Considering the effect of batch dispersion in a batch production environment: A Simulation Study

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December 2016

Considering the effect of batch dispersion in a batch

production environment: A Simulation Study

DDM Technology and Operations Management

Master Thesis

By

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Master’s Thesis TOM-DD Newcastle EBM028A30.2015-2017 Date: 12/12/2016. Words: 13,140

MSc. Technology & Operations Management

University of Groningen, Faculty of Economics and Business

Student number: s2059541 L.L.P.Uitdewilligen@student.rug.nl

MSc. Supply Chain Management

Newcastle University, Business School

Student number: b5064496 L.Uitdewilligen2@newcastle.ac.uk

Supervisors: Dr Onur Kilic Dr Adrian Small

University of Groningen Newcastle University

Faculty of Economics and Business Operations Management

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Master Thesis – Considering the effect of batch dispersion in a batch production environment -4-

Abstract

Food safety incidents lead to major changes in the food supply chain. It is not only relevant to reduce the consequences of food-related crisis by an efficient traceability system; nowadays it is necessary to minimise the probability of a food contamination. Limiting the amount of dispersion of production batches throughout the food supply chain can decrease the diffusion of potentially contaminated products, but on the other hand, reduces production efficiency as well. Based on this, one can conclude that a trade-off between these two KPIs is prevalent in food processing industries. This research developed a single-stage batch production system with stochastic elements to the production stage and integrated batch dispersion into production policies. This Thesis demonstrated that production policies can be adapted to incorporate food safety issues and control batch dispersion. By using simulation, experiments have been conducted to evaluate the effect of different production policies on the performance of the KPIs. Based on the findings, it can be concluded that production policy decisions captured in the input parameters can have many implications. In particular, the dispersion rate with corresponding standard deviations shows large variations.

Keywords: Traceability; Food safety; Batch dispersion; Food supply chain; Batch production

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List of Figures

Figure 2-1. Dispersion of food products through the FSC (Rong & Grunow, 2010) ... 16

Figure 3-1. Schematic overview of the proposed batch production model ... 20

Figure 3-2. Schematic overview of the order queue and initiation of a batch ... 21

Figure 3-3. Schematic overview of Policy_FIFO ... 23

Figure 3-4. Schematic overview with KPIs ... 24

Figure 3-5. Continuous versus discrete time ... 25

Figure 4-1. Overview of the simulation model with policies ... 28

Figure 4-2. Distributions of the mean number of orders per batch for each policy ... 33

Figure 4-3. Distributions of batch sizes for each policy ... 34

Figure 4-4. Trade-off between dispersion and efficiency ... 35

Figure 4-5. Graphs with the number of orders per batch and dispersion rate against efficiency for each policy ... 36

Figure 4-6. Relation between dispersion rate and waiting time for the 14 policies ... 39

List of Tables

Table 2-1. Characteristics food processing industry ... 10

Table 3-1. The three main KPIs ... 23

Table 4-1. Outcomes of the simulation for policy 1, 2, 3 and 4 ... 30

Table 4-2. Data results of alternatives of policy 1 ... 37

Table 4-3. 14 policies with different orders in batch limitation ... 38

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1 Introduction

The Food Supply Chain (FSC) represents one of the leading industrial sectors in the global economy (Mattevi & Jones 2016; Roth et al. 2008). The EU food and drink industry turnover exceeds €1,200 billion and is an enormous contributor to Europe’s economy, ahead of other manufacturing industries such as the automotive industry (Food Drink Europe 2015). In recent years, however, food safety incidents lead to major changes in the FSC and consequently to strategic and operational implications for the food process industry.

Globalisation challenged the FSC with ever-faster developments in the business environment where food products are distributed quicker and more widely than ever before. The globalisation of this industry and the amount of FSC complexity nowadays has led to a growingly important concern on food safety. The complexity originates from the continuous quality changes that food products show throughout the supply chain (Akkerman et al. 2010). Food scandals and incidents further strengthen this concern (Beulens et al. 2005). The number of incidents with food contamination increases and their hazardous consequences becomes more influential. High-profile scares such as salmonella, foot and mouth disease (FMD), dioxin in milk and meat industry and microbial contamination of fresh products occur more often (Piramuthu et al. 2013; Roth et al. 2008). A new report of World Health Organization (2015) showed that an estimated 600 million — or almost one in 10 people in the world — fall ill after eating contaminated food every year. Consumers have developed an increasing need for transparent information on quality assurance and product liability, and this leads to fundamentally new ways of operating in this industry (Trienekens & Beulens 2001).For example Nestlé, world’s second largest company in the ranking of global agri-food companies based on turnover has implemented a quality policy ‘’through the application of our Nestlé Quality Management System’’ to ensure the safety and quality of their products (Nestlé 2014, p.4).

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potential food safety risk. The development of internal safety and tracking systems has reached reasonable levels nowadays. Nevertheless, to reach full supply chain network control, traceability developments alone are not enough.

Traceability does not reduce the probability of the occurrence of a food crisis and therefore the focus should not be limited to efficient traceability systems (Dupuy et al. 2005). The point is not only to trace the products efficiently but also to decrease the probability of a recall by limiting batch dispersion in the operational processes. Batch dispersion is defined as the amount of retailers served by a certain production batch (Rong & Grunow 2010). The underlying problem here is that one single batch of raw material could result in a widespread of contaminated products. Limiting the number of different end-products or retailers served by the same batch will, therefore, reduce risks associated with food safety. However, limiting batch dispersion throughout the operational processes will result in an increased number of batches and therefore less efficient operations (Wang et al. 2009). Besides, the number of batches and setups will have an impact on service quality in terms of waiting times per order or retailer. As a consequence, there is a continuing trade-off between dispersion, production-efficiency and service quality. These three elements will be considered as Key Performance Indicators (KPIs) for companies in the FSC. The implications of integrating dispersion into operational processes have not been widely discussed throughout the literature. This introduction leads to the following initial research question:

How can food processing companies integrate risk-management caused by batch dispersion in their batch production policies?

