To pool or not to pool: decision making on inventory pooling in science laboratories

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To pool or not to pool:

decision making on inventory pooling

in science laboratories

Master Thesis

MSc Technology and Operations Management

University of Groningen, Faculty of Economics and Business January 2016

Isabella Boscaro

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Abstract

The purpose of this Thesis is to study the opportunity for pooling inventories among science laboratories. In detail, the intent is to find the most desirable inventory pooling policy among decentralization, centralization and lateral transshipment, by taking into account both financial and non-financial criteria and their trade-offs.

This study was realized in the Department of cell biology of the UMCG. The main methodology to conduct the research is represented by the Analytic Hierarchy Process which allows the study of the interactions among criteria and their impact on the entire system and the determination of the preferred alternative (Saaty, 1997). In order to implement the AHP, a series of interviews with the stakeholders were conducted to narrow down the number of the criteria identified through a literature review, from a list of 25 to a shorter list, which include only the most relevant for science laboratories, as suggested by HajShirmohammadi and Wedley (2004). Moreover, an analysis was carried out to assess the performance of the three policies over the identified criteria, to help the decision makers make the pairwise comparisons requested by the AHP.

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Acknowledgements

This Thesis is submitted in fulfillment of the requirements for the degree of Master of Science in Technology and Operations Management at University of Groningen.

This project was undertaken at the Department of cell biology of the UMCG and went to completion in five months, from September 2015 to January 2016.

My deepest gratitude goes to the Head of the Department, Prof. Dr. Harrie Kampinga, for giving me the opportunity to investigate the inventory management in his laboratories and for being always available during the conduct of my research. This Thesis would not exist if it were not for him. I extend my appreciation to the Principal Investigators, the Technicians and the Managing Director Assistant who participated in this study. I thank them for their cooperation, the stimulating discussions, their inspiring ideas and their infinite patience. I could not be more grateful for the priceless help they all provided. My sincere gratitude to my first supervisor, Dr. van Foreest, and my co-assessor, Dr. Fazi, for their guidance and precious feedback. I truly enjoyed our meetings and I am pleased I got the chance of working with them.

Finally, my beloved husband deserves my most heartfelt thanks. He relentlessly supported me during this Master Programme. His love, assistance and neverending encouragement gave me the strength to accomplish this challenge. Without him, I never would have made it.

January, 2016

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Out beyond ideas of wrongdoing and rightdoing there is a field. I’ll meet you there.

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1. Introduction

In the last years, the natural science research in European Universities has faced a significant budget cut. It is increasingly difficult to obtain funds from the governments and it is not uncommon for crucial research to be put on hold. Due to the need to provide results with fewer resources, it has become mandatory for science laboratories to reduce their expenditures without hurting the quality of their research. One of the quality management instruments used by laboratories is represented by the Good Laboratory Practices (GLPs), a series of suggestions proposed by the World Health Organization to ensure the uniformity, consistency, replicability, quality and integrity of the results of laboratories’ research. A proper inventory management can contribute in the achievement of these goals since it relates to the choice, availability and quality level maintenance of the material adopted, factors that are fundamental to perform research as advised by the GLPs.

In an attempt to cut the inventory costs while maintaining the GLPs, the Department of cell biology at the University Medical Center of Groningen (UMCG) is considering the adoption of an inventory pooling policy among the different science laboratories, for the chemicals and life science reagents whose costs are rising every year. Currently, each of the three floors of laboratories of the Department holds its own inventory and, since commonalities exist in the use of these materials, there may be some potential for cost reduction by implementing an inventory pooling policy.

Inventory pooling is a form of risk pooling applied in the context of inventory management and it was introduced by Eppen in 1979. In an inventory pooling scenario, different agents decide to centralize their inventories into a single location, from which they can source the items they need (Hartman and Dror, 2003; Benjaafar et al., 2005; Berman et al., 2011). The agents may also decide not to consolidate their inventories but to allow movements of stocks among them, in case of need. This particular policy is called lateral transshipment.

Inventory pooling has been abundantly studied in the literature and there is almost unanimity in deeming this type of inventory control effective at reducing costs within an organization in many cases (Cai and Du, 2009).

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2 Moreover, it is necessary to consider the trade-offs among the criteria: in effect, each policy performs well on some criteria and worse on others. It is, hence, difficult to decide which policy is the best as its appropriateness depends on the different importance that is assigned to the different criteria.

The main purpose of this research is to answer the following research question:

What is the most desirable inventory pooling policy in the cell biology Department for the chemicals and life science reagents,

considering the trade-offs among both financial and non-financial criteria? In order to answer this question, it is necessary to address the following sub-questions:

S.Q. 1 What are the financial and non-financial criteria to be considered in inventory pooling decisions for the chemicals and life science reagents, in case of science laboratories?

S.Q. 2 How do the alternative inventory pooling policies perform according to the criteria? S.Q. 3 How are the criteria ranked in terms of importance?

These issues have not been investigated by the current academic literature, to the author’s best knowledge. This Thesis attempts to reduce this gap by analysing the case of the Department of cell biology at the UMCG.

The answers to the stated questions could help managers of science laboratories find the most suitable inventory policy and increase the knowledge of both academics and practitioners over the criteria that should be considered when taking decisions about inventory pooling, in the case of science laboratories. This Thesis addressed S.Q. 1 through the execution of a series of interviews with the stakeholders to identify the most important criteria to be considered in the decision making on inventory pooling in science laboratory. Then, different inventory pooling policies were assessed in relation to the criteria identified through the interviews, to answer S.Q. 2.

The results of this research were used to apply the Analytic Hierarchy Process (AHP), an instrument widely used in multi criteria decision making (MCDM) because of its ability to consider trade-offs among multiple criteria, both financial and non-financial (Rangone, 1996). The AHP’s purpose is twofold: to study the functional interactions of these criteria and their impact on the entire system and to respond to the question of what is preferred among alternatives (Saaty, 1997). Therefore, it was adopted to answer S.Q. 3 and, finally, the main research question.

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2. Theoretical background

In this section the concepts of inventory and the three main inventory pooling policies, namely inventory decentralization, centralization and lateral transshipment, are presented, together with a literature review realized to highlight the benefits and drawbacks of these policies. Following, a discussion about the criteria and trade-offs that have to be considered in decision making about inventory pooling is proposed.

2.1 Inventory theory

Inventory plays a central role in operations management. Although for the popular “Just-in-Time” concept inventory is deemed a waste, it is actually a fundamental need in every company, as it allows performing the activities required by the specific nature of the business.

