆 < 𝛼₀ 0 < 𝛼₀ < 1 0 < 𝛼_𝑆 < 1 𝜇, 𝜏, 𝑐₀, 𝜃 > 0 𝑊 > 𝑐₀ 𝑃 > 𝑐0 𝛽𝑃 < 𝐷0

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4. Results and Findings

Based on possible scenarios in procuring material, there will be two scenarios for model extension. In-house procurement scenario and procurement outsourcing scenario which are going to be discussed in this section.

4.1. In-House Procurement Scenario

In this scenario, the OEM will procure the materials by herself. Since the price and material quality are determined by the OEM, she will make the decision in order to gain the maximal profit for herself. Let 𝜋_𝑂𝐸𝑀𝐼 as profit of the OEM under in-house procurement scenario while 𝛼 and 𝑃 as the quality of material and selling price that is chosen by the OEM respectively. Therefore, the profit which can be obtained by the OEM can be described as:

𝜋_𝑂𝐸𝑀𝐼 (𝑃, 𝛼) = 𝑃𝐷(𝑃) − 𝑐(𝛼)𝐷(𝑃) − 𝑅𝑂𝐸𝑀(𝛼)𝐷(𝑃) − 𝑟(𝛼)𝐷(𝑃).

The OEM gets her revenue from selling the product to her customer. The amount of the revenue depends on the selling price (𝑃) that is set by the OEM. On the other hand, the cost elements for the OEM in this scenario are material cost (𝑐(𝛼)), quality related cost (𝑅_𝑂𝐸𝑀(𝛼)), and rework cost (𝑟(𝛼)). The OEM buys the material by herself, thus the material cost is considered as the cost incurred by the OEM. The material cost depends on the material quality, better quality material has higher price than lower quality material. The quality related cost for the OEM is the cost that is caused by defective product that is sold. This cost may be in form of brand damage and losing market share (Yang et al., 2016). Since the material is procured by the OEM, therefore she has to be responsible for the rework that is caused by defective product. In addition, the quality related cost and rework cost depend on material quality. All the mentioned elements are measured in product unit. Thus, the profit function depends on the number of products sold which follows the demand. However, the demand is influenced by the selling price due to price sensitivity.

Proposition 1. The OEM’s profit function (𝜋𝑂𝐸𝑀𝐼 ) is concave in 𝑃 for any given 𝛼.

Since this function is concave in selling price, thus the optimal selling price to obtain the maximum profit for the OEM can be given by:

𝑃∗(𝛼) =𝐷0 + 𝛽𝑐0− 𝛽𝑐0𝛼 + 𝛽𝜑𝛼

2

2𝛽 , 𝑤ℎ𝑒𝑟𝑒 𝜑 = 𝜇 + 𝜃.

By setting the selling price as the optimal solution, thus, the optimal material quality in order to achieve the maximum profit for the OEM can be formulated as:

𝜋𝑂𝐸𝑀𝐼 (𝑃∗(𝛼), 𝛼) = (( 𝐷0+ 𝛽𝑐0− 𝛽𝑐0𝛼 + 𝛽𝜑𝛼2 2𝛽 ) − (𝑐0(1 − 𝛼) − (𝜇𝛼 2_{) − (}_𝜃_𝛼2_{)) (}1 2(𝐷0− 𝛽𝑐0+ 𝛽𝑐0𝛼 − (𝜇 +𝜃)𝛽𝛼2_)).

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11 Since the concavity of the OEM’s profit function is influenced by 2𝜑 − 𝑐₀, there will be two cases when 2𝜑 − 𝑐₀ ≤ 0 and 2𝜑 − 𝑐₀ > 0. The condition when 2𝜑 ≤ 𝑐₀ or 2(𝜇 + 𝜃) ≤ 𝑐₀ means that the quality related cost for the OEM – such as brand damage and losing market share – and rework cost combined is less than half of the material cost. In practice, this condition is less likely to happen. The rework cost is the cost of making a new product to replace defective product which means it often needs new material. Thus, the rework cost is often higher than the material cost. Although for some cases the rework does not need new material, it is more likely for the quality related cost and rework cost to be higher than half of the material cost. Therefore, it is interesting to analyze the case when 2𝜑 > 𝑐0 since it is more practical.

Proposition 3. In condition when 2𝜑 > 𝑐₀, the OEM’s profit function is concave when 𝛽𝑐02

4 <

𝜑(𝐷₀− 𝛽𝑐₀). In this case, the optimal solution for the OEM will lie in interval 𝛼₁ ≤ 𝛼∗ ≤ 𝛼₂ or 𝛼 = 0 or 𝛼 = 1.

In case when 2𝜑 > 𝑐₀ which is more practical, there is a condition when 𝛽𝑐0 2

4 < 𝜑(𝐷0− 𝛽𝑐0)

which has to be fulfilled in order to make the OEM’s profit function is concave and resulting maximum value. If the condition when 𝛽𝑐0

2

4 < 𝜑(𝐷0− 𝛽𝑐0) is not fulfilled, then the OEM’s profit

function will be convex for any 𝛼 hence the maximum profit will be reached when either 𝛼∗ = 0 or 𝛼∗ = 1 which is not practical. Furthermore, the condition when 𝛽𝑐02

4 < 𝜑(𝐷0− 𝛽𝑐0) makes a

condition that 𝐷₀− 𝛽𝑐₀ must be positive 0 since 𝑐₀, 𝛽, and 𝜑 are always positive. However, 𝐷₀− 𝛽𝑐0 > 0 condition will always be true under the assumption that demand is always positive 𝐷0−

𝛽𝑃 > 0 and selling price is always higher than material cost 𝑃 > 𝑐0, that will make 𝐷0 > 𝛽𝑃 >

𝛽𝑐₀ , hence 𝐷₀− 𝛽𝑐₀ > 0 should always be true.