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2 Theoretical Background

Food Supply Chain technically spans the entire ‘farm-to-fork’ process, it refers to the processes that describe how food from agricultural producers via the food industry ends up at customers (Dani & Deep 2010). This food chain is controlled by the management of food distribution networks (Akkerman et al. 2010). The management of food distribution networks is receiving more and more attention, both in the literature as in daily newspapers. , the dynamics of perishable food supply networks are complex due to the degradation in quality of food items during the manufacturing stage (Piramuthu et al. 2013).New customer’s requirements, low-profit margins and limited shelf lives of food products make the food processing industry a challenging area. Because several characteristics of the food processing industry will be addressed throughout this Thesis, an overview of various characteristics is given in Table 2-1. These characteristics will be considered in the assumptions, parameters and constraints of the batch production model later on. In the following section, the Food Supply Chain will be further discussed and a theoretical background on the most relevant topics will be given.

Table 2-1. Characteristics food processing industry

Characteristic Author(s)

Customers’ growing concern towards quality assurance and

product liability lead to safety regulations (Beulens et al. 2005; Akkerman et al. 2010) Most food products are perishable and therefore subject to

quality degradation which leads to a complex process

(Rong & Grunow 2010; Piramuthu et al. 2013) Variable prices of raw material and low margins on

end-products is considered to be a major characteristic (Akkerman et al. 2010; Van Donk 2001) Production processes usually consist of divergent and

convergent processes, splitting and mixing of batches are common activities in food processing

(Trienekens & Beulens 2001; Dupuy et al. 2005; Van Donk 2001)

In food processing industries, capacity is often an issue.

Resources are limited and production capacity has to be shared among a lot of end-products

(Van Donk 2001)

2.1 Food Safety in the Food Supply Chain

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consequences. Research conducted by the European Commission in 1998 showed that 11% of the food products in the industry did not comply with the quality standards set by the EU legislation (Trienekens & Beulens 2001). As a consequence, the focus on quality assurance, product liability and proactive food safety policies has become the focus of attention in the food industry. Developments in raw material processing, food manufacturing, transportation, packaging, education and training became extremely relevant over the last decade (Beulens et al. 2005).

Among recent food safety incidents, a recognisable example is the recall of peanut butter in the USA due to the presence of salmonella in 2008. It involved more than 200 food manufacturers and it turned out to be the largest product recall ever in the history of the country (Piramuthu et al. 2013). Overall, the cost of salmonella infections in the EU yearly is around 3 billion euros (Aung & Chang 2014). Another example is the beef meat contaminated with BSE (mad cow disease). At the end of last century, the first cases of the severe Creutzfeldt-Jakob disease were discovered as a result of consumption of this meat. Most of these problems were caused by the use of contaminated raw materials or associated with poor cleaning processes in production or set-up (Rong & Grunow 2010).

Besides these safety incidents, a report of the World Health Organization (2002) shows that terrorist threats to food supply chains are very real and these threats could have signiﬁcant global consequences. These food safety scandals have called international governments into action. The General Food Law developed in 2002 is one of the most noticeable effects. This General Food Law requires full traceability for all food products in the FSC and this Article has been applicable since 1st_{January 2005 (European Parliament and Council 2002). The General}

Food Law has additionally established the Rapid Alert System for Food and Feed (RASFF) (Kleter et al. 2009). RASFF is a system for reporting food safety issues within the European Union. Whenever any potential risk relating to food safety appears, this information will be immediately processed and spread out across the involved network (European Commission 2015). As a consequence of governmental demands, leading retailers such as AHOLD and TESCO require certified suppliers. For instance, growers of fruit and vegetables must further decrease their use of pesticides in order to supply these retailers.

2.2 Traceability

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consumer towards transparent information and ultimately more confidence in the food industry. Many definitions of traceability exist, in which this subject is defined and interpreted in different ways. According to Matevvi and Jones (2016), traceability is the ability to track and trace forward and backwards a product and its history through the whole Food Supply Chain. Traceability provides information to all stakeholders on the origin, location and life history of a product (Opara 2003). The European Commission (2007, p. 1) presents a general description of traceability: “food traceability is defined as the ability to trace and follow food, feed, and ingredients through all stages of production, processing and distribution.” Despite the different definitions, traceability is widely recognised as pro-active strategy to safety management and food quality (Akkerman et al. 2010; Rong & Grunow 2010; Mattevi & Jones 2016)

However, traceability systems do not only emphasise food safety. Traceability systems can provide substantial benefits to the industry and offer new business opportunities. It could provide economic and commercial incentives for companies since traceability can generate benefits in meeting consumers high standards (Dupuy et al. 2002) and reduce the impact of expensive and embarrassing recalls (Roth et al. 2008). Recent developments in technology such as RFID (radio frequency identification) and WSN (wireless sensor networks) offer new features (Ruiz-Garcia et al. 2010) which might lead to improved efficiency through close collaboration between participants of the supply chain whereby waste can be reduced.

New technologies such as blockchain can further expand the benefits of a traceability system by creating significant savings in time, cost and transparency (IBM 2016). Because Opara (2003, p. 2) included the track and trace function and other opportunities traceability can provide, his comprehensive definition will be used: ‘’product traceability determines the physical location of a product at any stage in the supply chain to facilitate logistics and inventory management, product recall and dissemination of information to consumers and other stakeholders’’ whereby the main objective of traceability is to manage food crisis and its consequences. Two kinds of traceability are defined by Trienekens & Beulens (2001) the literature; upstream and downstream traceability.

 Upstream traceability is the capacity to find the origin of the product and is used to determine the source of the problem of the contaminated product.

 Downstream traceability is the capacity to determine the location of each product that was produced out of, for example, the same contaminated batch.

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unique unity: no other unit can have the same or comparable characteristics (Dupuy et al. 2002). It is important to point out that traceability can assist reducing the consequences of a food-related crisis. However, traceability does not reduce the probability of the occurrence of a food crisis (Dupuy et al. 2005; Saltini & Akkerman 2012). The focus should therefore not be limited to efficient traceability systems alone. These insights form the basis for further research in the field of food safety measures in the food processing industry.