Nevertheless, many trade-offs have to be considered in inventory management: reducing inventory levels leads to a reduction of holding costs, namely the opportunity cost for the capital linked to the inventory and the costs related to the material handling, storage, damage and obsolescence, insurance, and taxes (Axsäter, 2015) that are variable with the stock level. However, a too low level of stock may increase the stock-out costs because it fails to protect from variability in demand and in lead times. Holding little inventory may also increase the ordering and transportation costs, as smaller quantities have to be purchased more often than larger amounts, and may prevent gaining from quantity discounts.

A proper inventory management is, hence, necessary to maintain a balance between the need of carrying stocks and of keeping costs down. This goal can be achieved through the implementation of an inventory pooling policy.

Three main scenarios can be considered when making a decision on whether to adopt an inventory pooling policy: decentralized inventory, centralized inventory and lateral transshipment.

2.1.1 Characteristics of decentralized inventories

An inventory is decentralized when a unit of an organization administrates its own inventory without any interaction with the inventories of the other units of the same organization.

In decentralized inventory scenarios, an independent decision maker manages all the decisions that involve the inventory management, including procurement. All considerations about what to buy, when to buy, in what quantity, the stock level to keep, are made at local level.

The main objective of the decision makers in such contexts is to minimize their own cost functions by selecting their individual inventory policies and base stock level (Netessine and Rudi, 2003; Jemai and Karaesmen, 2007) and the action of the single actor have no effect on the actions of the other actors in the same organization (Zhao et al., 2006).

The demand is also satisfied only by the individual unit. In case of out-of-stock, the unit has usually two options: backlog the demand, which means that the customer is put on hold and has to wait until company’s stock is restored, or lose the sale, which means that customers will refer to another company to have their demand satisfied.

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4 inventory and there is no interaction among them. In the case of the Department, when the demand is not satisfied because of an out-of-stock, it can only be backlogged since the users are not allowed to refer to other units to obtain the desired items.

Supplier Individual unit

Individual unit Individual unit

Flow of Material

Figure 1 Decentralized Inventory

2.1.2 Characteristics of centralized inventories

In a centralized inventory scenario, different agents decide to consolidate their inventories into a single location, from which they can source the items they need (Hartman and Dror, 2003; Benjaafar et al., 2005; Berman et al., 2011).

When holding a centralized or consolidated inventory, an organization decides to delegate the activities related to the inventory management to a central structure. This structure will be responsible for the purchasing of the material from the supplier for all organization’s units and for the control of the stock. Differently from the decentralized system scenario, the decision maker in a centralized environment has as a main goal the minimization of the inventory-related costs of the entire organization instead of the minimization of the costs of the single unit.

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Supplier Central Inventory Individual unit

Flow of Material

Figure 2 Centralized Inventory

2.1.3 Characteristics of lateral transshipment

Lateral transshipment is a form of inventory pooling. According to the definition by Paterson et al. (2011), lateral transshipment consists in “stock movements between locations of the same echelon”. Lateral transshipment differs from inventory centralization as there is no inventory consolidation among the locations. Every location holds its own inventory in its own warehouse/stock point instead of allocating it into a common environment. It differs from inventory decentralization as movements of stocks are allowed from one inventory to another.

In traditional supply chains, usually, products flow hierarchically from an echelon to the next, from the raw material supplier to the end consumer. Lateral transshipment, as illustrated in figure 3, allows products to be transferred also within the same echelon, like, for instance, from retailer to retailer (Paterson et al., 2011).

This transfer can occur when one unit is in an out-of-stock situation and asks to be replenished by another unit and it is known as reactive transshipment.

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Supplier Individual unit

Flow of Material

Figure 3 Lateral Transshipment

2.2 Centralization versus decentralization: a comparison of inventory pooling policies

The literature about the different performance of inventory decentralization, centralization and lateral transshipment is vast and often oriented to compare these policies on their ability to reduce inventory costs, stock levels and lead times. This section proposes an overview of the main articles in the field. A large part of the academic literature about inventory pooling is based on the seminal article by Eppen (1979). He demonstrates that inventory holding costs and stock-out costs are higher in a decentralized system than in a centralized one. Moreover, he proves that the correlation of the demands at the individual locations affects negatively the magnitude of the savings obtained by the introduction of a centralized system and that costs increase as the square root of the number of locations.

Stulman (1987) finds that the relative benefits of a centralized system compared to a decentralized one increase with the number of locations and with the increase of the probability of a stock-out at an i location. Zinn et al. (1989) demonstrates the superiority of centralization systems over decentralization also on the reduction of the aggregate safety stock level.

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7 Transportation costs has also been considered by Evers (1997), who concludes that decentralization leads to minor transportation costs than lateral transshipments; by Das and Tyagi (1997), according to whom greater centralization decreases safety stocks but increases transportation costs and that the trade-off on whether to centralize or decentralize is based on inventory costs versus transportation costs; and by Wanke (2009), who states that distribution costs are higher in centralized scenarios than in decentralized. Evers (1999) claims that lateral transshipment has also a lead time pooling effect, as late arriving orders at one location can be compensated by an early arriving order at another location. This type of benefit cannot be accomplished by centralization nor decentralization policies.

Wanke and Saliby (2009), studying whether or not centralize inventories, compare different policies according to their contribution to reduce inventory holding costs and transportation costs and to increase service level. They find that transportation costs under a centralization policy are higher than in case of lateral transshipments, which in turn are higher than under decentralization policies. Inventory holding costs are instead lower in case of centralization and higher in case of decentralization. Finally, fill rate levels are better when lateral transshipment is allowed and worse in centralized systems.

Herer et al. (2002) also claim that the cost reduction in the total system costs derived from lateral transshipments also occurs because of the reduction in procurement costs.

2.3 Criteria for decision making on inventory pooling

All the above mentioned articles have the merit of offering significant insights of the advantages and disadvantages of the different policies for inventory pooling and of the trade-offs that occur, but they focus on a limited amount of factors, mostly of financial nature.

According to Merchant and Van der Stede (2012), this type of financial measures is widely used by companies because of their being timely, precise and objective. Moreover, their popularity is also due to their understandability, as most of the managers are familiar with these concepts, and because they represent an easy and inexpensive way to assess performance. However, a decision making process based on only financial measures has many pitfalls. First of all, they ignore the non-financial aspects of performance that are often critical aspects for the success of a project (Saleh et al., 2001). Moreover, they are not reliable indicators of future performance as they focus on the past, as opposed to non-financial measures (Merchant and Van der Stede, 2012). Accounting performance measures can cause investment myopia: short-term measures induce decision makers to reduce or not make investments because they cannot recognize possible long term benefits that derive from intangible assets (Merchant and Van der Stede, 2012).