In practice, the material quality that exists may not always result in perfect product nor always result in defective product. Therefore, the OEM’s profit function should not be concave for any value of 𝛼. Thus, in real case scenario, it is safe to assume that there may be critical points where the OEM’s profit function is concave in the range between these critical points. Let 𝛼̅ as the point when the second derivative of the OEM’s profit is less than zero and 𝛼₁ and 𝛼₂ as the critical points when the second derivative of the OEM’s profit equals to 0 and where 0 < 𝛼₁ < 𝛼̅ < 𝛼₂ < 1, thus the OEM’s profit function is concave in interval 𝛼₁ < 𝛼 < 𝛼₂ and convex outside the mentioned range. Thus, the OEM’s maximum profit will be achieved when 𝛼1 ≤ 𝛼∗ ≤ 𝛼2 or may

be achieved when 𝛼∗ _{= 0 or 𝛼}∗ _{= 1. However, the optimal solution is not tolerable if it is either 0}

or 1 since that means the material never produce defective product or always produce defective product.

Furthermore, the optimal material quality for the OEM is obtained by solving below equation: (𝑐0 2 − 𝜑𝛼 ∗_{) (𝐷} 0− 𝛽𝑐0) + 𝛽𝑐₀2_𝛼∗ 2 − 3 2𝛽𝑐0𝜑𝛼 ∗2_{+ 𝛽𝜑}2_𝛼∗3 _{= 0.}

In conclusion, the condition when 𝛽𝑐0 2

4 < 𝜑(𝐷0− 𝛽𝑐0) must be satisfied in real world situation –

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12 the OEM is exist. However, 𝛽𝑐0

2

4 < 𝜑(𝐷0− 𝛽𝑐0) will always be satisfied since the demand is

always positive and the selling price is always bigger than the material cost. In practice, the optimal solution material quality must not be 0 or 1 since there is no material that never nor always results in defective product. Hence, the optimal solution is accepted only when 𝛼₁ ≤ 𝛼∗ _{≤ 𝛼}

2.

4.2. Procurement Outsourcing Scenario

In this case, the OEM sets the selling price before she cedes the procurement rights to the CM. Therefore, the CM may decide the material quality after the OEM has already set the selling price. Since this scenario has sequential decision making, therefore this problem can be solved by adopting Stackelberg game which aims the equilibrium where the decision making is done sequentially and affects the interest of both parties. In this scenario, the OEM acts as the leader since she is the one who make the first decision in setting the selling price while the CM acts as the follower which later determines the material quality based on the selling price. Based on this theory, since each party aims for its own interest, the decision of the follower should be anticipated by the leader to achieve the equilibrium in Stackelberg Game. Therefore, in order to obtain the optimal solution for both parties, the optimal solution calculation should consider the follower’s interest first, in this case the material quality that is chosen by the CM. Let 𝜋_𝐶𝑀𝑆 as profit of the CM under procurement outsourcing. Therefore, the CM’s profit function will be:

𝜋_𝐶𝑀𝑆 (𝛼𝑆) = 𝑊𝐷(𝑃) − 𝑐(𝛼𝑠)𝐷(𝑃) − 𝑅𝐶𝑀(𝛼𝑠)𝐷(𝑃) − 𝑟(𝛼𝑠)𝐷(𝑃) − 𝐼.

By letting 𝐾_𝛼 as the improvement cost, 𝛼₀ as the initial material quality, and 𝛼_𝑆 as the desired material quality, and adopting the material quality improvement based on investment by Zhu, et al. (2007), the investment cost is formulated as:

𝐼 = 𝐾_𝛼𝑙𝑛 (𝛼0 𝛼_𝑠).

In this model, the CM gets his revenue from the compensation (𝑊) for procuring material. The compensation is paid by the OEM. On the other hand, by procuring material, there will be costs incurred by the CM for material cost (𝑐(𝛼_𝑠)), quality related cost (𝑅_𝐶𝑀(𝛼_𝑠)), rework cost (𝑟(𝛼_𝑠)), and investment cost (𝐼). These costs are influenced by the material quality which is the decision that has to be made by the CM. Since the CM procures the material, therefore he has to pay for the material and he is responsible for the rework cost. The quality related cost for the CM is the cost that is caused by low quality material such as make the production more difficult and accelerating the depreciation of tools and machine (Yang et al., 2016). The investment cost is can be treated as incentive that is given by the CM to his supplier in order to increase the material quality form his supplier. Battigali et al. (2007) indicated that supplier will do investments in order to improve material quality based on the incentive from buyer. The investment cost will be treated as the incentive from buyer to its supplier in order to improve the material quality. The investment is assumed will improve initial material quality (𝛼₀) to the desired material quality (𝛼_𝑆).

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13 considerably low and the CM desire a high quality material, then the investment cost will be bigger since the gap is considerably high. All the mentioned elements are measured in product unit. Thus, the CM’s profit function depends on the number of products sold which follows the demand. Furthermore, the selling price which is set by the OEM influences the demand due to price sensitivity.

Based on the model, the decision variable for the CM will be how far he will improve the material quality which is denoted as 𝛼_𝑆. The decision also affects the material cost, quality related cost, and the rework cost since these costs depend on the material quality.

Proposition 4. The CM’s profit function is concave for any given 𝛼_𝑆. Since the CM’s profit function (𝜋_𝐶𝑀𝑆 _(𝛼

𝑆)) is concave for any given 𝛼𝑆, hence the optimal material

quality for the CM in this scenario will be obtained by: 𝛼_𝑆∗ = 𝑐0𝐷 + √𝑐0

2_𝐷2_{+ 8𝜔𝐾} 𝛼𝐷

4𝜔𝐷 , 𝑤ℎ𝑒𝑟𝑒 𝜔 = 𝜏 + 𝜃. … (𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 1)

The demand (𝐷) is used as decision variable to make the calculation easier. Therefore, from this point on, the OEM will decide how many demand that need to be fulfilled. However, by knowing the demand, the selling price can be calculated based on the price sensitivity of the demand. By knowing the follower’s decision, thus the leader can make the optimal solution which satisfies both parties’ interests. Using the optimal material quality for the CM, the OEM can determine the optimal demand as follow:

𝜋_𝑂𝐸𝑀𝑆 (𝐷, 𝛼𝑆∗(𝐷)) = 𝑃(𝐷)𝐷 − 𝑊𝐷 − 𝑅𝑂𝐸𝑀(𝛼𝑆∗(𝐷))𝐷.