2.3 Safety risks in the Food Supply Chain

Despite the fact that traceability could reduce the consequences of food safety problems, contaminations frequently occur in the food industry and these risks have to be integrated with a company’s policy. The risk for food products is defined as the probability and severity of an adverse health effect (European Parliament and Council 2002). As long as the risk is at an acceptable level, the food products can be placed on the market. Food processing companies are always responsible for the products they trade on the market; even if the contamination did not originate within their firm (Trienekens & Beulens 2001). These safety risks can have a massive negative impact, as stated earlier. An extensive report of the World Health Organization (2008) identifies the risks of foodborne disease outbreaks and gives guidelines for investigation and control. Different potential causes of food safety hazards, control measures and procedures to effectively communicate and perform a recall are provided.

If a contaminated production batch is distributed throughout diverse channels to several customers, the consequences of a recall are enormous (Rong & Grunow 2010). Not only reducing the consequences of food-related crisis by an efficient traceability system is relevant, nowadays it is also necessary to reduce the probability of distributing a contaminated product. To decrease the amount of a recall, a food processing company can limit the number of batches of raw material in a finished product. The other way around, limiting the number of raw material batches processed together in one batch can also decrease potential recall size. Based on this understanding, decisions made in the planning and scheduling process of a food processing company can limit the occurrence of potential safety hazards.

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2.4 Dealing with batch dispersion

Due to setup costs, fixed capacity constraints or efficiency requirements, batch production is prevalent in the food industry (Rong & Grunow 2010). The products in a batch go through the whole process together, and the end-product is unable to be unassembled to its original raw material. Large batch sizes ensure smooth production flows and large batch sizes are aimed to increase capacity utilisation and competitiveness. Nevertheless, large batch sizes will result in a wide diffusion of food products through the food supply chain, and this will subsequently lead to more risk. If a contamination problem is caused by a particular batch of raw material, the company will use their traceability system to identify and recall all end-products made out of that contaminated batch. Therefore, food processing companies could reduce the probability of significant recall-costs and negative media impact by reducing batch sizes and batch mixing. To reduce risks associated with food safety, the point is not only to trace the products efficiently but also to decrease the probability of a recall by limiting batch dispersion through controlling the number of retailers served by a particular batch (Rong & Grunow 2010). Limiting the amount of dispersion of production batches throughout the FSC can decrease the amount of products recalled. Larger batch size means more customers will be affected by contaminated products (Memon et al. 2014).

Taking the importance of food safety and batch dispersion into consideration, this research considers batch dispersion as a Key Performance Indicator (KPI) for food processing companies. Changing batch-sizes or limiting the number of orders in one batch is a method to control dispersion. However, limiting batch sizes to control batch dispersion has considerable implications. First of all, the setup costs for making use of smaller batches are considerable (Wang et al. 2009). These costs consist of several factors. Each changeover stops the machine for at least a few moments which decreases the utilisation of the equipment. Besides these opportunity costs, each setup will lead to extra labour costs, material costs and cleaning costs (Ashayeri et al. 2006). Next to this, the machine has less idle time while serving the same amount of retailers in the end. This leads to reduced flexibility in fluctuating demand, and maintenance of the machine is more difficult to schedule. Because the fill-rate of the batch processing machine drops with smaller batch sizes, production efficiency decreases. Since production-efficiency is vital for all production companies, production-efficiency will become the second KPI.

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industries. In addition, service quality is influenced by the way how orders are being processed in different batches. For example, service quality in terms of waiting times can benefit from small batches because orders will be produced faster. This research considers service quality as the third KPI which should be considered in the FSC. In fact, there is a continuing trade-off between dispersion, service quality and production-efficiency. This will lead to the research objective and the research question.

2.5 Research Objective

To summarise, recent developments in the food supply chain which currently occur in the food supply chain lead to the following trade-off:

1. Focus on efficiency: the competition is fiercer and more competition lead to an increasingly focus on efficiency of operations

2. Focus on safety: a growing number of food contaminations and stricter rules lead to an increasingly focus on food safety

To deal with the effects that arise from this trade-off, the food industry should integrate both aspects in their operational processes. Therefore, this research will build in the direction of a quantitative production control model in the Food Supply Chain. First, existing batch dispersion models of Dupuy et al. (2005) and Rong & Grunow (2010) have been analysed. For their research, Dupuy et al. (2005) used an industrial case which was characterised by a 3-level bill of material (raw materials, components and ﬁnished products). They defined dispersion as the sum of raw material batches used to end product batches and proposed a mathematical model to reduce batch dispersion. This definition of dispersion neglects the fact that even a small batch can consist of several orders which can be distributed over a wide area. Therefore, this research does not use their definition of batch dispersion. The proposed MILP model cannot be used to schedule or plan different production cases and direct benefits for food processing companies are not presented. However, Dupuy et al. (2005) initiated the subject of batch dispersion and introduced some new definitions and insights.

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served by a batch: Db = n(n − 1)/2 where n is the number of retailers served by batch b. The concept is illustrated in Figure 2-1. A small change in number of orders in one batch can result in a large difference in dispersion rate. This research uses this definition of dispersion to reflect the aim to prevent the distribution of batches to numerous retailers.

Figure 2-1. Dispersion of food products through the FSC (Rong & Grunow, 2010)

However both papers presented some interesting insights as stated above, their models (Dupuy et al. 2005; Rong & Grunow 2010) showed that real-world examples resulted in extremely complex models. For that reason, this research considers a simple production structure with a different production environment. Furthermore, both researchers proposed deterministic models where everything is known with certainty. Customer orders and time-frame in which these orders had to be fulfilled were known. A single production policy determines what the system should do in what situation. Stochastic elements were not captured within their models, and this leads to a research gap.