It is, hence, very simplistic to think that a decision on whether to adopt an inventory pooling policy and which one to select can be made by considering only these terms. This is especially true in the case of non-profit organizations, like science laboratories, whose goals are many and the assessment of the goodness of a policy cannot be limited to few financial measurements.

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8 issue in non-profit organizations are different than those that are involved in for-profit environments, or at least have a different strength.

According to the literature, there are many criteria that can be identified when making a decision on whether or not to pool inventories. A research executed by the author lead to the collection of 25 criteria, both financial and non-financial. This list is by no means exhaustive but it has the merit of gathering the most frequent criteria that can be found in literature and practice.

Table 1 summarizes the findings and illustrates the trade-offs that have to be made in the decision making on inventory pooling. For each criterion, the three previously identified inventory pooling policies are rated on a scale from 1 to 3 according to their ability to positively influence the criterion, according to academic research and practice general findings. The best performing alternative is rated with 1, while the worst is rated with 3. This scale does not represent the magnitude of influence but only which alternative is recognized to perform better in most cases.

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9 Table 1 Criteria for inventory pooling decision making and performance of the alternatives

Criterion Definition Decentralization Centralization Transshipment

Financial Criteria

Holding costs 1,2 _{The opportunity cost for the capital linked to the inventory and the costs}

related to the material handling, storage, damage and obsolescence, insurance, and taxes (Axsäter, 2015) that are variable with the stock level.

3 1 2

Lost sales costs 1 _{The cost the organization bears when it is not able to fulfil the end user’s}

request

2 3 1

Transportation costs 2 _{The cost of the delivery from the supplier to the company, excluded the}

cost of the item delivered

1 3 2

Financial resources 1 _{The amount of financial resources that are necessary to modify the}

arrangement of the organization from a situation of decentralization

1 3 2

Purchasing 3 _{The ability to obtain quantity discounts from the supplier} ₃ ₁ ₂

Non-financial Criteria

Inventory level 1 _{The amount of stock that is available in the organization at a certain}

time

3 1 2

Delivery precision 1 _{The degree to which the delivery to the final user is carried out correctly 2} ₁ ₂

Number of employees 1

The number of employees who are necessary to perform the inventory related activities

2 1 2

Peaks of demand

balance 1

The degree to which the different demands patterns of each unit of the organization compensate each other

3 1 2

Delivery time The amount of time needed to the final user to obtain the desired item

from the inventory when the item is in stock

2 3 1

Service level 2 _{The percentage of time the final user finds the desired item in stock} ₂ ₃ ₁

Competences 1 _{The level of ability to perform the inventory activities} ₂ ₁ ₂

Rearrangement need 1_{The degree to which it is necessary to modify the physical arrangement}

of the organization from a situation of decentralization

1 3 2

Managerial resources 1

The number of managers that are necessary to modify the arrangement of the organization from a situation of decentralization

1 3 2

Level of information

detail 4

The degree to which the person who is in charge of the inventory activities has intimate knowledge of the behaviour of the environment of a unit in the organization

1 3 2

Ownership 5 _{The degree to which the person who is in charge of the inventory}

activities feels responsible for the proper performance of those activities

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Coordination 5 _{The degree to which coordination among the different units of an}

organization is necessary to perform the inventory activities

1 3 2

Bureaucracy 6 _{The amount of administrative activities necessary to perform the}

inventory activities

1 3 2

Complexity of the IS 6 _{The degree of complexity of the Information System to manage the}

inventory activities.

1 3 2

Information secrecy The degree to which the information about the activities of a unit are

shared with the other units

1 3 2

Risk of losing the

stock 7

The degree to which the organization risks to lose all the stock because of a natural disasters or other calamities

2 3 1

Alignment to

company’s strategy 7

The degree to which the decisions taken by the person who is in charge of the inventory activities follow the overall strategy of the organization

2 1 2

Material handling 8 _{The amount of time and resources needed to handle the deliveries from}

the suppliers

2 1 3

Stock deterioration 8 _{The level of risk that the stock will perish before it is used} ₃ ₁ ₂

Cost allocation The ease of allocating the costs of the items used by each unit to the

correct unit

1 3 2

________________________ 1 _{Pedersen et al. (2012)} 2 _{Wanke and Saliby (2009)} 3 _{Munson and Hu (2010)} 4 _{Lee and Whang (1999)}

5 _Fallon_{http://www.evansincorporated.com/centralizing-and-decentralizing/}_{Last access [Jan. 8th 2016]} 6 _{Andersson and Marklund (2000)}

7 _{Halliday (2014)}

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3. Methodology

In this section, a scenario description is provided and the methodology adopted to answer the research question and sub-questions is discussed.

In order to supplement the economic appraisal methods in decision making, many authors (e.g. Kumar et al., 1996; Chan et al., 2001) suggest the use of techniques that include also non-financial criteria.

This approach is at the base of the studies over the Multi Criteria Decision Making (MCDM), which is the process through which a person or a group, the decision maker(s), selects the solution that better fits certain requirements, values and/or preferences, among alternatives. These requirements are called criteria and can be in conflict among with other. When none of the alternatives is able to fulfil all the criteria, which is often the case, it is necessary to perform trade-offs, which is considered one of the most challenging activities in decision making (Hammond et al., 1998).

MCDM has been studied across the most disparate disciplines and many tools have been developed for assisting the decision maker in this strenuous process. Among these tools, the Analytic Hierarchy Process (AHP) is one of the most popular and it is often suggested for investments appraisal (e.g. Archer and Ghasemzadeh, 1999; Chan et al., 2001), especially by virtue of its ability to include trade-offs among criteria, both financial and non-financial (Rangone, 1996).

Despite the extensive existent literature in the field of AHP, very few research has been conducted on inventory management or centralization issues: in the inventory management area, Korpela and Tuominen (1996) study the warehousing site selection process; Korpela and Tuominen (1997) apply AHP in inventory forecasting; Cakir and Canbolat (2008) create a web based decision support system for inventory classification; Naesens et al. (2007) use the AHP to assess the strategic compatibility between two potential partners for inventory pooling; while Wong (2010) presents the AHP as a tool for inventory management but with no focus on centralization. Centralization has been studied by Karger and Hennings (2009) in the field of electricity generation and by HajShirmohammadi and Wedley (2004) in maintenance management.