Since demand is used in previous function, therefore the OEM' will determine the optimal demand to gain her best interest. In this scenario, the OEM gains her revenue by selling the product. The amount of the revenue depends on the selling price which is based on the optimal demand. Since the CM procures the material, the OEM has to compensate for the material cost that is paid by the CM. Thus, it will be the expense for the OEM. In addition, the OEM may suffer from quality related cost that is caused by the material quality. Therefore, the quality related cost of the OEM depends heavily on the CM’s decision regarding the material quality.

When the optimal material quality is chosen by the CM, thus, the OEM’s profit function using the optimal material quality can be formulated as:

𝜋_𝑂𝐸𝑀𝑆 (𝐷, 𝛼𝑆∗(𝐷)) = 𝐷 ( 𝐷0− 𝐷 𝛽 − 𝑊 − 𝜇 ( 𝑐0𝐷 + √𝑐02𝐷2+ 8𝜔𝐾𝛼𝐷 4𝜔𝐷 ) 2 ).

Proposition 5. The OEM’s profit function is convex when 0 ≤ 𝐷 < 𝐷̅ and concave when 𝐷 > 𝐷̅. However, this paper aims for the maximum profit for the OEM, therefore, this optimal demand is only accepted when 𝐷 > 𝐷̅.

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14 𝐷₀− 2𝐷∗ 𝛽 − 𝑊 − 𝜇𝑐0(√𝑐02𝐷∗2+ 8𝜔𝐾𝛼𝐷∗+ 𝑐0𝐷∗) 2 16𝜔2_𝐷√𝑐 02𝐷∗2+ 8𝜔𝐾𝛼𝐷∗ = 0. … (𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 2)

The optimal demand based on this calculation has considered the CM’s optimal material quality. Which means, the OEM has already anticipated the CM’s decision in choosing material quality in order to find the equilibrium in Stackelberg’s Game.

4.3. Comparison

Based on the optimal solutions formulation from previous section, the maximum profit for the OEM can be calculated for each scenario. The OEM should choose the scenario which result in higher profit. A basic setting that meets the condition for both scenario is set for a fair comparison. Furthermore, regarding the fairness, the parameters must be set when the OEM and the CM share the same quality related cost since the quality related cost may be the reason why the OEM outsources her procurement activities in the first place. Moreover, the parameters are set according to the constraints. The constraints also include the condition when the OEM and the CM share the quality related risk equally. In addition, some parameters are set to fulfill a condition (𝛽𝑐02

4 <

(𝜇 + 𝜃)(𝐷0− 𝛽𝑐0)) in order to obtain the maximum profit. Some parameters that have no

references are adjusted so the value of these parameters do not violate the constraint when the sensitivity analysis is performed. The parameters value are set as follow: the initial demand 𝐷0 =

2000, the price sensitivity 𝛽 = 4, the initial material cost 𝑐₀ = 50, the quality related cost for the OEM and for the CM 𝜇, 𝜏 = 50, the rework cost 𝜃 = 50, the compensation 𝑊 = 50, the improvement cost 𝐾_𝛼 = 40, and the initial material quality 𝛼₀ = 0.9.

Since this thesis aims to find when should the company outsource its procurement activities, thus the main focus is the profit for the OEM. The OEM may outsource her procurement activities when her profit is higher under procurement outsourcing scenario. Based on the basic setting, the OEM’s profit under in-house procurement scenario (𝜋_𝑂𝐸𝑀𝐼 _{) is 208164.06, while the OEM’s profit}

under procurement outsourcing scenario (𝜋_𝑂𝐸𝑀𝑆 ) is 173764.80.

In other words, the OEM will have more profit by 17% under in-house procurement scenario. Thus, in general, procurement outsourcing scenario decreases the OEM’s profit. Although procurement outsourcing result in less profit, there may be some reasons for the OEM to outsource her procurement activities such as to be more focused on other activities, reducing overhead cost, reducing the risk of delivery or reducing the delivery time. In this case, the OEM will look for the condition when the procurement outsourcing will give the least profit gap for her further consideration regarding procurement outsourcing decision. Let 𝛾 as the OEM’s profit gap, and 𝛾 can be formulated as:

𝛾 = ((𝜋𝑂𝐸𝑀

𝐼 _{− 𝜋} 𝑂𝐸𝑀𝑆 )

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15 By setting the OEM’s profit gap as the performance measure, the influencing factors of procurement outsourcing decision can be addressed based on the sensitivity analysis for each parameter. A parameter can be considered as influencing factor if it significantly impacts the OEM’s profit gap. In addition, the condition when the OEM should outsource her procurement activities can be identified by addressing the condition where the OEM’s profit gap gives the least value.

5. Numerical Study and Discussion

Based on the profit comparison, it can be said that procurement outsourcing will make the OEM get less profit. Suppose that the OEM has to choose procurement outsourcing scenario, therefore the she has to really consider in which condition the procurement outsourcing will result the least disadvantage. Therefore, the sensitivity analysis for each parameter needs to be performed in order to identify the influencing factors of the profit gap. Furthermore, if a parameter is considered as significant towards the OEM’s profit gap, the condition when outsourcing gives the least disadvantage for the OEM may be determined.

This section will be divided into four subsection which each subsection will discuss the sensitivity of: the quality related cost and rework cost, the initial demand and price sensitivity, the material cost and compensation, and the investment cost.

5.1.1. The Quality Related Cost and Rework Cost

The quality related cost influences the profit for both the OEM and the CM. The OEM has to suffer from brand damage and losing her market share by selling defective product while the CM may have accelerated depreciation of his machine or more manufacturing cost by using low quality material (Yang et al, 2016). Although the quality related costs have different forms for each party, they both are caused by low material quality. The rework cost is the cost to rework the defective product which is paid by the party who procures the material. Therefore, the OEM is responsible for the rework cost in in-house procurement scenario while the CM is responsible for the rework cost in procurement outsourcing scenario.