In order to fill this gap, this Thesis will develop a batch production model with stochastic elements to the production stage. This research will assume a single-stage Make-to-Order production environment where orders will be processed according to the First-In-First-Out principle. The order arrivals and order sizes are not known, and this results in the stochastic element. To process the orders, a production policy initiates the batch and tells the system what to do. This production policy can be adapted in order to control different aspects, such as batch dispersion or production efficiency. A simulation will be used to simulate multiple policies and analyse the outcomes of the three KPIs. The use of different policies to analyse the impact on batch dispersion have not been discussed throughout the literature and therefore, this effect constitutes the foundation of the following research objective:

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2.6 Research Question

To assess the impact of decisions made in the planning and scheduling process of a food processing company on batch dispersion, an MTO batch production model with some inherent randomness will be developed. Based on different production policies, the model can fulfil demand by grouping orders together in batches. This research aims to demonstrate that production policies can be adapted to incorporate food safety issues and control batch dispersion. Therefore, the following research questiofn is created:

What is the effect of incorporating batch dispersion into a firm’s batch production policy on the outcomes of the KPIs batch dispersion, production efficiency and service quality?

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3 Methodology

In this part, the methodology will be presented. First, the research method will be explained and subsequently, the research design with the batch production system and the policies will be provided.

3.1 Research Methods

In order to answer the research question, this Thesis will use quantitative modelling. Quantitative modelling in operational research orientates towards real-life problem solving in Operations Management (Karlsson 2009). Quantitative models are built based on a set of variables that explain the behaviour of real-life operational processes. Managerial problems can be included and these problems will be translated into a mathematical model. This Thesis will be a prescriptive research, where-in strategies are developed and where actions will be performed to achieve the research objective. The purpose will be to find new insights and a solution for the defined research question. This Thesis will make use of tools such as model building and simulation. Simulation serves as a computational or mathematic representation of reality that provides managerial insights and can support decision making (Terzi & Cavalieri 2004). Moreover, simulation enables a study to conduct experiments with the model to evaluate the effect of different strategies on the performance of the KPIs.

In the next section of the methodology, the developed model will be explained. First, the batch production system will be presented and the assumptions will be explained. After that, the policies will be explained. In section 4, the simulation data will be analysed in the numerical analysis. The results are considered in the context of the research objective and the research question. This solution will provide the literature with some new insights and the results will be discussed. These insights can be used to solve or answer the research objective stated earlier and new questions can emerge from these results after the conclusions.

3.2 Batch production system

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processing stage is the most important stage regarding batch dispersion. The packaging stage is not considered within the scope of this system.

This research will consider a batch production environment to mimic the food industry. Batch production processes are prevalent in the food processing industry (Rajaram & Karmarkar 2004). Within batch manufacturing, formulations or recipes are used for the transforming of raw materials into a batch. The products in each batch go through the whole process together, and the end-product is unable to be unassembled to its original raw material. In this paper, we focus on the food processing industry where customers demand identical, perishable products.

3.2.1 Assumptions of the batch production system

Since the complexity of the real world is very large, this Thesis will use a simplified version of reality in a general setting with simple rules. Some assumptions had to be made to simplify the situation and to focus on the most important aspects of the problem:

1. Make-to-order

The model uses a Make-To-Order (MTO) environment. As stated before, this paper focuses on the food processing industry with products having a short shelf-life. Limited shelf life induces MTO production because the processed material cannot be stored for a long time (Akkerman & Donk 2009). Finished goods inventory can be reduced to zero. Besides, a company can customise the order and produce exactly in quantity wanted by the customer with the MTO system.

2. Raw material and end-products

This model considers an unlimited stock of raw material which is available at any time. All raw materials have the same characteristics and can be mixed in a batch. Removing material from the processing machine can only begin after the process is finished. At that moment, the batch can be distributed and sent to the customers.

3. Transportation times and storage are neglected

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4. Capacity machine: minimum and maximum batch size

The machine has a minimum and maximum fill rate and this condition can be used as a tool to increase or decrease batch sizes and therefore batch dispersion.

5. The machine has a fixed processing time

After an order has arrived in the queue and subsequently adjusted to a batch, the batch has to be processed. In the proposed model, one machine processes the batch if the machine is available. Regardless the batch size, the raw material needs the same processing time in the machine. The processing time, the time before the machine becomes available again includes cleaning activities and setup time for a new batch.

3.2.2 How the batch production system runs

The single-stage batch production environment is characterised as a Make-to-Order system having a single product and single machine, where orders arrive randomly. It is assumed to be a compound binomial process because there are two stochastic elements involved. The random arrival process is considered as the first stochastic process. It is a binomial distribution and therefore a discrete-time stochastic process. In each discrete time unit, there is a probability (q) that an order arrives. At one time unit, at most one order can arrive. Therefore, the discrete time units are assumed to be small enough. If an order arrives, the incoming orders will be connected with the time t of that moment and an order size. Related order size is stochastic with another distribution function, f.

The incoming orders are linked with an order size and they end up in a queue, the order queue. At this moment, the policy decides which orders to fill into a batch. This batch, consisting of several orders, will be processed by the machine if the machine is available. After the batch is processed, the orders can leave the system and will be sent to the customer. Figure 3-1 presents an overview of the model so far.

Figure 3-1. Schematic overview of the proposed batch production model

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Figure 3-2. Schematic overview of the order queue and initiation of a batch

3.2.3 Production Policy

After the orders end up in the order queue, the production policy determines which orders are allocated to a batch. Basically: the policy tells what to do. The policy operates following the FIFO principle. FIFO stands for First-in First-out and is probably the most well-known queuing system; the oldest items are used first. This model focuses on food product with a short shelf-life and the FIFO policy is a common policy in the food industry with perishable products (Karaesmen et al. 2011). A FIFO principle does not always deliver the optimal solution. However, it is considered as the fairest approach towards customers regarding waiting time. There is no room to give preference to certain customers and the system is simple to understand.

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After some orders arrive, they will end up in the order queue. P, m and w are the input-parameters for the conditions that represent as thresholds to start a batch. When the system hits the threshold, the policy determines which orders to take in the batch. For example, P ranges from 0 to 1 and is the input parameter for the first condition, considering efficiency. This condition implies that if the sum of all order sizes in the order queue is equal or greater than p * capacity, the policy starts filling a batch with orders from the order queue at that moment. M is the input parameter for the number of orders before starting a batch. If for example, M is four, the policy will decide to start processing the batch if there are four orders in the queue. A policy that focuses on limiting dispersion will, therefore, have a lower m than a policy that focuses on efficiency. W represents the input parameter for the total waiting time. If the total waiting time of the orders in the queue exceeds w, the policy will initiate the batch.