In none of these cases the special situation of non-profit organizations has been taken into account. The AHP is used in this Thesis in the context of the Department of cell biology of the UMCG to investigate the opportunity to adopt an inventory pooling policy.

3.1 Scenario description

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12 Nine groups, which are coordinated by the Head of the Department (HoD), Harrie Kampinga, work in the Department. Each group is responsibility of a Principal Investigator (PI) who receives grants to buy equipment and material for the research they are pursuing. The groups are formed by a variable amount of Post-Doc researchers, PhD, Master and Bachelor students and technicians. There is also administrative staff, such as the general manager and his assistant, who takes care of the administrative and financial issues of the Department, and the secretary. At present, the whole Department counts approximately eighty employees.

Currently, mainly four technicians are responsible for the inventory management which includes, but is not limited to, the purchasing of products, the negotiation of prices with the suppliers, the handling of the deliveries, the control of stocking levels and the proper storing. The single researchers (PIs, PhD students, graduate and undergraduate students) are also, although for limited activities, responsible for the correct maintenance of the inventory. They are in charge of checking the inventory level, of warning the technicians that an item is missing or about to miss and are responsible for storing the items in the correct stock point. All these tasks are performed independently by each floor, with almost no interaction among them and no standardization of inventory procedures.

The stock that is held on one floor is its exclusive property. Sometimes one group’s material can be also used by the researchers of another group on the same floor but it is very rare that it is shared with other floors.

3.2 The Analytic Hierarchy Process (AHP)

The AHP is a quantitative technique that is able to capture different kinds of information and consider uncertainty, multiple factors and subjective judgments; these characteristics make it a tool that can provide managers with a more realistic reflection of the environment (Meredith and Suresh, 1986). The AHP was introduced in 1980 by Saaty to reduce “the study of intricate systems to a sequence of pairwise comparisons of properly identified components”. It is based on the concept of hierarchy, defined as a model or abstraction of a real life system that includes its most important elements and their relationships. A hierarchy is formed by different levels, with at the top the goal that has to be achieved and at the lower levels the elements that can influence the factors belonging to the next higher level. Purpose of the AHP is to study the functional interactions of these factors and their impact on the entire system. In detail, the aim is to understand which of the factors of the lower levels has the highest importance on the next higher level factors and how strong this importance is.

Since “its thrust is to tell how things are rather than to prescribe how they should be”, “the AHP is intended to be a descriptive theory” (Saaty, 1997) as its results “will typically identify components, patterns, systems and structures” (Karlsson, 2009). Moreover the AHP is commonly used as a guide in decision making for its ability to provide a ranking among alternative solutions to a problem.

The AHP proposes a way for ranking and weighting based on pairwise comparison of the factors within and across the different levels of the hierarchy. The decision maker is asked to compare two of the factors with each other according to their importance in achieving the factor of the next higher level. This process has to be repeated for every pair of factors.

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13 1. Identify the most relevant criteria for decision making in inventory pooling.

2. Structure a hierarchy of different levels constituting goal, stakeholders, criteria and alternatives. 3. Compare each element in the corresponding level and calibrate them on the following numerical scale

(Saaty, 1980). Intensity of

importance

Definition Explanation

1 Equal importance Two activities contribute equally to the objective

3 Weak importance of one over another Experience and judgment slightly favour one activity over another

5 Essential or strong importance Experience and judgment strongly favour one activity over another

7 Very strong or demonstrated importance An activity is favoured very strongly over another; its dominance demonstrated in practice

9 Absolute importance The evidence favouring one activity over another is of the highest possible order of affirmation

2,4,6,8 Intermediate values between adjacent scale

values

When compromise is needed

Reciprocal of above non-zero

If activity i has one of the above non-zero numbers assigned to it when compared with activity j, than j has the reciprocal value when compared with i.

4. Calculate the maximum Eigen value, consistency index (C.I.), consistency ratio (C.R.), and normalized values for each criterion/alternative.

5. If the C.R. is satisfactory (C.R. < 0.1), the decision is taken based on the normalized values; otherwise the procedure is repeated.

For a more in-depth explanation of the AHP, please refer to Appendix I. 3.2.1 Interviews for criteria selection

The first stage of the AHP was performed through a series of interviews to the stakeholders in order to narrow down the number of the criteria for inventory pooling, from a list of 25 (see section 2.3) to a maximum of 9, as suggested by HajShirmohammadi and Wedley (2004).

The stakeholders were identified in the Head of the Department (HoD), who is responsible for the research and the activities of the Department; the Assistant of the Managing Director (AMD) who is in charge of the ongoing administrative and financial issues of the Department; the PIs, who run their own groups financially; the technicians, who are responsible for the logistics and the general administrative tasks of the Department. Three PIs and three technicians have been selected as representatives of their category. Individual interviews were performed for two purposes:

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14 each interviewee. This step is of paramount importance since the stakeholders must be familiar with the subject to make informed decisions (Gubrium and Holstein, 2002).

2. Obtain stakeholders’ selection of the criteria they would consider when making decisions on inventory pooling.

An interview protocol was used to assist the interviewer in collecting information and contained a script, a visual illustration of the policies and a questionnaire (see Appendix II). The protocol was developed following the guidelines offered by Karlsson (2009) and de Leeuw et al. (2008) and was examined by fellow Master’s students and a PhD student for feedback on clarity, wording and pre-testing.

The interview consisted in two parts: in the first part, the policies were discussed with the interviewee with the support of a visual illustration to improve the understanding of the topic. In the second, the participant’s opinion about the criteria was gathered through the use of a nominal scale, namely a multiple choice items technique (Karlsson, 2009). The participant was asked to select at most 9 criteria that he/she would consider when deciding about inventory among the 25 identified.

Once the answers to the questionnaires were gathered, a weight was given to the participants’ answers, according to the strength of their influence in the decision making process. The validity of these weights was discussed with and approved by the AMD.

The opinions of the HoD were given a weight of 0.20 since he is in charge of the Department in its whole and therefore his opinion has a high degree of importance. The opinion of the AMD obtained a weight of 0.15 since he is the most knowledgeable person about the administrative tasks in the whole Department. The opinion of the PI’s was given an overall weight of 0.35 since they are the holders of the grants with which inventory items are bought and, therefore, they have great influence of inventory administration. The opinion of the technicians was given an overall weight of 0.30 since they are those who practically manage the inventory; therefore, their opinion is highly valuable when considering modification in the inventory management.

The results from this step were used to perform the AHP and to answer to SQ 1.