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16

Figure 5.1 The Impact of The Quality Related Cost on the OEM’s Profit Gap

It can be seen in Figure 5.1 that the quality related cost for the OEM (𝜇) does not have significant effect towards the profit gap. Thus, the OEM may outsource her procurement activities regardless of her quality related cost. On the other hand, the quality related cost for the CM (𝜏) has considerably low impact on the profit gap. This means, in condition when the CM is faced with high risk of quality related cost, procurement outsourcing scenario should be preferred by the OEM although the gap is not significant.

This condition is caused by the CM who will choose better quality material under procurement outsourcing scenario when he has high 𝜏. By having better material quality, the OEM’s cost will decrease since the quality related cost is the only cost element that depends on the material quality. High quality material will reduce the related quality cost function for the OEM (𝑅_𝑂𝐸𝑀(𝛼𝑆)) since

𝛼_𝑆 value is small. As a reminder, material quality (𝛼_𝑆) is represented by the material defection rate and they both are inversely related which means high quality material is represented by low value of 𝛼_𝑆. The impact of quality related cost to the material quality selection can be observed in Figure 5.2.

Figure 5.2 The Impact of The Quality Related Cost on the Material Quality Selection

0% 5% 10% 15% 20% 25% 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 𝛾

The Impact of The Quality Related Cost on the OEM's Profit Gap

μ τ 0 0.1 0.2 0.3 0.4 0.5 0.6 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 αS

The Impact of The Quality Related Cost on the Material Quality

Selection

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17 It is interesting to find why the profit gap does not shift much although the optimal material quality has shifted to high quality material. The answer is related to Stackelberg game which prioritize the decision of the follower over the leader. Since the CM acts as the follower, therefore he has to choose the optimal material quality in order to gain his best interest. On the other hand, the OEM, who acts as the leader, adjusts her decision according to the CM’s decision in order to achieve the equilibrium. As can be seen in Figure 5.3, to achieve the equilibrium, the OEM tends to increase the selling price as the quality related cost for the CM’s increases. Therefore, the demand will decrease and make the increasing of 𝜏 is insignificant towards the OEM’s profit gap.

Figure 5.3 The Impact of The Quality Related Cost on the Selling Price

On the other hand, the rework cost (𝜃) has significant effect towards the OEM’s profit gap. The sensitivity of 𝜃 can be seen in Figure 5.4. This phenomenon happens since the rework cost depends on the scenario which will affect the OEM’s profit in both scenarios. Since the OEM is responsible for the rework cost under in-house procurement scenario, the profit of the OEM under in-house procurement (𝜋_𝑂𝐸𝑀𝐼 ) will decrease as 𝜃 increases. On the contrary, the OEM’s profit under the procurement outsourcing scenario (𝜋_𝑂𝐸𝑀𝑆 ) increases as 𝜃 increases. This is caused by the CM will choose higher quality material (refer to Figure 5.5) when the rework cost is high which will impact on lower quality related cost for the OEM. In addition, the OEM’s profit is higher under in-house procurement scenario (𝜋_𝑂𝐸𝑀𝐼 > 𝜋_𝑂𝐸𝑀𝑆 ). Knowing that 𝜋_𝑂𝐸𝑀𝐼 is decreasing, 𝜋_𝑂𝐸𝑀𝑆 is increasing, and 𝜋_𝑂𝐸𝑀𝐼 > 𝜋_𝑂𝐸𝑀𝑆 , thus the profit gap is decreasing.

286 288 290 292 294 296 298 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 P

The Impact of The Quality Related Cost on the Selling Price

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18

Figure 5.4 The Impact of The Rework Cost on the OEM's Profit Gap

Figure 5.5 The Impact of The Rework Cost on the Material Quality Selection

It is interesting to find the reason why the effect of 𝜃 is more significant compared to the effect of 𝜏. The explanation is because 𝜏 only affects 𝜋_𝑂𝐸𝑀𝑆 while 𝜃 affects both 𝜋_𝑂𝐸𝑀𝐼 and 𝜋_𝑂𝐸𝑀𝑆 . Higher 𝜏 makes 𝜋_𝑂𝐸𝑀𝑆 decreases while keeping 𝜋_𝑂𝐸𝑀𝐼 constant. Furthermore, since 𝜋_𝑂𝐸𝑀𝐼 > 𝜋_𝑂𝐸𝑀𝑆 , thus the profit gap is decreasing. If it is compared to the effect of 𝜃, the effect of 𝜏 is less significant since 𝜋_𝑂𝐸𝑀𝐼 is constant.

In conclusion, the quality related cost is insensitive to the OEM’s profit gap, since it does not significantly affect the procurement outsourcing decision. The OEM may make outsourcing decision without considering the condition when both parties share unequal quality related cost. On the other hand, the rework cost is sensitive to the OEM’s profit gap since it has significant impact on the OEM’s profit gap. Furthermore, under procurement outsourcing scenario and when the rework cost is considerably high, the OEM will have smaller loss compared to when the rework cost is low. There may be a condition when procurement outsourcing will result in profit for the OEM if the rework cost is very big. In addition, regardless of the profit gap, higher quality material

0% 5% 10% 15% 20% 25% 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 γ 𝜃

The Impact of The Rework Cost on the OEM's Profit Gap

0 0.1 0.2 0.3 0.4 0.5 0.6 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 αS 𝜃

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19 is preferred under the procurement outsourcing scenario when the quality related cost of the CM and the rework cost is high.

5.1.2. The Initial Demand and Price Sensitivity

The profit functions that are used in this paper are measured in unit. Therefore, the number of the unit sold influences the profit for both parties. However, the demand is influenced by the selling price that is set by the OEM. Higher selling price will decrease the demand due to price sensitivity. Since the selling price is decided by the OEM and the demand affects the profit, thus it is interesting to observe the impact of the price sensitivity to the profit.

Based on the result as presented in Figure 5.6, the initial demand (𝐷₀) has significant impact for the OEM’s profit gap. The OEM’s profit gap decreases as 𝐷0 increases. This means, when the

OEM is in a condition when she is obliged to outsource her procurement activities, she will receive less disadvantage of procurement outsourcing when 𝐷0is considerably high.