K is the last input parameter and is expressed in one of the constraints. K is the maximum number of orders that can be filled into one batch. Even if the order queue consists of many orders, k restricts the policy to fill the batch with more than k orders. C represents a constraint as well, but this parameter is a fixed number: the capacity of the machine.

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3.2.4 How the policy are analysed using outcomes of the KPIs

As mentioned before, the three KPIs defined are batch dispersion, production efficiency and service quality. These KPIs are general and prevalent in the food processing industry. As mentioned in previous part, the policy has input parameters. By changing these input parameters, policies with different objectives can be designed. These different policies will lead to different KPI outcomes, as stated earlier. The relation of these KPIs (Table 3-1) and how they are measured forms the basis of the trade-off considered in the food supply chain.

Table 3-1. The three main KPIs

KPI Measured by

1. Dispersion # orders per batch

2. Production efficiency Utilisation (batch size / capacity)

3. Service quality Waiting time

All three KPIs are explained in more detail on the next page. Thereafter, Figure 3-4 provides a schematic overview with the Key Performance Indicators and how they act in the batch production system.

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1. Dispersion is measured as a function of the number of orders in a batch: Db = n(n − 1)/2 where n is the number of retailers served by batch b. There is a minimum of orders in a batch (1) and the production policy controls with m and k what the maximum number of orders in a batch is.

2. Production efficiency is measured as the utilisation of the machine. This utilisation is measured as the batch size (sum of all order sizes in that particular batch) divided by the capacity of the machine. Since a machine setup in batch production can be very expensive, this utilisation is an important measure for the production efficiency. P is the main parameter for this KPI.

3. Service quality is measured as the function of waiting time per order. Strictly speaking, the time between an order arrived and a finished batch. For every order in a batch, the waiting times are summed up to reach the total waiting time per batch. If this waiting time exceeds the value of input parameter w, the batch should be processed as soon as the machine becomes available.

The policy decides how to process these orders in batches and Figure 3-4 shows how the KPIs act and become visible from the simulation. The orderbook represents the order queue where the orders arrive.

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3.3 The simulation and validation

The batch production environment and the production policy have been presented in the previous sections. In order to analyse how the different policies act in this production system, the different KPIs can be calculated and compared. In order to solve the problem analytically, the use of explicit equations gets you from data to results. However, the batching concept in the proposed batch production system and the production policy with four input parameters are more demanding. This problem is too complicated to solve analytically and therefore, numerical simulation is used in this Thesis. Simulation can deal with variability, interconnectedness and complexity (Robinson 2004). To obtain the KPI outcomes of a given policy, several simulation runs are used to obtain the data and process it to results.

Since the arrival process is assumed to be a compound binomial process, discrete-event simulation is the required way to simulate the system. The information that is being simulated does not evolve or move smoothly and continuously, a discrete-event simulation models the events in a discrete sequence (Figure 3-5). The behaviour of a system can be evaluated and analysed under different sets of conditions. Discrete models are more general, correspond to observed data more clearly and are easier to simulate on computers (Babulak & Wang 2010).

Figure 3-5. Continuous versus discrete time

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4 Numerical Experiment

This research aims to consider the effects of integrating batch dispersion into different production policies of a food processing company. By changing the input parameters, policies can be made more favourable to one KPI or the other. Different policies with different objectives will be defined. The outcomes of the simulation will be used to analyse the effect of integrating batch dispersion on the production efficiency. Service quality is considered as a third KPI; however, this KPI will have a limited role in the analysis. First, the research design is presented after which the findings of the experiment are provided. The findings of the different experiments are discussed within this numerical study and conclusions are drawn after section 4.

The experiments with the batch production simulation model are divided into four sets of experiments. To begin with, an initial set of policies is introduced to analyse the outcomes of the KPI in depth. The policies range between a strong focus on limiting dispersion (Policy 1) to a strong focus on efficiency (Policy 4). Policy 2 and 3 are intermediate policies. Within this discussion, the most prevalent trade-off, dispersion against production efficiency, will be analysed. Second, a set of 8 alternative policies will be designed in order to understand how these alternative policies act. These alternative policies have some minor changes in the input parameters, to see how the KPIs respond to these changes. Third, a set of 18 policies will be designed to analyse the third KPI: service quality. The outcomes of the waiting time will be discussed and compared with the outcomes of batch dispersion and production efficiency. At last, the two initial policies (dispersion-focused and efficiency-focused) will be adapted in a way that they meet each other half where they show the same production efficiency. Other factors, such as dispersion rate and standard deviations, will be analysed to see how the policies performs and how these production policies can be adapted in order to control the KPIs.

4.1 Design of experiment

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a sample space of {x1 = 50, x2 =100, x3 = 150, …, x14 = 700} in litres. The capacity c of the model is 2200L.

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Master Thesis – Considering the effect of batch dispersion in a batch production environment -28- Orderbook = [] Servedbook = [] Simulation Initialise Policy_FIFO 8 12 25 … T end 300 50 700 … X Time (T) Ordersize 1 2 3 … N # λ λ System available? Call Policy to fill batch

Orderbook Orders arrive with P = 0.15 and get an order size of 50, 100, …, 700. They end up in the queue.

For all T

Batch filled?

YES NO

NO  Update servedbook

 Delete batchlist

 Delete orders from orderbook

Compute KPIs  # order in batch  Batchsize  Waiting time Y-A xi s X-Axis 1 2 3 4 5 Bar graph

If conditions are True:

 Sum(ordersize) ≥ p*capacity

 # orders in orderbook ≥ m

 Sum(waiting time) ≥ w Start

FIFO with orders untill:

 Batchsize + ordersize(n+1) ≥ c or:

 # orders in batchlist => 5 Fill batchlist

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4.2 In-depth numerical analysis of the initial four policies

In order to analyse the impact of different production policies on the outcome of the three KPIs, an initial set of four different policies will be considered. The four policies are provided below and the numbers between the parentheses represents the input parameters p,m,w,k. Policy 1 has a clear focus on limiting dispersion and policy 4 aims to obtain high production efficiency with larger batches. The other input parameters of the policies are set to zero or to infinity ∞ to obtain the most widely separated policies. Policy 2 and 3 are the intermediate policies with a less strong focus on one KPI.