3.2.2 Questionnaire for the ranking of the criteria

A questionnaire was sent via email to all the stakeholders previously involved in the interview phase to collect their pairwise comparisons of criteria identified in the previous step. The questionnaire was built following the example by Sahin et al. (2013) with instructions for filling it (see Appendix III). The stakeholders were asked to compare criteria according to a scale of importance from 1 to 9, when 1 represents equal importance and 9 represents the highest level of importance of one criterion against the other.

3.2.3 Analysis for inventory pooling policies appraisal

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15 This analysis was necessary to make the pairwise comparisons required in the third step of the AHP. In effect, it provided knowledge on the performance of the three alternatives and information to use when judging the strength of the alternatives in relation to certain criteria.

3.2.4 Performance of the AHP calculations

The data obtained from the previous steps were used to perform the AHP. The software “Super Decisions” was adopted to facilitate the calculations of the priorities and to perform the sensitivity analysis. This software has been chosen since it was freely available and developed by Saaty’s team, which guarantees the goodness of the results from the computer program. This instrument helped with the computation of the C.R. and the normalized values for each criterion and alternative.

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4. Results

4.1 Results from the interviews for criteria selection

The interviews illustrated in section 3.2.1 lead to the narrowing down of the criteria for inventory pooling from the list of 25 criteria to only 6, which were judged the most important by the stakeholders. These criteria, in effect, have all a weight higher than 0.5 which means that they were deemed important by the majority (in terms of influence in the decision making) of the stakeholders. The identified criteria, not ranked by importance, are: bureaucracy, holding costs, ownership, transportation costs, purchasing and service level (Table 2).

Table 2 Results from the interviews for criteria selection

Criteria Weight Bureaucracy 1,00 Service level 0,77 Purchasing 0,73 Ownership 0,58 Holding costs 0,57 Transportation costs 0,55 Delivery precision 0,47 Delivery time 0,47 Cost allocation 0,43 Information secrecy 0,30 Coordination 0,27 Complexity of the IS 0,22 Stock deterioration 0,22 Financial resources 0,15

Peak of demand balance 0,12

Competences 0,12

Level of information detail 0,12 Risk of losing the stock 0,12

Lost sales costs 0,00

Inventory level1 _0,00

Number of employees 0,00

Rearrangement need 0,00

Managerial resources 0,00

Material Handling 0,00

Alignment to company's strategy 0,00

1

1_{The criteria “inventory level” has been discharged in the final data analysis since its definition were deemed not}

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17 With the results from the interviews, it was possible to build the final hierarchy that was used in the AHP and that is illustrated in figure 4.

Most desirable inventory pooling policy

AMD PI 1

Bureaucracy Service Level Purchasing

Goal

Stakeholders

Criteria

PI 2 PI 3 Tech 1 Tech 2 Tech 3

Transp. costs Ownership

Decentralization Centralization Lateral transshipment

Alternatives

HoD

Holding costs

Figure 4 Hierarchy applied in the AHP

The first level is represented by the goal, which is to decide which alternative inventory pooling policy is the most desirable for the Department.

The second level is formed by the stakeholders that have been interviewed and who filled the questionnaires. The same weights applied for the criteria selection (see section 3.2.1) were assigned to the stakeholders, according to their importance to achieve the main goal.

The third level is represented by the criteria that are considered when a decision about inventory pooling has to be taken in the Department.

Finally, the fourth level is represented by the alternatives among which a choice has to be made: decentralization, centralization and lateral transshipment.

4.2 Results from the analysis for inventory pooling policies appraisal

This section illustrates the performance of each alternative in relation with the six criteria that resulted from the interviews, namely, bureaucracy, service level, ownership, purchasing, transportation costs and holding costs. The performances were estimated through a literature review and brainstorming sessions with the stakeholders.

4.2.1 Bureaucracy

This Thesis defines “Bureaucracy” as the amount of administrative tasks performed for the inventory activities. These activities include, but are not limited to, products purchasing products, prices negotiation with suppliers, deliveries handling, control of stocking levels and proper storage and are performed mainly by four technicians and, with a smaller extent, by researchers.

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18 applicable to the UMCG or to the technician who placed the order. It may happen, in effect, that the single technician negotiates special prices directly with the suppliers, which are applicable only to his/her orders. The products are delivered to the single floors and their handling is responsibility of the technician. The order is then noted as arrived and the researcher is informed.

The cost of the product is directly allocated on the account of the researcher, or of the group the researcher is part of. The control of the stocking level is up to the single researcher, as well as the correct storage of the products.

According to literature, centralization increases bureaucracy due to the increased number of hierarchy levels. However, it is believed that this would not be the case at the Department. All the above mentioned tasks would be centralized and become responsibility of one single person for the whole Department. Centralization would, therefore, lead to a decrease of the overall amount of activities, since only one person would be in charge of them, avoiding duplication and overlapping of tasks.

The inventory activities performed by the researchers would be limited to the ordering of those products whose demand is discontinuous and for which inventory is not held. Centralization would, consequently, lead to a decrease of administration tasks and researchers would be able to pay more attention to science activities and avoid worrying about inventory control. The inventory levels and the correct storage of the items would be managed by one person in charge, relieving others from this burden.

There is, however, an additional task that would be performed in case of centralization, compared to decentralization, which is the cost allocation of the item to the user. In effect, every time an item is used, its consumption has to be tracked to allow allocating the cost of the item to the person or group who used it. Consumption tracking is not performed in the current situation as every group owns its inventory and is charged with its cost at the moment of the order.

Despite this additional activity, all in all, it is possible to state that centralization performs strongly better that decentralization in relation with bureaucracy, since centralization helps avoid duplication and overlapping of activities, reducing the total amount of bureaucracy at Department level. From the four technicians who currently perform the same activities, only one would remain in charge of the inventory for the whole Department. The amount of inventory-related administrative activities would decrease by 75% in the whole Department, without considering the reduction of the tasks performed by the researchers.

In lateral transshipment, inventory management would still be responsibility of all technicians and researchers, in the same fashion as in decentralization. However, some additional inventory related activities would have to be completed. First of all, every time an order had to be placed, it would first be necessary to verify whether that product is already on stock on another floor. This is a supplementary task compared to decentralization where, when an item is needed, an order is placed immediately. Moreover, it would be necessary to contact that floor to ask for permission to take the item, go to retrieve it and finally, withdraw the cost of the item from the account of the previous owner to the account of the new user.

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19 The results of this analysis are summarized in table 3.