Figure 5.6 The Impact of Initial Demand on The OEM's Profit Gap

On the contrary, the price sensitivity (𝛽) has the opposite result with the 𝐷₀. If the product is considered as price sensitive, then the OEM’s profit gap will be big. As can be seen in Figure 5.7, the OEM’s profit gap increases as 𝛽 increases.

Figure 5.7 The Impact of Price Sensitivity on The OEM's Profit Gap

0% 10% 20% 30% 40% 50% γ D0

The Impact of Initial Demand on The OEM's Profit Gap

0% 20% 40% 60% 80% γ β

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20 Based on the profit function, the OEM will have more cost elements under in-house procurement scenario compared to when she is under procurement outsourcing scenario. The OEM bears material cost and the rework cost under in-house procurement scenario and she will give the responsibility for these costs to the CM under procurement outsourcing scenario. Since these costs depend on the actual demand (𝐷), thus by eliminating them, the OEM will have more revenue and less cost under procurement outsourcing scenario when the 𝐷 is high. The demand depends on 𝐷₀ and 𝛽. Moreover, 𝐷₀ and 𝛽 have opposite effect on 𝐷 which makes 𝐷 will be high when 𝐷₀ is high or 𝛽 is low. Thus, the OEM’s profit gap decreases when 𝐷0 increases or 𝛽 decreases.

The interesting thing is, there is a certain value of 𝛽 when the OEM’s profit gap rises more significantly beyond this value. Since the concavity does not change, therefore this phenomenon may be related to the optimal demand function (refer to equation 2).

In conclusion, the initial demand and price sensitivity has significant effect to the OEM’s profit gap. Therefore, the OEM should really consider about the initial demand and price sensitivity regarding procurement outsourcing decision. In condition when the initial demand is high or the product is not price sensitive, the OEM will get less disadvantage from procurement outsourcing. Furthermore, there is a certain value of price sensitivity when the price sensitivity is more sensitive to procurement outsourcing loss. However, further analysis is required to explain this phenomenon.

5.1.3. The Material Cost and Compensation

The material cost will be imposed to the party who procures the material. However, under procurement outsourcing scenario, the CM who procures the material will be compensated by the OEM. The compensation will be the revenue for the CM but on the other hand, it will be the expense for the OEM. Since these parameters affect the revenue and the expense for both the OEM and the CM in both scenarios, thus it is interesting to observe the impact of these parameters to the profit for both parties.

The material cost will be imposed to the CM under procurement outsourcing scenario. As can be seen in Figure 5.8, the incremental of material cost will result in lower profit gap for the OEM.

Figure 5.8 The Impact of The Material Cost on The OEM's Profit Gap

0% 5% 10% 15% 20% 25% 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 γ c₀

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21 The material cost (𝑐0) influences the material quality selection. As can be seen in Figure 5.9, high

𝑐₀ will make the party who procures the material tends to choose high 𝛼. Although it seems that both scenarios have the same optimal material quality, actually they are slightly different. In addition, since the material cost function (𝑐(𝛼)) is linear function while the other cost functions are quadratic functions in terms of material quality, thus the 𝑐₀ has bigger impact to the profit function of the party who procures the material.

Figure 5.9 The Impact of The Material Cost on The Material Quality Selection Behaviour

In this case, the OEM will suffer more when she procures the material by herself. This implies to the OEM’s profit decreasing rate which affects the OEM’s profit gap. The OEM’s profit gap is getting smaller because the OEM’s profit under in-house procurement scenario (𝜋_𝑂𝐸𝑀𝐼 _{) decreases}

more significant compared to the OEM’s profit under procurement outsourcing scenario (𝜋_𝑂𝐸𝑀𝑆 ). The compensation (𝑊) can be considered as the expense for the OEM and the revenue for the CM. High compensation will decrease the OEM’s profit while increasing the CM’s profit. The compensation impact on the OEM’s profit gap is shown in Figure 5.10.

Figure 5.10 The Impact of The Compensation on The OEM's Profit Gap

0 0.1 0.2 0.3 0.4 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 α c0

The Impact of The Material Cost on The Material Quality Selection Behaviour In-House Procurement Procurement Outsourcing 0% 5% 10% 15% 20% 25% 30% 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 101 103 105 γ W

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22 It can be said that 𝑊 is sensitive to the OEM’s profit gap since it has significant effect on the OEM’s profit gap. The OEM’s profit gap increases as 𝑊 increases. Based on the OEM’s profit function, 𝑊 does not depend on any decision variables. Moreover, 𝑊 is considered as the expense for the OEM. Therefore, 𝑊 does not do any good for the OEM. Higher compensation will only result on lower profit for the OEM. This means that the OEM should have the lowest compensation as possible in order to reduce the disadvantage of procurement outsourcing. However, if the compensation is too low, the CM may experience loss due to his income is smaller than his cost. In conclusion, the material cost is sensitive to the OEM’s profit gap. When the material cost is considerably high, the OEM may get smaller loss under procurement outsourcing scenario. Therefore, the OEM will receive less disadvantage of procurement outsourcing when the material cost is high. On the other hand, the compensation that is given to the CM should not be big since it does not do any good to the OEM. High compensation will only decrease the OEM’s profit. However, the compensation value should be considered since if it is too low, then the CM may suffer loss and the procurement outsourcing proposal may be rejected by the CM. Thus, a further research in order to get the optimal compensation value may be interesting to be conducted.

5.1.4. The Investment Cost

The investment cost consists of two parameters. The first parameter is the cost of improving the material quality or the improvement cost which can be denoted as 𝐾_𝛼. The second parameter is 𝛼₀ which can be described as the initial material quality that is going to be improved. In practice, 𝛼0

can be considered as product that is offered by certain supplier which will be used as raw material for the manufacturing process by the CM. Thus, the product offered by the supplier has certain level of quality that represents material quality for the CM. On the other hand, the CM which acts as the buyer in this case, has an initiative to give some incentives to his supplier in order to improve its product quality. By improving the supplier’s product quality, the CM also improves his raw material quality that will be used to manufacture the OEM’s product. Improving machine, providing better raw material, and have better inspection are some endeavors to improve the supplier’s product quality. However, the investment for quality improvement is measured based on the gap of the material quality before and after the improvement. The impact of the 𝐾_𝛼 on the OEM’s profit gap is presented in Figure 5.11.