1. Policy_1 (0.01, 0.01, 0.01, 4): Focus on dispersion

This policy has a clear focus on limiting dispersion by limiting the maximum orders per batch to four. This is the minimum amount of dispersion a policy can aim for; otherwise, the arrival rate is bigger than the exit rate. Since there are no limitations to initiate a batch anymore, the policy states that the model starts a batch if the order queue is greater than 0. Every time the machine becomes available again, the batch will be filled immediately. 0.01 as input parameter is small enough to make sure that these parameters do not have an influence. Having 0 as input would result in initiating a batch even if there is no order queue.

2. Policy_2 (0.6, 5, 60, 7): Intermediate dispersion policy

Policy 2 is considered to be an intermediate production policy with a mild attention for limiting dispersion. This policy does not have a rigorous dispersion limitation however it does limit the maximum orders to the value of 7. There is a maximum total waiting time of w=60 to aim for decent service quality.

3. Policy_3 (0.6, ∞, ∞, 9): Intermediate efficiency policy

Policy 2 is considered to be an intermediate production policy with a moderate attention for high efficiency. Therefore, this policy has a high dispersion restriction with a maximum of 9 orders per batch. However the total order size restriction is set to 0.6 * capacity, the other parameters (p and w) are set to infinity as well to obtain a decent efficiency rate.

4. Policy_4 (0.9, ∞, ∞, ∞): Focus on efficiency

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A summary of results of the simulation for these four policies is provided in Table 4-1. After the representation of the data in the table, explanations and remarkable outcomes will be provided and discussed.

Table 4-1. Outcomes of the simulation for policy 1, 2, 3 and 4

Policy Dispersion Intermediate Intermediate Efficiency 1_ (0.01, 0.01, 0.01, 4) 2_(0.6, 5, 60, 7) 3_(0.6, ∞, ∞, ∞) 4_(0.9, ∞, ∞, ∞)

Simulation

Total number of orders: 15187 15187 15187 15187

Total number of batches: 4952 3786 3435 2933

Batch started because:

Capacity 4952 2798 3435 2933

# of orders: 4952 1315 0 0

Waiting time 4792 1291 0 0

Dispersion

Mean # orders in batch 3.07 4.01 4.44 5.18

Std. # orders in batch 1.06 0.90 1.07 1.30

Dispersion rate 3.73 6.44 8.13 11.66

Std. Dispersion rate 2.35 3.32 4.57 6.67

Efficiency

Mean batch sizes (L) 1,141 1,493 1,646 1,927

Std. batch sizes 517 358 217 163

Utilisation machine 51.9% 67.9% 74.8% 87.6%

Time machine is running 99.0% 75.7% 68.7% 58.7%

Service quality (in h)

Mean wait. time 1st_order 18.37 21.13 23.93 32.71

Std. wait. time 1st_order 9.06 7.19 11.34 14.27

Mean wait. time per order 14.12 11.94 13.45 19.52

The table starts with the simulation data. The total number of orders is identical for all policies because the random generator is initialised. The total number of batches decreases if batch sizes increase. The next rows, “batch started because of”, present the condition for initiating a batch. The thresholds before starting a batch at the dispersion policy 1 are practically always achieved since the input parameters are set to almost zero.

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and the efficiency-focused policy significantly differs. This implies that the input parameters have a strong impact.

4.2.1 Analysis of the effect of the different policies on dispersion

In this section, the first KPI, batch dispersion, will be discussed and analysed. The KPI dispersion includes the most essential data by presenting the mean number of orders per batch with its corresponding standard deviation. The aim of the different policies is clearly reflected in the outcomes of the simulation. An increase is visible in the average number of orders per batch. Where dispersion-focused policy 1 has on average 3.07 orders per batch, the efficiency-focused policy has considerably more with 5.18 orders per batch on average. This is a growth of 68.7%. This growth is caused by the infinite dispersion limitation allowing outliers of 11 orders per batch.

Second, after the mean orders per batch, the mean dispersion rate per policy is given. As stated earlier, the dispersion rate is measured as a function of the number of retailers served. The dispersion-focused policy, policy 1, shows a dispersion rate of 3.73. Since dispersion is unavoidable, this is a controllable result. However, the dispersion rate increases incredibly fast. Even the dispersion rate of the intermediate dispersion-focused policy increases with almost 73% to a rate of 6.44. The most efficiency-focused policy has a dispersion rate of 11.66. This is a whopping increase of 212.6% and therefore the increase is considerably higher than the increase shown by the average number of orders per batch. These findings demonstrate that an increase in batch sizes result in a significantly higher increase in dispersion rate. These results reflect the idea to limit the number of orders per batch and subsequently, the distribution of batches to numerous retailers. However, assuming that there is a peak in order arrivals, a higher dispersion rate is unavoidable in order to fulfil the demand. If a food processing company is aware of a high dispersion rate and considering this in the production planning, the company can take actions to limit the risks associated with the dispersion. For example, food processing companies can try to fulfil batches with orders coming from the same customer, or customers close to each other. By keeping this in mind, you prevent the dispersed batches to be spread over a great area.

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deviation. This effect leads to highly unpredictable processes. The more unpredictable a process is, the greater the risk and associated costs. Due to high variation, demand expectation forecasts is more challenging. Required machines and personnel are difficult to predict and processes more tough to manage.

4.2.2 Analysis of the effect of the different policies on efficiency

In this part, the second KPI will be analysed and discussed. The second KPI, production efficiency, is calculated as the utilisation of the machine. The mean batch sizes have therefore a direct relation with the efficiency rates because efficiency is calculated as batch size divided by the capacity. Consequently, a small average batch size results in a low efficiency rate.