Table 3 Performance of inventory pooling policies over the criterion Bureaucracy

Bureaucracy Centr. Decentr. Lat. Trans. Weight Rank

Centralization 1 5 7 0,7306 1

Decentralization 1/5 1 3 0,1884 2

Lateral Trans. 1/7 1/3 1 0,0810 3

4.2.2 Service level

To make the analysis for the criterion “Service level” it is first necessary to establish the service level that the laboratory requires. Not all the items are equal in relation to the availability that is necessary to achieve: some products demand a service level of 100% and stock-outs are not allowed; these items must always be available as their absence would cause great damage to the laboratory science activities. One of these products is the DMED, a medium for cell culture. If the laboratory ran out of this product, the cell cultures would die, forcing the researchers to discard all experiment material and start their research from the beginning, with a consequent waste of time and money. According to Ballou and Burneats (2003), in the case of these products, it is unimportant which kind of inventory pooling policy to apply. Indeed, the inventory levels must be planned so that demand is always satisfied regardless to whether the inventory is centralized or decentralized.

However, in case of stock-outs caused by unpredictable late delivery or other accidents, lateral transshipment could reveal beneficial: the location in out-of-stock can ask another location to fulfil its needs. This advantage is not present in neither centralized nor decentralized inventories since, when a stock-out occurs, the demand simply cannot be filled (Evers, 1997). In the case of the Department, however, this unfavourable situation could be buffered by controlling the demand: when a situation of out-of-stock is likely to occur, it is still possible, within some limits, to ask researchers not to start new experiments until the normal situation is restored. Consequently, the benefits of lateral transshipment compared to decentralization and centralization still exist, even if with a limited extent.

Concluding, for those items whose 100% service level is a must, inventory decentralization and centralization perform equally in “service level”, while lateral transshipment gives some little advantage over the others.

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20 It still remains uncertain if either centralization or lateral transshipment performs better than the other. According to Evers (1997) lateral transshipment helps gain a better service level because of lead time pooling. But in centralization, items are available to everyone and there is no need to ask for the permission to take a product, as occurs in lateral transshipment. Given these considerations we can conclude that lateral transshipment and centralization perform equally in service level and both better than decentralization.

In summary, for the products that require 100% service level, all policies are equal with only lateral transshipment performing very slightly better than the others. For the other items, lateral transshipment and centralization perform equally well in service level increasingly outperforming decentralization according to the product variability of demand (the higher the variability, the higher the risk pooling effect and the service level).

The results are summarized in table 4.

Table 4 Performance of inventory pooling policies over the criterion Service Level

Service Level Centr. Decentr. Lat. Trans. Weight Rank

Centralization 1 5 1/2 0,3420 2

Decentralization 1/5 1 1/6 0,0811 3

Lateral Trans. 2 6 1 0,5769 1

4.2.3 Ownership

In this Thesis “Ownership” is defined as the degree to which the person who is in charge of the inventory activities feels responsible for the proper execution of these activities.

It has been widely recognized by the literature (see e.g. Merchant and Van der Stede, 2012; Sople, 2012) that decentralization has a larger effect on employees’ sense of ownership because it provides them with higher responsibility for the correct execution of the activities they are entrusted with. Employees feel part of the company and highly motivated to perform at their best, leading to higher quality of their work (Malone, 1997). According to Fayol’s principles of management, decentralization “increases the importance of the subordinate’s role” (Wood and Wood, 2002).

In the Department, current decentralization is optimal for fostering ownership in the vast majority of laboratory members. Both technicians and researchers feel that their contribution is important to maintain the desired inventory level and avoid stock-outs, and participate in the proper maintenance of inventory. They are aware that they are responsible for the inventory-related activities and strive to guarantee the smooth running of everyday work.

This sense of ownership, or empowerment, is not easily achievable with inventory centralization. Indeed, if all the responsibility for inventory management is given to a single person for the entire Department at a higher hierarchical level, the other employees may feel that their contribution is neither important nor necessary.

Moreover, the inventory would not be owned by any of the floors as it is now, but it would be property of the entire Department. A “non-of-my-business” attitude may occur, leading to sloppiness or lassitude and consequent increased difficulty in proper inventory management.

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21 However, the difference in the sense of ownership in case of decentralization and lateral transshipment is limited because the property of and the responsibility for the inventory would still be maintained at local level.

Table 5 summarizes the results.

Table 5 Performance of inventory pooling policies over the criterion Ownership

Ownership Centr. Decentr. Lat. Trans. Weight Rank

Centralization 1 1/6 1/4 0,0890 3

Decentralization 6 1 2 0,5876 1

Lateral Trans. 4 1/2 1 0,3234 2

4.2.4 Purchasing

The criterion “Purchasing” is defined in this Thesis as the ability to obtain quantity discounts.

According to the literature, centralization is always effective in gaining lower prices from quantity discounts since the amount of product per order is higher than in decentralization. For instance, Karjalainen (2011) states that the centralization of the purchasing activities, which is implicit in inventory centralization, is beneficial, as it leads to lower prices and economies of processes. Significant volume discounts can be achieved even with the centralization of few locations.

Virtually all main chemical suppliers of the Department, such as Sigma-Aldrich, Thermo Fisher or NEB, offer discounts when larger quantities of a product are bought. One instance is the Fibroblast Growth Factor-basic or FGF Factor-basic, abundantly used in cell and tissue culture laboratories: buying the 1 mg package of product instead of 50 μg helps gain 80% of discount. Another example is the Hepatocyte growth factor or HGF: buying larger quantities helps gain from 52 to 76% on the cost per μg. This is only a small example of the impact that centralization can have on the ability of obtaining quantity discounts since this reasoning is valid for most items, with obvious differences among products and brands.

Centralization also helps acquire stronger negotiation power, fundamental to obtain additional discount. Besides, centralization offers the chance to standardize the used products: for instance, currently every floor uses different brands and qualities of DMEM (medium for cell culture), DNA polymerase and reverse transcriptase kits (enzymes for molecular biology) and ethanol. Centralization would help reasoning about the real need to adopt different brands and/or qualities for these products. In case the differences are not justified by any real scientific need or research purpose, one single brand and/or quality can be adopted by the whole Department, increasing even further the ability to obtain discounts and negotiation power. In decentralization, quantity discounts can be realized only by the floor that uses a specific item the most, or not be achieved at all. The single floors buy only the quantities that are strictly necessary to satisfy their immediate demand and their orders are significantly smaller than those that would have been placed in case of centralization.

Negotiation power is lower than in centralized situations, impeding the achievement of deals with suppliers at the same extent that would be possible with centralization.

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22 floor to gain from quantity discounts. However, it can also realize the contrary behaviour: the tendency to buy less and lower the safety stock because the products could be available somewhere else. In this latter case, lateral transshipment decreases even further the ability of having quantity discounts. Nevertheless, lateral transshipment per se is not a way to gain from quantity discounts more than decentralization. The results of this analysis are summarized in table 6.

Table 6 Performance of inventory pooling policies over the criterion Purchasing

Purchasing Centr. Decentr. Lat. Trans. Weight Rank

Decentralization 1/5 1 1 0,14286 2

Lateral Trans. 1/5 1 1 0,14286 2

4.2.5 Holding costs

Both inventory centralization and lateral transshipment provide benefits in terms of savings in holding costs compared to decentralization, according to the majority of literature (see e.g. Hu et al., 2005; Paterson et al., 2011; Pedersen et al., 2012). This saving is due to the reduction of the inventory level as a consequence of the demand pooling made possible by the two policies. Indeed, in independent inventories, usually a higher safety stock is hold as a protection against demand variability and to avoid stock-outs. In case of lateral transshipment, safety stocks at each inventory location can be lowered because demand variability can be buffered by the possibility of sourcing the item from another inventory in case of out-of-stock. Centralization allows the reduction of safety stocks as well, since the collective demand has less variability than the demands of single unit and the peaks of demand are balanced. Less inventory is needed to cope with the demand and to provide the same service level. In centralized inventories safety stocks reduction is higher when the demands of the individual locations are independent from each other (Eppen, 1979), as in the case of the Department. Both policies contribute in avoiding duplication of inventories for low demand items: products that are already in stock in the Department can be shared among all the researchers instead of being bought by every floor. Several papers (see e.g. Ballou and Burnetas, 2003; Lejeune and Yakova, 2005) demonstrate the substantial stock reduction for these products when lateral transshipment is applied.

This decrease of inventory levels leads to a consequent decrease of the costs that are variable with the inventory levels.

Compared to lateral transshipment, however, in the case of the Department, centralization would bring more advantages in terms of costs. In effect, with lateral transshipment, three separate stocking points have to be maintained, one for each floor, instead of one for the whole Department, keeping fixed warehousing costs higher. Moreover, there would still be a duplication of the inventory-related administrative activities that in case of lateral transshipment would be still performed by multiple people. Centralization allows a better control of the overall inventory at Department level and an increased rationalization of the resources, leading, as a consequence, to fewer holding costs.

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23 For judging the performance of the inventory pooling policies over the criterion “Holding costs” it has been, therefore, decided to express conservative opinions. Centralization is deemed strongly better than decentralization in reducing holding costs because of its ability to reduce safety stocks, stocking points and rationalize resources. Lateral transshipment is considered from moderately to strongly better than decentralization because it helps reduce inventory levels but it lacks the capacity to decrease stocking points and to rationalize resources at the same extent as centralization. The small difference in performance between centralization and lateral transshipment is due to the opinion that the reduction in safety stocks that both policies can achieve leads to a much larger cost saving than reducing stocking points and rationalize resources. It was also assumed that the reduction in inventory level would be the same for both policies as it was not possible to have a reliable quantification of the reduction value.

The results of this analysis are summarized in table 7.

Table 7 Performance of inventory pooling policies over the criterion Holding Costs

Holding costs Centr. Decentr. Lat. Trans. Weight Rank

Lateral Trans. 1/2 4 1 0,3331 2

4.2.6 Transportation costs

“Transportation costs” are defined, in this Thesis, as the cost of the delivery from the supplier to the Department. They are strictly linked to the amount of orders placed by the Department with a positive relation between the number of orders and the costs: the higher the amount of orders, the higher the total transportation costs.

According to Evers (1997), lateral transshipment generates higher transportation costs than decentralization because of the cost suffered to deliver items from one location to another. Wanke (2009) also states that inventory centralization usually provokes higher transportation costs than decentralization and lateral transshipment because of the costs of the warehouse-to-customer transportation costs. In their research, however, both authors include only the costs that occur when moving products among units (in the case of lateral transshipment) or between the central warehouse to the units (in the case of centralized inventory) and neglect the transportation costs from the supplier to the inventory locations (centralized or decentralized), which are, instead, considered in this Thesis. Moreover, they assume the existence of costs for lateral transshipments and for delivering the items from the consolidated inventory to the single locations. In the case of the Department, these assumptions are not correct. In effect, the movement that would occur in lateral transshipment is free of charge. The only cost that is involved is the cost for the time that is necessary to execute the administrative tasks for managing the movement of the material (see section 4.2.1).

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24 In a hypothetical inventory centralization, the movements of products from the central inventory to the single floors would also be free of charge, as in the case of lateral transshipment. Das and Tyagi (1997) state that, in a scenario in which there are no transportation costs from the inventory to the final user, a complete centralization of inventory is optimal.

Centralization can be more effective than decentralization and lateral transshipment in saving transportation costs for two main reasons:

- Centralization leads to fewer orders compared to decentralization (Pedersen et al., 2012). If the same product or different products of the same brand are needed by different floors, it would be convenient to place one single order instead of multiple, as the Department would be charged for one delivery only.

- It increases negotiation power and the possibility to gain from shipping special offers. It is, indeed, very common for suppliers to offer deals on transportation costs when more items are bought at the same time or when the total value of the order is above a certain threshold. Centralizing procurement increases the likelihood of obtaining these deals as larger orders can be placed. Some companies, however, demand a delivery fee that is formed by a fixed charge per order and a price that is variable to the number of items included in the order or the volume (or weight) of the shipment. Nevertheless, as long as the variable component is lower than the cost that should have been borne when making a new order, there will always be savings when the delivery is only one.

None of the above mentioned advantages can be achieved neither by decentralization nor lateral transshipment.

The results of this analysis are summarized in table 8.

Table 8 Performance of inventory pooling policies over the criterion Transportation Costs Transp. costs Centr. Decentr. Lat. Trans. Weight Rank

Lateral Trans. 1/5 3 1 0,1884 2

An overview of the results is presented in table 9.

Table 9 Summary of the results from the inventory pooling policies analysis

Alternative Service level Bureaucracy Ownership Purchasing Holding costs Transp. costs

Centralization 0,342 2 0,731 1 0,089 3 0,714 1 0,57 1 0,731 1

Decentralization 0,081 3 0,188 2 0,588 1 0,143 2 0,097 3 0,081 3

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25 4.3 Results from the performance of the AHP calculation

Two results are obtained through the performance of the AHP: a ranking of the criteria according to their importance and the most suitable alternative for the Department among centralization, decentralization and lateral transshipment.