Figure 5.11 The Impact of The Investment Cost on The OEM's Profit Gap

0% 5% 10% 15% 20% 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 γ 𝐾𝛼

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23 Based on the result, 𝐾_𝛼 has no effect to the OEM’s profit gap. It is caused by 𝐾_𝛼 has extremely low impact on the CM’s decision regarding material quality selection (refer to Equation 1). Since the CM does not shift his optimal material quality, thus the OEM will always get the same profit. However, 𝐾𝛼 has negative effect on the CM’s profit due to the CM will spend more for material

quality improvement.

As can be seen in Figure 5.12, the result for the impact of 𝛼₀ on the OEM’s profit gap shows the same result as the impact of 𝐾𝛼. It is caused by 𝛼0 has no effect on the CM’s decision regarding

material quality selection (refer to Equation 1). This means, the CM desires the same material quality level regardless of 𝛼0. By having same material quality level for any value of 𝛼0, therefore,

the OEM’s profit gap will never change. However, as the 𝛼0 increase, the CM’s profit will decrease

since he will spend more for the investment cost.

Figure 5.12 The Initial Material Quality Sensitivity Towards the OEM's Profit Gap

In conclusion, the improvement cost and the initial material quality are not sensitive to the OEM’s profit gap. Furthermore, both of them do not motivate the CM to choose a better quality material. On the other hand, the CM’s profit decreases when the improvement cost and initial material quality are increasing.

6. Conclusion

Procurement outsourcing turns out to result on less profit for the OEM. However, there must be a condition when the OEM is obliged to outsource her procurement activities such as to be more focused on her other core competencies, reducing overhead cost, reducing the risk of delivery or reducing the delivery time. In this case, the OEM absolutely has to consider the procurement outsourcing decision. In case when she chooses to outsource her procurement activities, she should be aware of the factors that may affect her profit. By comparing the OEM’s profit under both scenarios and setting the OEM’s profit gap as performance measure, the parameters can be identified whether it has significant effect to the OEM’s profit gap or not. Thus, the first research question regarding the determining the influencing factors of procurement outsourcing decision is

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 0.275 0.3 0.325 0.35 0.375 0.4 0.425 0.45 0.475 0.5 0.52 5 0.55 _0.575 0.6 _0.625 0.65 _0.675 0.7 _0.725 0.75 _0.775 0.8 _0.825 0.85 _0.875 0.9 _0.925 0.95 _0.975 γ 𝛼0

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24 answered. Moreover, there may be a condition which may make the OEM receives less disadvantage from procurement outsourcing scenario. Here, the second research question of when should the OEM outsource her procurement is answered by analyzing the parameters of procurement outsourcing; in what condition procurement outsourcing scenario gives less disadvantage for the OEM.

The models which are used in this paper adopt the procurement outsourcing model by Yang et al, (2016). The basic model by Yang et al, (2016) uses the cost minimization as the objective function and considers bargaining power as the main factor for the procurement outsourcing decision. The profit maximization is used in this paper as the objective function, which makes it different with the model created in Yang et al (2016). Since profit is a function of demand, thus it is necessary for the model to consider the demand which is influenced by the selling price and price sensitivity. Meanwhile, the selling price is determined by the OEM. On the other hand, the CM has to make the decision of material quality selection which will affect the profit for both parties. Therefore, the model becomes more dynamic and interesting since the decision of both parties will affect the profit which will be the consideration in choosing procurement scenario.

The results show that the rework cost, the initial demand, the price sensitivity, the material cost, and the compensation have significant impact on the OEM’s profit gap. Therefore, these parameters are the influencing factors of the procurement outsourcing decision. The rework cost is paid to the party who procures the material. The rework cost makes higher quality material is preferred and this will lead to the decreasing level of quality related cost. In addition, the OEM does not have to bear the rework cost when she outsources her procurement activities. Thus, the OEM will have less disadvantage of the procurement outsourcing scenario when the rework cost is high. However, the sharing of the quality related risk does not have significant to the OEM’s profit gap. The OEM may make the procurement outsourcing decision regardless of the condition when the quality related risk favors the OEM or favors the CM. The initial demand and the price sensitivity influences the demand which directly affects the profit for both parties. Furthermore, the initial demand and price sensitivity has contradicting effect on the demand. Higher demand means more products are produced and sold. Since the selling price must be bigger than production price, then higher demand will result in more profit. Therefore, the OEM may have less loss under procurement outsourcing scenario when the initial demand is high or the product is not price sensitive. The material cost significantly affects the profit for the party who procures the material. Thus, higher material cost will greatly increase the OEM’s profit under procurement outsourcing scenario. Therefore, it may be more beneficial for the OEM to choose procurement outsourcing activities when the material cost is high. On the other hand, the compensation has negative impact on the OEM’s profit. Thus, the compensation should be as low as possible. However, the amount of the compensation may have result in loss for the CM and may make the CM to reject the procurement outsourcing scenario.

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25 choose the same quality material regardless the investment cost. Thus, the OEM’s profit is not influenced by the investment to improve the material quality.

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26

Appendix

Proof of Proposition 1.

The profit of the OEM in in-house procurement scenario can be formulated as: 𝜋_𝑂𝐸𝑀𝐼 (𝑃, 𝛼) = (𝑃 − 𝑐0+ 𝑐0𝛼 − 𝜇𝛼2− 𝜃𝛼2)(𝐷0− 𝛽𝑃) 𝜕𝜋_𝑂𝐸𝑀𝐼 𝜕𝑃 = 𝐷0− 2𝛽𝑃 + 𝛽𝑐0− 𝛽𝑐0𝛼 + 𝛽𝜇𝛼 2_{+ 𝛽𝜃𝛼}2 𝜑 = 𝜇 + 𝜃 𝜕𝜋_𝑂𝐸𝑀𝐼 𝜕𝑃 = 𝐷0− 2𝛽𝑃 + 𝛽𝑐0 − 𝛽𝑐0𝛼 + 𝛽𝜑𝛼 2 𝜕2𝜋_𝑂𝐸𝑀𝐼 𝜕𝑃2 = −2𝛽

Since β is always positive, thus the second derivative function will always be negative which implies that 𝜕

2_𝜋 𝑂𝐸𝑀 𝐼

𝜕𝑃2 is concave in 𝑃 for any given 𝛼.