The dispersion limiting policy has a very low efficiency rate, as expected. This policy produces a lot of small batches (on average 1,141L) and this result in a utilisation of 51.9%. This cannot be lowered anymore because of the time the machine is running almost reaches 100%. The most efficiency-focused policy has an average batch size of 1927L with a corresponding efficiency of 87.6%. This efficiency thus grows with 68.7% in comparison with the dispersion-focused policy. Because of this higher efficiency rate, the percentage of time the machine is running is quite low with 58.66%. This does imply that the machine has more idle time. Since the efficiency-focused policy waits before starting a batch until the order queue has a total order size of 0.9 * capacity, you would expect an efficiency of at least 90%. However, because of the FIFO principle, orders are processed in the sequence that they arrive. Resulting from the simulation, it seems to occur that after initiating the batch, not every order can be filled into that batch.

The standard deviation of the mean batch sizes decreases where the mean batch sizes itself increases. This is due to the fact that the conditions before starting a batch tend to become more severe. Therefore, small batch sizes are excluded in the efficiency-focused policies. For example, the most efficiency-focused policy does not have batches with a size below 1500L. As a result, the batch size data points range between 1500L and 2200L and therefore the data points are located close to the mean. This will become visible in the distributions of these batch sizes. The distributions of these mean batch sizes of these four initial policies are presented in 4.2.4.

4.2.3 Analysis of the effect of the different policies on waiting time

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4.2.4 Distributions of the initial set of four policies

To analyse the initial set of four policies in further depth, this section provides a comprehensive analysis of the KPI results. The mean values of the different KPI outcomes were presented in Table 4-1. Because large variations have been discovered, this section presents the whole distributions of the two main KPIs: average number of orders per batch and batch size. To emphasise the differences between the numbers of orders per batch for each production policy, the graphs of the distributions are presented in Figure 4-2. Policy 1 represents the most dispersion-focused policy and policy 4 represents the most efficiency-focused policy. Policy 2 and 3 are the intermediate policies.

Figure 4-2. Distributions of the mean number of orders per batch for each policy

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even more, disadvantages than the widespread of potentially contaminated food products alone. These, more scattered distributions, results in more unpredictable processes as discussed before. Besides the number of orders per batch, Figure 4-3 presents the distribution of the batch sizes for each production policy.

Figure 4-3. Distributions of batch sizes for each policy

Because dispersion-focused policy 1 does not have any limitations before starting a batch, the batch is filled with orders arrived while processing the previous batch. This results in a variation of very small and very large batch sizes. Intermediate policy 3 and efficiency-focused policy 4 shows batch sizes of 1500L and higher. This is because of its strict conditions before initiating the batch. Because batch sizes of policy 1 have significantly different batch sizes, the standard deviation is way greater than the standard deviation of policy 4. Policies with a higher level of dispersion show less variability considering batch size.

4.2.5 Analysis of the trade-off between dispersion and efficiency

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left-to-right in Figure 4-4. The x-axis represents the efficiency while the y-axis represents the number of orders in a batch and the dispersion rate.

Figure 4-4. Trade-off between dispersion and efficiency

The two before mentioned policies, dispersion-focused 1 and efficiency-focused 4, are the two outer dots in Figure 4-4. The two middle dots are related to two intermediate policies. First, the number of orders in a batch is considered. As mentioned earlier, they increase from 3.07 to 5.18 which is a growth of 68.7%. Corresponding efficiency values are 51.9% and 87.6% which seem to be a growth of 68.7% as well. This implies that there is a linear relationship between efficiency and number of orders per batch.

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Figure 4-5. Graphs with the number of orders per batch and dispersion rate against efficiency for each policy

It might be logical to think that the advantages of a perfectly efficient production system can perhaps beat the advantages of a system with a low dispersion rate. Though, according to Memon et al. (2014), potential recall costs are way higher than extra production or setup cost. Recalls have several direct and indirect costs associated with them and their simulation showed that batch size is directly proportional to expected recall cost. Saltini & Akkerman (2012) found that adopting a production strategy on a low dispersion strategy would lead to a reduction of potential product recall between 6% and 16% in case of contaminated processing batch. Since even a small decrease in the probability of a potential recall could be highly valuable, a reduction of 6 to 16% can be worth more than the linear efficiency loss of about 6 to 16%

As shown with the simulation of the first policies of this research, small changes in these production policies can lead to great differences in dispersion rate. Therefore, in order to prevent high recall cost and other consequences, food processing companies should adjust their risk attitude towards this phenomenon. This risk attitude can be adapted in the policy by limiting the maximum number of orders per batch or decreasing average batch sizes.

4.3 Numerical analysis of large set of alternative policies

So far, four representative policies have been analysed. Two corner cases, the most dispersion-focused policy and the most efficiency-dispersion-focused policy, and two intermediate cases. But obviously, our policy framework can capture a lot more variety as compared to just these four. The aim of this section is to see what is happening with the KPI outcomes by using more different production policies. The results of the simulation have been analysed in detail for the initial four policies, following section presents the abstract measures for 8 policies. Section 4.3.2

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will analyse and discuss the waiting times through presenting 14 policies. The last section will bring the two most widely separated policies together in order to explore how the KPIs act.

4.3.1 Discussion on the effect of 8 policies on efficiency and dispersion

Because the wide separated policies 1 and 4 showed the most interesting results and differences, these policies will be further analysed in this part. Three alternatives of both policies are considered to understand how changes in a production policy can affect the KPI outcomes and presented in a more condensed fashion. Together with the dispersion-focused policy, three alternatives have been created and presented as the first four policies in Table 4-2. Although these policies still have a maximum dispersion rate of 4, the restricted bounds before starting a batch are increased in order to achieve a higher efficiency. Four alternative policies of the efficiency-focused policy are designed and presented as the last four alternative policies in Table 4-2. These alternative policies have less strict conditions than the “base-case” and therefore batches are processed earlier.

Table 4-2. Data results of alternatives of policy 1

Policy Dispersion Efficiency Service (waiting time (h))

# orders (sd) Dispersion (sd) Utilisation First order Average

(0.01, 0, 0, 4) 3.0 (1.06) 3.7 (2.35) 51.9% 18.4 14.1 (0.3, 3, 30, 4) 3.2 (0.84) 3.9 (2.09) 54.8% 19.6 13.9 (0.6, 6, 60, 4) 3.7 (0.49) 5.2 (1.40) 63.1% 24.3 15.9 (0.9, 9, 90, 4) 3.9 (0.28) 5.7 (0.82) 66.4% 31.2 21.7 (0.9, 3, 30, 9) 3.4 (1.07) 4.7 (3.65) 58.1% 17.3 10,70 (0.9, 6, 60, 9) 4.3 (0.95) 7.5 (3.78) 72.7% 23.9 13,73 (0.9, 9, 90, 9) 4.7 (1.04) 9.4 (4.63) 80.% 27.8 15.96 (0.9, ∞, ∞, 9) 5.2 (1.30) 11.7 (6.67) 87.6% 32.7 19,52

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a batch and will be further discussed in the next section. Based on these findings, it can be concluded that production policy decisions captured in the input parameters can have many implications for all three KPIs.

4.3.2 Discussion on the effect of 14 policies on the waiting times

After having analysed and discussed the trade-off between dispersion and efficiency extensively, this section will analyse the third KPI waiting times more in depth. In order to do so, 14 policies have been considered. The first seven policies all have strict conditions before starting the batch. The next seven policies have no conditions before starting the batch with input parameters of 0.01. All 14 policies have an incremental maximum number of orders to understand the effects of this measure. The policies are presented in Table 4-3 with the standard deviations provided between the parentheses.

Table 4-3. 14 policies with different orders in batch limitation

# orders (sd) Dispersion (sd) Utilisation First order Average

(0.9, ∞, ∞, 3) 3.0 (0.00) 3.0 (0.00) 50.7% 789.7 772.9 (0.9, ∞, ∞, 4) 3.9 (0.21) 5.9 (0.64) 66.9% 40.2 30.5 (0.9, ∞, ∞, 5) 4.7 (0.59) 8.7 (2.19) 78.7% 35.1 23.2 (0.9, ∞, ∞, 6) 5.0 (0.93) 10.5 (4.02) 84.8% 33.6 20.8 (0.9, ∞, ∞, 7) 5.1 (1.17) 11.4 (5.54) 87.1% 32.9 19.8 (0.9, ∞, ∞, 8) 5.2 (1.27) 11.6 (6.30) 87.6% 32.8 19.6 (0.9, ∞, ∞, 9) 5.2 (1.30) 11.7 (6.67) 87.6% 32.7 19.5 (0, 0, 0, 3) 3.0 (0.05) 3.0 (0.08) 50.7% 766.9 751.0 (0, 0, 0, 4) 3.1 (1.06) 3.7 (2.35) 51.9% 18.4 14.1 (0, 0, 0, 5) 3.1 (1.32) 4.0 (3.42) 52.0% 15.0 11.2 (0, 0, 0, 6) 3.1 (1.39) 4.1 (3.90) 52.0% 14.9 10.8 (0, 0, 0, 7) 3.1 (1.41) 4.2 (4.03) 52.0% 14.9 10.7 (0, 0, 0, 8) 3.1 (1.41) 4.2 (4.03) 52.0% 14.9 10.7 (0, 0, 0, 9) 3.1 (1.41) 4.2 (4.03) 52.0% 14.9 10.7

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policies. The average arrival rate during the processing time is bigger than the limitation of 3 orders per batch. This illustrates that a certain amount of dispersion is unavoidable and inevitably linked with batch production. Second, on average, the waiting time for the first set of policies is longer than the policies of the second table. Because of the high condition parameters (0.9 and infinity), the fill rate of the machines is higher, and therefore orders have to wait longer before processing. It can be concluded that waiting time is highly correlated with the input parameters or initial conditions of a production policy.

To visualise the differences, graphs of both sets of policies are presented in Figure 4-6. On the x-axis, the seven different policies are shown and the y-axis represents dispersion rate on the left side and waiting time on the right side.

Figure 4-6. Relation between dispersion rate and waiting time for the 14 policies

The first set of policies is analysed first. If we neglect policy 3, we see a 289% increase in dispersion rate between policy 4 and 9 while the waiting time drops with 36%. If a company is hesitating between different policies and balances its decisions based on the trade-off among dispersion rate and waiting times, policies higher than policy 5 should be eliminated. These graphs demonstrate that slight improvements in waiting time can lead to huge increases in dispersion rate. This shows once again that small variations in production policies can have considerable impact.

Here, the set with dispersion-focused policies is discussed. Small batch sizes lead to low efficiency, however, they lead so low dispersion rates as well. Another substantial difference is that these policies all have small waiting times. These small waiting time results have several benefits. Variations are significantly lower which results in more reliable and flexible operations. All different policy alternatives show that all KPIs are controllable with production policies. 0 6 12 18 24 30 36 0 2 4 6 8 10 12 3 4 5 6 7 8 9 W ait in g ti me ( h ) Di sp ers io n rate

First 7 policies (max. no of orders per batch)

Dispersion rate Waiting time 0 6 12 18 24 30 36 2 4 6 8 10 12 3 4 5 6 7 8 9 W ait in g ti me ( h ) Di sp ers io n rate

Last 7 policies (max. no of orders per batch)

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4.3.3 Moving the initial two outer policies towards each other

The numerical experiment started with an initial set of 4 policies whereby policy 1 and policy 4 represented two outer policies. Policy 1 has a clear focus on limiting dispersion and policy 4 aims to obtain high production efficiency with less, but larger batches. This last section will bring the two most widely separated policies together to obtain the same efficiency level. It could be interesting to explore how the other KPIs and data points act.

In order to understand how both policies act while having the same efficiency outcomes, two alternatives have been designed. Both policies have been adapted in a certain way that they still have characteristics of their initial policy. The policies with corresponding outcomes are presented in Table 4-4.

Table 4-4. Two outer policies moved toward each other

# orders (sd) Dispersion (sd) Utilisation First order (sd) Average (0.6, 5, 100, 5) 4.18 (0.75) 6.94 (2.68) 70.8% 22.9 (9.24) 22.71 (0.8, 8, 55, 8) 4.18 (1.02) 7.11 (3.79) 70.8% 12.9 (6.09) 13.02

Considering the effect of batch dispersion in a batch production environment: A Simulation Study