To obtain the ranking of the criteria, the pairwise comparisons gathered through the questionnaires were inserted in the AHP software. Table 10 illustrates the results.

Table 10 Ranking of the criteria for importance

Criteria Weight Service level 0.3034 Bureaucracy 0.2044 Ownership 0.1674 Purchasing 0.1125 Transportation costs 0.1112 Holding costs 0.1012

The three non-financial criteria scored higher than the financial ones. Service level is the criteria with the greater score (0.3034) and its importance is almost equal to that of all the financial criteria combined (0.324). Bureaucracy ranked second for importance, followed by ownership. The three financial criteria score almost equally: the difference in weight is limited to few decimal digits and therefore insignificant. Finally, the results from the AHP are presented in table 11: from the three inventory pooling alternatives presented, the highest priority alternative is centralization with a weight of 0.48719, followed by lateral transshipment with a weight of 0.31642 and by decentralization (0.19638).

In detail, Lateral transshipment is 64.95% as good as Centralization while Decentralization only 40.31%. It is possible to conclude that for the Department of cell biology of the UMCG the most suitable inventory pooling policy for chemicals and life science reagents is centralization.

Table 11 Ranking of inventory pooling alternatives as outcome from the AHP Alternative Normal Weight Ideal

Centralization 0.4872 1

Lateral Transshipment 0.3164 0.6495

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26 4.3.1 Treatment of inconsistency

Table 12 and 13 illustrates the results obtained from the analysis of the raw data obtained from the pairwise comparisons questionnaires submitted to the stakeholders to gather their preferences over criteria.

Table 12 Ranking of inventory pooling policies with the use of inconsistent data Alternative Normal Weight Ideal Centralization 0.4872 1 Lateral Transshipment 0.3164 0.6495 Decentralization 0.1964 0.4031

Table 13 Ranking of the criteria with the use of inconsistent data Criteria Weight Service level 0.3034 Bureaucracy 0.2044 Ownership 0.1674 Purchasing 0.1125 Transportation costs 0.1112 Holding costs 0.1012

Since many of the questionnaires contained inconsistencies (C.R.>0.1), some of the judgements have been revised to obtain more coherent data, while maintaining the new scores compatible with the original ones. For instance, in case one criterion was judged slightly more important than another (3) but, according with the rest of the comparisons the most consistent score was 2, this latter score was used to achieve consistency. These new marks were then implemented in the AHP with the following results:

Table 14 Ranking of inventory pooling policies with the use of consistent data Alternative Normal Weight Ideal Centralization 0.4875 1 Lateral Transshipment 0.3167 0.6497 Decentralization 0.1958 0.4016

Table 15Ranking of the criteria with the use of consistent data Criteria Weight Service level 0.3020 Bureaucracy 0.1966 Ownership 0.1673 Purchasing 0.1170 Transportation costs 0.1146 Holding costs 0.1024

It is possible to notice how the results remains practically unchanged after the inconsistency reduction, meaning that, in some cases, the results from the AHP are insensitive to inconsistency and reliable even if C.R. is higher than the commonly established limit of 0.1.

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27 4.4 Sensitivity analysis

Given the impossibility of making empirical observations of the different scenarios or simulate them because of the lack of data, the scores of the alternatives over the criteria were derived from brainstorming with the stakeholders and literature research. Since these judgements may be subjective and not accurate although reasonable and rational, a sensitivity analysis was performed to evaluate the influence of different scores in the alternatives appraisal analysis on the final ranking.

The results show that the extent of the score is not fundamental as every level gives the same results.

Bureaucracy

The analysis showed that the final ranking would not change unless decentralization weighted 0.9394 on bureaucracy (figure 5), which implies decentralization scoring 45 over centralization and lateral transshipment on a scale from 1 to 9. Needless to say, this score is irrational.

Figure 5 Sensitivity Analysis: different outcomes for different weights of decentralization on bureaucracy

The sensitivity analysis also showed that even if lateral transhipment performance were extremely worse than decentralization and centralization instead of slightly the final ranking of alternatives would not change. A modification of the final results would change only if lateral transshipment performed strongly better than centralization and decentralization which is not realistic under any condition since, to perform lateral transshipment, more activities are always necessary.

Service level

There is very little doubt that centralization and lateral transshipment provide a higher service level compared to decentralization given a certain inventory. However, the extent is unsure. It has also been difficult to assess the difference between centralization and lateral transshipment; it was assumed that lateral transshipment performed slightly better than centralization. The sensitivity analysis showed that changing the extent (in better or worse) of centralization and lateral transshipment performance does not modify the final ranking of alternatives.

The final result would not change even if lateral transshipment performed extremely better or worse than centralization. In any case the most suitable alternative remains centralization.

0,1 0,2 0,3 0,4 0,5 0,6 0,2 0,4 0,6 0,8 1,0

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28 Holding costs

The sensitivity analysis showed that even if all the alternatives scored equal in this criterion, the final ranking would not change, leaving centralization the most suitable alternative.

For Ownership, Transportation costs and Purchasing, the sensitivity analysis indicated that no changes in the results would apply even if the degrees of the scores for each criterion were different.

In conclusion, it is possible to claim that the final results of this research are quite robust as they don’t easily change after modifications in the judgements about the performance of the policies.

A second sensitivity analysis was performed to evaluate the robustness of the final results in case of different degree of importance of the criteria in achieving the final goal.

In case of Bureaucracy, Purchasing, Transportation costs and Holding costs, the final result does not change for any modification in their weights, and centralization would remain the preferred option, as illustrated by figure 6.

Figure 6 Sensitivity Analysis: different final outcomes for different weights of bureaucracy, purchasing, transportation costs and holding costs

Decentralization would become the most desirable alternative only if ownership’s weight increased by 184.5%, passing from 0.1674 to 0.4763 (figure 7).

0,1 0,3 0,5 0,7 0,2 0,4 0,6 0,8 1 Bureaucracy 0,1 0,3 0,5 0,7 0,2 0,4 0,6 0,8 1 Purchasing 0,1 0,3 0,5 0,7 0,2 0,4 0,6 0,8 1 Transportation costs 0,1 0,2 0,3 0,4 0,5 0,6 0,2 0,4 0,6 0,8 1 Holdingcosts

To pool or not to pool: decision making on inventory pooling in science laboratories