Proof of Proposition 2.

The profit function for the OEM using the optimal selling price can be formulated as:

𝜋𝑂𝐸𝑀𝐼 (𝑃∗(𝛼), 𝛼) = (( 𝐷0+ 𝛽𝑐0− 𝛽𝑐0𝛼 + (𝜇 + 𝜃)𝛽𝛼2 2𝛽 ) − (𝑐0(1 − 𝛼) − (𝜇𝛼 2_{) − (𝜃𝛼}2_{)) (}1 2(𝐷0− 𝛽𝑐0+ 𝛽𝑐0𝛼 − (𝜇 + 𝜃)𝛽𝛼2)) 𝑑𝜋_𝑂𝐸𝑀𝐼 𝑑𝛼 = 1 2(𝑐0𝐷0− 𝛽𝑐0 2_{+ 𝛽𝑐} 02𝛼 − 𝛽𝑐0𝜑𝛼2) − 𝐷0𝜑𝛼 − 𝛽𝑐0𝜑𝛼 − 𝛽𝑐0𝜑𝛼2+ 𝛽𝜑2𝛼3 𝑑𝜋_𝑂𝐸𝑀𝐼 𝑑𝛼 = ( 𝑐0 2 − 𝜑𝛼) (𝐷0 − 𝛽𝑐0) + 𝛽𝑐₀2𝛼 2 − 3 2𝛽𝑐0𝜑𝛼 2_{+ 𝛽𝜑}2_𝛼3 𝑑2𝜋_𝑂𝐸𝑀𝐼 𝑑𝛼2 = −𝐷0𝜑 + 𝛽𝑐0𝜑 + 𝛽𝑐₀2 2 − 3𝛽𝑐0𝜑𝛼 + 3𝛽𝜑 2_𝛼2

In order to get the maximum profit for the OEM, the profit function must be concave. This condition only happens when 𝑑

2_𝜋 𝑂𝐸𝑀 𝐼

𝑑𝛼2 is negative. Since it cannot be determined whether

𝑑2𝜋𝑂𝐸𝑀𝐼

𝑑𝛼2 is negative or not, thus, the property of this function must be analyzed.

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27 𝑓′′_{(𝛼) = 𝛽6𝜑}2

Since 𝜑 and 𝛽 are always positive, thus 𝑓′′(𝛼) will always be positive. Therefore, 𝑓(𝛼) is a convex function. Furthermore, to determine whether 𝑓(𝛼) is increasing or decreasing convex, the property of 𝑓′(𝛼) must be identified. If 𝑓′_{(𝛼) is always negative for any value of 𝛼, then 𝑓(𝛼) is decreasing}

convex and otherwise if 𝑓′_{(𝛼) is always positive then 𝑓(𝛼) is increasing convex.}

𝑓′_{(0) = −𝛽3𝑐} 0𝜑

𝑓′(1) = 6𝛽𝜑2_{− 3𝛽𝑐} 0𝜑

𝑓′(1) = 3𝛽𝜑(2𝜑 − 𝑐0)

Based on this result, 𝑓′(𝛼) starts from negative value to unidentified value when 3𝛽𝜑(2𝜑 − 𝑐₀). Therefore, the concavity of the OEM’s profit function 𝑓(𝛼) is influenced by (2𝜑 − 𝑐0). There are

two cases when 2𝜑 − 𝑐0 ≤ 0 and 2𝜑 − 𝑐0 > 0 which determine the concavity of the OEM’s profit

function. The condition when 2𝜑 − 𝑐₀ ≤ 0 means that the quality related cost for the OEM – such as brand damage and losing market share – and rework cost combined is less than half of the material cost. In practice, this condition is less likely to happen since the combined quality related cost and rework cost often higher than the material cost. Therefore, it is more interesting to analyze the case when 2𝜑 − 𝑐0 ≥ 0 since it is more practical.

Proof of Proposition 3.

In order to achieve the maximum profit for the OEM, the OEM’s profit function must be concave. The OEM’s profit function is concave when 𝑑2𝜋𝑂𝐸𝑀𝐼

𝑑𝛼2 gives negative value. 𝐿𝑒𝑡 𝑓(𝛼) =𝑑 2_𝜋 𝑂𝐸𝑀𝐼 𝑑𝛼2 , 𝑡ℎ𝑒𝑛 𝑓′(𝛼) = 6𝛽𝜑2_{𝛼 − 3𝛽𝑐} 0𝜑 𝑓′(0) = −3𝛽𝑐0𝜑 𝑓′(1) = 3𝛽𝜑(2𝜑 − 𝑐0) 𝑓′′(𝛼) = 6𝛽𝜑2

Referring to Proposition 2, the concavity of the OEM’s profit function 𝑓(𝛼) is influenced by (2𝜑 − 𝑐₀). Therefore, in case when 2𝜑 > 𝑐₀, 𝑓′_{(𝛼) is negative when 𝛼 = 0 and positive when}

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28 𝑓′_{(𝛼̅) = 0.} 6𝛽𝜑2𝛼̅ − 3𝛽𝑐₀𝜑 = 0. 𝛼̅ = 𝑐0 2𝜑. 𝑓′_{(𝛼̅) < 0.} 𝑓(𝛼̅) = −𝐷₀𝜑 + 𝛽𝑐₀𝜑 +𝛽𝑐0 2 2 − 3𝛽𝑐0𝜑𝛼̅ + 3𝛽𝜑 2_𝛼̅2_. −𝐷0𝜑 + 𝛽𝑐0𝜑 + 𝛽𝑐₀2 2 − 3𝛽𝑐0𝜑𝛼̅ + 3𝛽𝜑 2_𝛼̅2 _{< 0.} 𝛽𝑐₀2 4 < 𝜑(𝐷0− 𝛽𝑐0).

The OEM’s profit function (𝜋_𝑂𝐸𝑀𝐼 _{) is concave when 𝑓′(𝛼̅) < 0 or when}𝛽𝑐02

4 < 𝜑(𝐷0− 𝛽𝑐0). If it

is assumed that 𝑓(𝛼) is negative for any value of 𝛼, then the OEM’s profit function will be concave for any value of 𝛼 which may be the best case scenario. In practice, the OEM’s profit function may have its optimal solution in a certain range of 𝛼. Let 𝛼1 and 𝛼2 as a point where

𝛼₁ < 𝛼̅ < 𝛼₂ and 𝑓(𝛼₁) = 0 and 𝑓(𝛼2) = 0 under the assumption that 𝑓′(0) and 𝑓′(1) are

positive. Since 𝑓(𝛼) is decreasing in interval 0 ≤ 𝛼 < 𝛼̅ and is increasing in interval 𝛼̅ < 𝛼 ≤ 1, therefore, there the OEM’s profit function will be convex for interval 0 ≤ 𝛼 < 𝛼₁ and 𝛼₂ < 𝛼 ≤ 1 while it is concave when 𝛼1 < 𝛼 < 𝛼2. This means that the OEM’s maximum profit lies in

interval 𝛼1 ≤ 𝛼∗≤ 𝛼2 or when 𝛼∗ = 0 or 𝛼∗ = 1. However, the optimal solution is not tolerable

if it is either 0 or 1 since that means the material never produce defective product or always produce defective product. 𝑓(𝛼) = 0. −𝐷0𝜑 + 𝛽𝑐0𝜑 + 𝛽𝑐₀2 2 − 3𝛽𝑐0𝜑𝛼 + 3𝛽𝜑 2_𝛼2 _{= 0.} ∆ = −𝐷₀𝜑 + 𝛽𝑐₀𝜑 +𝛽𝑐0 2 2 . 𝛽3𝜑2_𝛼2 _{− 3𝛽𝑐} 0𝜑𝛼 + ∆= 0. 𝛼1 = 3𝛽𝑐₀𝜑 − √(3𝛽𝑐₀𝜑)2_{− 12𝛽𝜑}2_∆ 6𝛽𝜑2 . 𝛼₂ = 3𝛽𝑐0𝜑 + √(3𝛽𝑐0𝜑) 2_{− 12𝛽𝜑}2_∆ 6𝛽𝜑2 .

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29 (𝑐0 2 − 𝜑𝛼 ∗_{) (𝐷} 0− 𝛽𝑐0) + 𝛽𝑐₀2_𝛼∗ 2 − 3 2𝛽𝑐0𝜑𝛼 ∗2_{+ 𝛽𝜑}2_𝛼∗3 _{= 0.}

The solution is accepted if 𝛼₁ ≤ 𝛼∗ ≤ 𝛼₂.

Proof of Proposition 4.

The CM’s profit and material selection optimization are provided in below calculation: 𝜋_𝐶𝑀𝑆 (𝛼_𝑆) = 𝑊𝐷(𝑃) − 𝑐(𝛼_𝑆)𝐷(𝑃) − 𝑅_𝐶𝑀(𝛼𝑠)𝐷(𝑃) − 𝑟(𝛼𝑠)𝐷(𝑃) − 𝐼. 𝜋_𝐶𝑀𝑆 (𝛼𝑆) = (𝑊 − 𝑐0+ 𝑐0𝛼𝑆− 𝜏𝛼𝑆2− 𝜃𝛼𝑆2)(𝐷0− 𝛽𝑃) − 𝐾𝛼𝑙𝑛 ( 𝛼₀ 𝛼_𝑆). 𝜕𝜋_𝐶𝑀𝑆 𝜕𝛼𝑆 = (𝑐0− 2𝜏𝛼𝑆− 2𝜃𝛼𝑆)(𝐷0− 𝛽𝑃) + 𝐾_𝛼 𝛼𝑆 . 𝜕2𝜋_𝐶𝑀𝑆 𝜕𝛼_𝑆2 = −2(𝜏 + 𝜃)(𝐷0− 𝛽𝑃) − 𝐾𝛼 𝛼_𝑆2.

Since (𝜏 + 𝜃) and demand (𝐷0− 𝛽𝑃) are always positive, thus the second derivative function will

always be negative which implies that 𝜕 2_𝜋

𝐶𝑀 𝑆

𝜕𝛼_𝑆2 is concave in 𝛼𝑆 for any given 𝑃. By having this

condition, the optimal solution of this function will result in maximum value. The optimal material quality for the CM in this scenario will be obtained when:

𝜕𝜋_𝐶𝑀𝑆 𝜕𝛼_𝑆 = 0. (𝑐0− 2𝜏𝛼𝑆− 2𝜃𝛼𝑆)(𝐷0− 𝛽𝑃) + 𝐾_𝛼 𝛼_𝑆 = 0. 𝐿𝑒𝑡 𝐷₀− 𝛽𝑃 = 𝐷 𝑎𝑛𝑑 𝜏 + 𝜃 = 𝜔, 𝑡ℎ𝑢𝑠: 𝛼_𝑆∗ = 𝑐0𝐷 + √𝑐0 2_𝐷2_{+ 8𝜔𝐾} 𝛼𝐷 4𝜔𝐷 𝑜𝑟 𝛼𝑆 ∗ ₌𝑐0𝐷 − √𝑐02𝐷2+ 8𝜔𝐾𝛼𝐷 4𝜔𝐷 . Since √𝑐₀2𝐷2_{+ 8𝜔𝐾} 𝛼𝐷 > 𝑐0𝐷, then 𝛼𝑆∗ = 𝑐0𝐷−√𝑐02𝐷2+8𝜔𝐾𝛼𝐷

4𝜔𝐷 is not tolerable since it will have

𝛼_𝑆 < 0. Thus, 𝛼_𝑆∗= 𝑐0𝐷+√𝑐0

2_𝐷2_+8𝜔𝐾 𝛼𝐷

4𝜔𝐷 will be used as optimal material quality for this scenario.

Proof of Proposition 5.

By using the optimal material quality that is chosen by the CM, the OEM can determine the optimal selling price as follow: