The effects of promotions on schedule stability in the process industry

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The effects of promotions on schedule stability in the process industry

Master Thesis by Jasper Dijkerman

University of Groningen Faculty of Economics and Business Newcastle University Business School

Msc Dual Degree Technology and Operations Management and Operations and Supply Chain Management

December 2016

Supervisor Groningen: Dr. O.A. Kilic Supervisor Newcastle: Dr. A. Small

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A

bstract

Preface

This dissertation is the end result of the final assignment of my Double Degree Master in

Operations Management. During the process of writing this dissertation I have known both

joyous moments of finding solutions to the problems at hand and moments of frustration were

nothing seemed to go right. It has been a journey in which I have learned a lot both in doing

research and in the development of programming skills which have both lead me to this end

result. It has not been a process in which I have stood alone and therefore I would like to

express my gratitude to the people who have helped me write this dissertation.

First of all, to my Groningen Supervisor Dr. Onur Kilic for all the insightful meetings, critical

feedback and his patience during the process. Secondly, I would like to thank my Newcastle

Supervisor Dr. Adrian Small for his support and positivity in the feedback and meetings.

Lastly, I would like to thank UCC Coffee for providing us with useful data and taking the

time out of their schedule to discuss the ins and outs of their processes.

This research has looked at the problem of rescheduling to satisfy an increase in demand caused by promotions whilst keeping the schedule sufficiently stable. The importance of the stability of a schedule can be derived from the fact that a schedule is the basis for the planning of activities such as supplier delivery agreements and the allocation of resources to internal operations. The measure of schedule stability used in this thesis is the sum of absolute deviations between baseline-schedule start times and post-promotion baseline-schedule start times. Several policies were created in order to deal with the increase of demand caused by promotions. The results show the stability and cost, measured in holding- and setup-cost per unit time, for schedules in each of these policies after a promotion was inserted. This research concludes that policies which spread demand of promotions over multiple production cycles and make use of inserting idle times provide the most stable way to deal with promotions but are associated with high costs per unit time.

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Table 4.1: Production, demand and cost data Table 4.2: Optimal production sequence Table 4.3: Schedule instability situation 1 Table 4.4: Schedule instability situation 2 Table 4.5: Schedule instability situation 3 Table 4.6: Schedule instability situation 4 Table 4.7: Schedule instability situation 5

Table 4.8: Comparison best policies for stability and cost per situation Table 9.1: Setup-time matrix

Table 9.2: Start times situation 1 Table 9.3: Start times situation 2 Table 9.4: Start times situation 3 Table 9.5: Start times situation 4 Table 9.6: Start times situation 5 Table 9.7: Company demand data Table 9.8: Company demand data

Figure 4.1: Policy schedules situation 1: Demand RB01 * 2 Figure 4.2: Policy costs situation 1: Demand RB01 * 2 Figure 4.3: Policy schedules situation 2: Demand RB01 * 10 Figure 4.4: Policy costs situation 2: Demand RB01 * 10 Figure 4.5: Policy schedules situation 3: Demand RB18 * 2 Figure 4.6: Policy costs situation 3: Demand RB18 * 2 Figure 4.7: Policy schedules situation 4: Demand RB18 * 10 Figure 4.8: Policy costs situation 4: Demand RB18 * 10

Figure 4.9: Policy schedules situation 5: Demand RB01 * 10, Duration T * 2 Figure 4.10: Policy costs situation 5: Demand RB01 * 10, Duration T * 2 Figure 9.1: Product Family sequence Rovemaline

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1. Introduction

Globalization, intense competition, new ways to reach customers and new ways to analyse data has increasingly made the management of demand, planning and scheduling activities more difficult (Garchkin, 2013). Especially in the process industry where profit margins are low and costs are high (de Matta & Guignard, 1994) the activity of production planning and scheduling is a complex task. Pinedo (2008) states that a schedule is the result of a decision making process which deals with the allocation of resources to tasks over a set period of time with the aim of optimizing one or multiple objectives. Scheduling involves trade-offs, e.g. about which processes to prioritize, when to execute them and who or what to assign to these processes, and is considered a complex problem because of its high number of alternatives (Bendoly, van Wezel & Bachrach, 2015).

Scheduling is not only concerned with the allocation of equipment or machines but also with the allocation of employees. Thus when a schedule changes employees are also affected by this. The benefits of change are difficult to perceive by employees which can result in resistance and a decrease in satisfaction of the working activities (Cawsey, Deszca & Ingols, 2015). Frequent changes to a schedule can further result in a general loss of confidence in the planning ability of the schedulers by operational staff (de Kok & Inderfurth, 1997). Furthermore, a schedule can be seen as the basis for other planning activities e.g. delivery agreements with suppliers (Akkan, 2015). An important criterion of a schedule therefore is its stability, where stability of a schedule refers to the degree of change in the schedule over time (Meixell, 2005). However, there is always the possibility of disruptions e.g. a change in demand. If a shift in demand occurs this requires the schedule to change in order to meet the demand. If the schedule is not changed it can lead to low service levels or high inventory costs (Pujawan & Smart, 2012). Hence, there is a trade-off between changing the schedule and minimizing costs, and maintaining schedule stability.

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Keeping the schedule sufficiently stable then refers to keeping the deviation between this baseline-schedule and the baseline-schedule after a promotion to a minimum. Within the scope of this paper there is a change in demand which is known at a certain point in time before it happens. The change in demand occurs as a result of action taken by the marketing department and is defined as a promotional activity. Promotion activities can have the effect of increasing demand or shifting the demand profile in time (Dickersbach, 2006), and can be seen as all activities promoting customer purchase (Gilbert, 2003). This increase in demand stemming from promotions is a good way to increase profits (Giri, Bardhan & Maiti, 2013).

The change in demand as a result of promotions, together with the fact that the specifics of promotions are prone to change even shortly before they are executed, drives manufacturers to incorporate shorter lead times and higher flexibility in their production process (Younes, 2012). In addition to this, manufacturers often operate under limited capacity. Adebanjo and Mann (2000) argue that because of this limited capacity, the increase in demand caused by promotional events is one of the greatest causes of manufacturing inefficiencies, stock surpluses or shortages, and poor customer service. From the above several important aspects can be derived, namely; schedules can be seen as the basis for planning other activities e.g. agreements with suppliers, customers or allocation of resources (Goren, Sabuncuoglu & Koc, 2012) and promotional activities are an important way to boost demand and through this profits. However, this increase in demand creates the need for the schedule to change in order to minimize cost, while at the same time these changes should be kept to a minimum in order to maintain schedule stability thus creating a trade-off. Even though separately scheduling and promotions are extensively discussed, there is no scheduling on the trade-off which arises as the result of a promotion. Hence, this clear gap needs to be addressed and this thesis will attempt to find a solution to this management problem by answering the following research question:

How can changes in demand caused by promotional events be incorporated into an existing schedule whilst keeping the schedule sufficiently stable?

2. Literature review

The literature review provides the context in which this thesis takes place. It will do this by first giving an overview of scheduling in general followed by scheduling in the process industry. In addition, the concepts of promotions and schedule stability will be explained.

2.1 Scheduling

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to choose and the result is a schedule which specifies what to do, when to do it and in what order it should be done (Bendoly et al., 2015). Aytug et al. (2005) discuss the different formulations of production scheduling, and state that these typically include assignments of scarce resources to different tasks over a period of time in order to optimize a form of system performance.

The research in this thesis takes place in the process industry, which differs in characteristics from discrete industries. The process industry consists of both continuous and batch production systems which usually produce a limited variety of products in large volumes (Kallrath, 2002). The production of these products is associated with high costs e.g. setup-costs, inventory costs and energy costs. In addition, these large volumes are usually produced under limited capacity and because of the high costs the profit margins on products are low (de Matta et al., 1994). Hence, an important objective of scheduling in the process industry is the minimization of costs. The aim of this research is to look at the scheduling problem of a single production line on which multiple products are produced which can undergo a promotion. In scheduling literature there are several models which look at scheduling problems on single facilities. Chatavithee, Piewthongngam and Pathumnakul (2015) look at a single-machine scheduling problem where multiple concurrent jobs are scheduled under limited capacity. Additionally, Herr and Goel (2016) created a model for single machine scheduling which aims at minimizing total tardiness for jobs with a given due date and takes into account the limited capacity of its resources.

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2.2 Promotions

This section outlines the importance of promotions and the influence it has on demand and therefore on production processes. The abolition of trade-barriers, decline of transaction costs and the increasing global competition requires companies to adapt to the environment in which they operate (Baily et al., 2005). Within this increasingly competitive environment supply chains aim to reduce costs and increase their profits. Expanding market demand through promotions is an useful way to enhance the profitability of a company (Giri et al., 2013). Promotions are defined as the activities associated with advertisements, before and after-sale services and repairs, price promotions and full replacements of defective products (Giri et al., 2013). The type of promotion most commonly used by manufacturers to increase sales are price promotions (Srinivasan, Pauwels, Hanssens & Dekimpe, 2004).

Promotions are instigated by the marketing department in order to boost demand. This change in demand requires the production department to adjust the schedule. In scheduling literature there is a similar phenomenon which requires the schedule to change in order to meet the demand, which is known as seasonality. However, even though both promotions and seasonality influence demand their characteristics are different. Seasonality follows a calendar and is repetitive. In addition, the information about when the effects occur is known long beforehand at the production department (Hopp and Spearman, 2008). With promotions this is not the case, the moment the promotion takes place is only known when the marketing department communicates this to the production department. Furthermore, promotions do not follow a calendar, usually comprise a shorter time-span and are therefore more disruptive than seasonality effects.

Promotional activities increase profits and help increase the competitive advantage through boosting demand, but the operational costs associated with promotions also rise (Su & Geunes, 2012). As can be seen in the previous section one of the main objectives of scheduling in the process industry is to keep costs to a minimum. In order to optimize the schedule and minimize the costs after a change in demand caused by promotions the schedule needs to change. However, changing the schedule too much can have negative effects on both internal and external operational activities. The next section describes the concept of scheduling stability and shows the importance of maintaining sufficient stability.

2.3 Schedule Stability

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The importance of schedule stability for this research is founded in a schedule constituting the basis for other planning activities (Akkan, 2015) as well as the effect changes have on the labour staff. De Kok and Inderfurth (1997) state that frequent change can negatively affect the overall confidence in the planning ability. In addition, frequently changing the schedule may even result in job dissatisfaction and increase managerial complexity (Hur, Mabert & Bretthauer, 2004). Thus, it is important when changing a schedule to keep deviations from the original schedule to a minimum. When a schedule is instable this is often referred to as “nervousness” in the schedule (Meixell, 2005; Rangsaritrasamee, Ferrel & Kurz, 2004).

However, nervousness refers to changes in the schedule resulting from random disruptions, while in practice many schedule changes come from important actions that are planned e.g. promotions (Meixell, 2005). It is the changes to the schedule that result from these planned changes that this thesis refers to when discussing schedule instability. Goren et al. (2012) state there are two approaches when dealing with disruptions leading to schedule instability; proactive and reactive. The proactive approach starts with finding the optimal schedule and introduces buffers within that schedule in order to deal with possible disruptions. The buffers can consist of, e.g. idle time in the schedule or producing safety stock. This approach is often used in situations where disruptions to the schedule are random and used in anticipation of those disruptions.

The reactive approach is concerned with devising an efficient method to deal with the disruption after they happen (Goren et al., 2012). In the case of this thesis it is a combination of these two approaches that needs to be used. The marketing department communicates the time and duration of a promotional activity together with the expected rise in demand to the production department. The production department then needs to reschedule in order to meet this demand. So the disruptions that occur are in a way random for the production department, they have no influence on when promotions take place. However, they are known some time in advance and thus in most cases there is time to reschedule and use a reactive approach. In the methodology section of this thesis the mathematical formulation of schedule stability will be defined together with a combination of pro-active and reactive approaches to deal with the stability of a schedule.

3. Methodology

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The proposed methodology to find a solution to the research problem is quantitative modelling. Quantitative modelling focusses on building objective models that explain part of the decision making problems that managers face in real-life operational processes (Åhlström & Karlsson, 2008). It is a simplification of these real-life operational processes and shows a causal relationship between variables. The research in this thesis focusses on the process industry. Within the process industry products are produced in high volume continuous or batch processes (Kallrath, 2002). Furthermore, the production processes and keeping of inventories are associated with high costs which results in low margins on products (de Matta et al., 1994). An important aspect of scheduling in the process industry is therefore creating schedules that keep costs at a minimum. Promotions, as can be seen in the previous sections, interfere with the schedules. They require them to change in order to meet demand, which decreases stability, which in turn increases costs and complexity in buyer and supplier relations (Aytug et al., 2005).

The case company, UCC-Coffee, from which data will be used to find a way to keep the schedule stable and accommodate changes caused by promotions, fits within this framework. It is a coffee make- and pack-plant operating in the process industry which uses both continuous and batch production systems. The production facilities at the company include roasters, grinders and several product packaging lines. The coffee is roasted and ground in batch production systems and then packaged by making use of continuous production packaging lines. There are multiple packaging lines which in total produce coffee-products with over 500 different types of packaging. Each packaging line has a number of dedicated products, resulting in each packaging line having their independent scheduling problem. Disruptions to the schedules caused by promotions is a large problem at the company. Multiple times a year the planning departments gets notified by the marketing/sales department that a promotion is coming up within a certain amount of weeks for a specific product. The planning department has no influence on the duration of this promotion or the magnitude of the increase in demand. At the point of this notification schedules have already been created, and in order to meet this new promotional demand rescheduling thus needs to take place. Within the process industry the production plans are usually transformed into schedules depicting the detailed operations over a time horizon of a few days (Kallrath, 2002). At the case-company schedules are created for periods of 2 weeks (10 production days), so for every new 2-week period a schedule is created to accommodate the demand in that 2-week period.

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As discussed the basis for the model used in this thesis is the ELSP model, which aims at creating a schedule for multiple products on a single facility whilst simultaneously minimizing corresponding setup- and holding-costs. In order to do this a schedule will be created based on data provided by the company by making use of the ELSP model. This schedule will be called the baseline-schedule and is thus considered the predictive schedule which is made in advance under the assumption that no disruptions will occur and which is used to guide planning decisions (Aytug et al., 2005). After this a promotion for 1 product will be inserted and the demand of that product will go up. Based on several different policies schedules will be created in order to deal with the promotional demand and these will be compared on both stability and cost. The next section will explain the model formulation, the quantification of schedule stability and the approach used to solve the model.

3.1 Model formulation

The ELSP model used in this thesis to create a schedule is best known as the common-cycle approach, which was first introduced by Hanssmann (1962). The common-cycle (CC) approach assumes that each product is produced only once in a schedule and that all products have the same cycle length. Cycle length is defined as the time between the start of production of product i until the time production of product i starts again. This approach restricts the number of feasible schedules that can be created but at the same time the complexity of the solution is greatly reduced (Hanssman, 1962). Furthermore, next to the ease of its implementation in practice and its simplification of the modelling, it has a major advantage of always finding a feasible schedule if one exists (Torabi, Karimi & Fatemi Ghomi, 2005). A disadvantage of the CC-approach is that the solution found is often not as good as the solutions of other approaches, e.g. basic-period or time-varying lot size approaches (Santander-Mercado & Jubiz-Diaz, 2016). This has the effect that the cost for the solution found through the CC-approach is an upper-bound on the cost of any feasible schedule (Elmaghraby, 1978) and that the cost found through other solutions might be lower. However, Narro Lopez and Kingsman (1991) argue that for instances where setup-times are sequence-dependent and the CC-approach is preceded by finding the production sequence that minimizes the total setup-times, solutions found through the CC-approach may be the best solutions in practice. In addition, the common-cycle approach best fits the situation described at the company, where the planning cycle for which schedules are made consist of 2 week periods and within these schedules each product is also produced only once and setup-times are sequence dependent. The next section provides the assumptions and parameters on which the model is based.

There are n different products and each product is indexed by i, where products thus range from

i = 1,…..n. The demand rates and production rates for each product are known and constant and specified

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For each schedule the amount of positions in which a product can be produced is equal to the amount of products n, each position index is given by j and the positions thus range from j = 1,……n for a given sequence of production. Setup-times between products are known and dependent on the sequence i.e. if a product i is produced in position j the setup-time before production can begin is then dependent on product i in position j-1. Setup-costs are dependent on the setup-time, where the longer the setup-time is the higher the cost becomes. The notation for setup-time and setup-cost is 𝑎𝑖𝑗 and 𝑠𝑖𝑗 respectively where i is the product index and j is the position in the sequence.

Furthermore, each product has a production time 𝑡𝑖, indicating the time spent in production during a cycle and an idle time 𝑢𝑖, indicating the time no production or setup takes place after the production run of a certain product i. In addition, the time in weeks between receiving a notification of the marketing department about an upcoming promotion, and the start of the cycle in which that promotion takes place is given by 𝜔. Furthermore, each product has a start time at which production takes place. The start time of a product is given by taking the cumulative sum of all previous production times, idle times and setup times in the sequence. The start times are thus determined by the previously produced products and dependent on the sequence, thus subscript j is used. In the baseline-schedule are denoted as 𝑆_𝑗0 and the start times in the post-promotion schedule are denoted by 𝑆𝑗. Table 3.1 gives a complete overview of all the model parameters together with a short description.

Table 3.1 - Model Parameters

𝒓𝒊: the demand rate for product i in units per time period.

𝒂𝒊𝒋: the setup-time for product i in position j in time.

𝒑𝒊: the production rate for product i in units per time period.

𝒕𝒊: the time spent in production for product i in hours per time period.

𝒉𝒊: the holding-cost for product i in cost per unit per time period.

𝒖𝒊: idle time for product i after production.

𝒔𝒊𝒋: the setup costs for product i in position j in cost per unit per time period.

𝑻: Cycle time for each product i.

𝝎: Time between notification of a promotion and execution of a promotion in weeks.

U: Total idle time available during a cycle.

𝑺𝒋𝟎: Starting time of production for product i in baseline-schedule

𝑺𝒋: Starting time of production for product i in post-promotion schedule

3.2 Quantification of Schedule Stability

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The importance of schedule stability comes from the fact that a schedule is often the starting point for the planning of different operational activities e.g. delivery of raw material agreements with suppliers, allocation of employees and production material, and due date agreements with buyers (Akkan, 2015; Goren et al., 2012). This is similar to the situation at the case company where there is a need for improvement of the supplier delivery agreements. In addition, they want to decrease the complexity for the planning department and create a more predictable situation for internal operations and logistics. These are all linked to schedule stability, if the moment of production for the different products is known, all operations can become more standardized.

For single-machine production systems there are two ways in which schedule stability is defined in literature. The first measure, which is used in numerous articles (Wu, Storer & Chang, 1993; Hall & Pots, 2004; Akkan, 2015), is to take the sum of absolute differences between pre-schedule (baseline-schedule) start times and post-disruption start times. The aim is then to minimize this deviation in order to maximize stability, thus the measure is in fact a measure of instability. The reason for defining schedule stability in this way comes from the importance of knowing when production takes place for which items. As stated this information serves as the basis for multiple activities e.g. contact with suppliers, delivery agreements, work-shift allocation and material requests. The second measure which is often used is the change in sequence of production (Wu et al., 1993; Hall & Potts, 2004). Maximizing stability here is achieved through minimizing this change in sequence of production. The need for changing the sequence comes from possibilities of disruptions like order cancelations, changes in order priority, changes in release dates or unavailability of raw material (Hall & Potts, 2004). In most of these cases changing the sequence is necessary to provide feasible schedules and measuring stability in the deviation in this sequence is thus appropriate. In the situation modelled in this thesis, there is no possibility of order cancelations or changes in priority and there is no inclusion of unavailability of raw materials. Furthermore, as previously discussed each product is produced exactly once and has a sequence-dependent setup-time which varies between products. Setup-costs are further associated with the length of setup-times. Hence, there is one production sequence which minimizes the total setup-time and thus the total setup-cost. As the aim of the ELSP model is to minimize holding-costs and setup-costs per unit time, it logically follows from this that the sequence which minimizes the setup-costs is thus the optimal sequence in which production should take place.

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al. (1993) also highlight this and state that changing the sequence so that the operation with the shortest production time comes first can in some situations increase stability. However, if a sequence is fixed all the requirements for production become much more predictable. It creates a situation where suppliers know the order in which raw materials need to be delivered making it easier to do this on time. Employees know the order of production and thus always know which setup to do after a production run and planners have one less possibility of change to the schedule decreasing their complexity. A fixed sequence thus provides the first stability in a schedule.

As described above, good delivery agreements with suppliers and allocation of internal resources are important aspects of performance both in literature and for the case company. This is especially true for a common-cycle approach, where it is already known that each product is going to be produced exactly once during a cycle. The order of production is also known through fixing the sequence. Then if the exact times for the start of production for each product are known, with a minimum deviation in that time, it provides the possibility to plan the additional activities more accurately around the schedule.

For the formulation of schedule stability, the definition used by Akkan (2015) is revised to accommodate the situation in this thesis. Akkan (2015) formulates schedule instability as follows; 𝐷̅ = ∑𝑛−1𝑗=1|𝑠𝑗0− 𝑆𝑗|/(𝑛 − 1) where 𝐷̅ is schedule instability, 𝑠𝑗0 is the start time of an operation in the preschedule and 𝑆𝑗 is the start time of an operation after rescheduling. Within the schedule each operation has a release time, a processing time and a due time. The situation is then that first a pre-schedule, or baseline-pre-schedule, is created after which a new operation is inserted and rescheduling is done to accommodate this new operation. All operations are scheduled to be executed on a single machine and the pre-schedule which is created is a finite-capacity schedule which is used for planning purposes as well as reservation of resources and due-time commitments (Akkan, 2015). Rescheduling is done after arrival of a new job but before the execution of the pre-schedule starts, so still in the planning phase. Within the pre-schedule there are then n-1 operations that have been scheduled. After insertion of a new operation and rescheduling there are n operations. The aim of the research is to find a new schedule which accommodates the new operation that is inserted and at the same time maximizes stability, and thus minimizes 𝐷̅, with minimal maximum tardiness (Akkan, 2015).

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However, this does not pose a problem for the adoption of the schedule instability measure, since in the research of Akkan (2015) instability is measured in the deviation of start times of production and due-times and release due-times only serve as constraints for rescheduling. In the research of this thesis they are used for the same purpose, after rescheduling for a promotion all the demand should be met before the end of the planning cycle, so before the due-time. In addition, creating a new schedule to accommodate a rise in demand caused by promotion cannot be done before the notification of this promotion is given, which can be viewed as the release time.

In the situation in this thesis there is no new operation that needs to be inserted, rather there is an existing operation that needs to be extended, namely the production of the promotional product with increased demand. However, this has the same effect, the start times of the production runs will differ, due dates might be violated and the operational activities of the shifts might have to change. This requires rescheduling in order to keep this change to a minimum. There is a slight difference in the adoption of the schedule instability measure which uses n-1 operations. In this thesis there are the same amount of operations in the baseline-schedule as in the post-promotion schedule and the notation of schedule instability then becomes:

𝐷̅ = ∑|𝑆𝑗 0_{− 𝑆} 𝑗| 𝑛 𝑛 𝑗=1

Where 𝑆_𝑗0 depicts the start time of production of a product in position j in the baseline-schedule and 𝑆𝑗 is the start time of production in position j after rescheduling. The objective is then to find a schedules which minimize 𝐷̅ and thus maximize schedule stability while satisfying demand. In addition, next to the stability of these schedules the costs will be taken into account. The approach to address this problem is provided in the next sections together with the policies for which schedules will be created.

3.3 Approach

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Table 3.2 - Model Formulae

1) Production time for product i:

_𝑡

𝑖= 𝑟𝑖 𝑝𝑖

𝑇

2) Total cost function:

𝑇𝐶 = ∑ [𝑠𝑖𝑗+ 𝑇 ℎ𝑖

2 (𝑝𝑖− 𝑟𝑖)𝑡𝑖] 𝑛

𝑖=1

3) Cost per unit of time:

𝐶 = ∑ [𝑠𝑖𝑗 𝑇 + 𝑇 ℎ𝑖𝑟𝑖 2 (1 − 𝑟𝑖 𝑝𝑖 )] 𝑛 𝑖=1

4) Schedule instability:

𝐷̅ = ∑|𝑆𝑗 0_{− 𝑆} 𝑗| 𝑛 𝑛 𝑗=1

5) Total available idle time:

𝑈 = 𝑇 − ∑(𝑡𝑖+ 𝑎𝑖𝑗) 𝑛

𝑖=1

6) Optimal cycle length:

𝑇̂ = √ 2 ∑ 𝑠𝑖𝑗 𝑛 𝑖=1 ∑ ℎ𝑖𝑟𝑖[1 − (_𝑝𝑟𝑖 𝑖)] 𝑛 𝑖=1

In order to create schedules the first thing that needs to be done is to find a sequence for production. This sequence is given by solving a simplified Traveling Salesman Problem (TSP) where each city is a product and each distance is a setup-time between the products (Hanssmann, 1962; Dobson, 1992). Where in the regular TSP the goal is to find the route which minimizes the distance, here the goal is then to find the sequence where the setup-times are minimized. Solving this sequence problem can be done off-line, meaning it only needs to be done once, after which the optimal sequence is determined and the corresponding individual setup-times and costs are given. Once we have the sequence a schedule needs to be found which satisfies demand and maximizes stability. The method proposed for this is to first solve the ELSP problem for the baseline-schedule and then insert idle times after each production. The introduction of idle-times creates a more robust baseline-schedule which is better suited to accommodate changes in demand (Akkan, 2015). After the baseline-schedule is created a promotion will be inserted for one product which increases demand. The ELSP problem is then solved again for three different policies and the schedules created will be compared on both stability and cost.

3.4 Policies

The situation is as follows; first a baseline schedule is made which is depicted by its start times of the different production runs. This is done through first calculating the necessary production time of each product through 𝑡𝑖 =

𝑟_𝑖

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All the additional time left in the planning cycle of 10 days, calculated through; 𝑈 = 𝑇 − ∑𝑛𝑖=1(𝑡𝑖+ 𝑎𝑖𝑗), is then taken as total idle time and spread equally over all the products that are produced, so after each product i there is 1

𝑛∗ 𝑈 = 𝑢𝑖 idle time inserted to deal with unexpected rises in demand. The choice for equal distribution of idle time comes from the assumption that every product has an equal chance of undergoing a promotion. Which product actually has a promotion only becomes clear after the notification given by the marketing department. If this was not the case it would in fact be better to allocate all the idle time available to the product which is expected to undergo a promotion. Leus and Herroelen (2007) show this in their research where they explicitly insert idle time for one job which is expected to have a disruption. They conclude that depending on the size of the idle time buffer that is inserted, significant stability gains can be achieved.

After calculation of the production, setup and idle times the baseline schedule is then created through calculating the start times of each production run. The start time of the first product in the sequence is set at zero, thus 𝑆_𝑗0= 0. Each subsequent start time is then calculated through taking the cumulative sum of all previous production times 𝑡𝑖, setup-times 𝑎𝑖𝑗 and idle times 𝑢𝑖. The next example illustrates this: three products are produced in the sequence 1-2-3. The start times are then 𝑆10= 0, 𝑆20= (𝑡1+ 𝑎1,1+ 𝑢1) and 𝑆30= (𝑡1+ 𝑎1,1+ 𝑢1) + (𝑡2+ 𝑎2,2+ 𝑢2) . The costs considered for the baseline schedule and each of the policies are the holding-costs and setup costs per unit time during the planning cycle in which the promotion takes place. The cost per unit time is denoted as C and calculated through: 𝐶 = ∑ [𝑠𝑖𝑗 𝑇 + 𝑇 ℎ𝑖𝑟𝑖 2 (1 − 𝑟𝑖 𝑝𝑖 )] 𝑛 𝑖=1

After the determination of the baseline schedule a promotion is inserted and policies are chosen to deal with this promotion. The choice for the policies is dependent on several factors; time until promotion takes place, the amount demand increases and the length of the promotion. Each of these policies has their own advantages and disadvantages as well as a degree of stability.

Policy 1. Rescheduling within planning cycle T

The first policy is concerned with rescheduling the promotional demand within the normal planning cycle T and considers 3 possible methods to do this. Policy 1.1 aims to deal with the increased demand by making use of the idle times inserted in the baseline-schedule. This intuitively always the first option which should be looked at. The increase in demand caused by a promotion is denoted as ∆𝑟𝑖. When demand for a product which undergoes a promotion increases with ∆𝑟𝑖 , the required production time of that product increases with ∆𝑟𝑖

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If ∆𝑡𝑖 ≤ 𝑢𝑖 then the promotional demand can simply be produced within that idle time 𝑢𝑖. This has the effect that no rescheduling needs to be done as the additional production time of promotional product i can be filled within the idle time of product i and all subsequent and previous start times of production thus stay the same. However, this policy is only applicable for smaller increases in demand and does not provide a solution for larger increases. If policy 1.1 is not applicable because ∆𝑡𝑖> 𝑢𝑖 two additional policies to reschedule within the planning cycle exist.

Policy 1.2 starts with a recalculation of the required production time for the promotional product through solving 𝑡𝑖 =

𝑟_𝑖+ ∆𝑟_𝑖

𝑝_𝑖 . It then checks if the sum of all the production times plus setup-times is smaller or equal to the cycle time, thus ∑𝑛𝑖=1(𝑡𝑖+ 𝑎𝑖𝑗) ≤ 𝑇. If this is the case the production for promotion can be facilitated within the planning cycle. Policy 1.2 reschedules without new insertion of the idle times. The starting times of production in the new schedule are then calculated by taking the cumulative sum of all previous production times 𝑡𝑖 plus all previous setup-times 𝑎𝑖𝑗. To illustrate this, take an example of 3 products where the sequence is 1-2-3, the start times are then given by 𝑆1 = 0, 𝑆2= (𝑡1+ 𝑎1,1), 𝑆3= (𝑡1+ 𝑎1,1) + (𝑡2+ 𝑎2,2). This method has several advantages; If ∑𝑛𝑖=1(𝑡𝑖+ 𝑎𝑖𝑗) < 𝑇 production of all demand will finish before the end of the planning cycle. This provides several possibilities; spare time at the end of the cycle can be used to produce inventories for products which are expected to get a promotion in future planning cycles. Furthermore, the expected biggest advantage is the savings on labour-cost. If the demand can be produced within less time than the planning cycle it might be possible to leave out shifts and thus save on the labour-cost of those shifts. However, there is a major disadvantage to this approach as well; if there is an additional promotion of another product, or even of the same product or any other disturbance, the entire schedule needs to be rescheduled again because there are no idle times and thus no buffer to accommodate the changes. In addition, start times between this method’s schedule and the baseline-schedule are expected to have a higher deviation, which means supplier delivery moments as well as allocation of resources can be less accurately planned from the baseline-schedule.

Policy 1.3 also recalculates the production time of the promotional product through solving 𝑡𝑖= 𝑟_𝑖+ ∆𝑟_𝑖

𝑝_𝑖 and checks the constraint ∑ (𝑡𝑖+ 𝑎𝑖𝑗 𝑛

𝑖=1 ) ≤ 𝑇 to see if all products can be produced within the planning cycle. If this constraint is met new idle times are then calculated through 𝑇 − ∑𝑛𝑖=1(𝑡𝑖+ 𝑎𝑖𝑗) = 𝑈 and again spread equally over the products through is 1

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One of the main advantages as opposed to policy 1.2 is the expected higher stability of this schedule. The renewed insertion of idle times allows the schedule to better accommodate additional disruptions. As Younes (2012) states promotions can still change even shortly before they’re executed, the inserted idle time which acts as a buffer can prevent having to completely reschedule again if such a change occurs. In addition, the way the schedule works is more similar to the baseline-schedule where each production run is also ended with a certain amount of idle time. Hence, the stability of policy 1.3 is expected to be higher than policy 1.2 because it makes complete use of the planning cycle.

The use of the entire planning cycle whilst providing higher stability also leads to a disadvantage; that of higher costs. If the available idle time is not inserted after each production run but instead is all situated after the production run of the last product in the sequence. It might be possible to leave out shifts at the end of the schedule and thus save on labour-costs. In addition, if the total available idle time

U is so small, that each individual idle time 𝑢𝑖 can only accommodate the absolute minimum of changes. The reason for insertion of idle time, buffering against future changes, becomes obsolete and it might be better to use policy 1.2.The cost per unit time for each of the methods within policy 1 are calculated in the same way as in the baseline schedule, through solving the equation 𝐶 = ∑ [𝑠𝑖𝑗

𝑇 + 𝑇 ℎ𝑖𝑟𝑖 2 (1 − 𝑛 𝑖=1 𝑟𝑖

𝑝𝑖)]. The only difference in the input for this policy is the extra demand for the promotional product.

The outcome of C then provides the cost per unit time during the planning cycle in which the promotion takes place.

Policy 2. Spread out demand over multiple planning cycles

Within this policy promotional demand for a certain product is produced by spreading the additional demand over several planning cycles. This can only be done if the notification 𝜔 given by the Marketing Department to the production department about a promotion that is coming up, is more than 2 weeks in advance (so more than 1 planning cycle). If this is not the case, the planning cycle before the planning cycle with a promotion has already started and it is no longer possible to reschedule. The spreading of demand over multiple planning cycles is done as follows; after it is decided that product i will have a promotion in a certain period the additional demand coming from the promotion is divided by the number of planning cycles it is spread over. Demand is thus spread equally over each planning cycle. Let x denote the number of planning cycles over which the promotional demand is spread. The additional demand to be produced during the planning cycle is then ∆𝑟𝑖

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For the methods within policy 2 the costs per unit time for the demand produced within the cycle with a promotion are calculated using: 𝐶 = ∑ [𝑠_𝑇𝑖𝑗+ 𝑇 ℎ𝑖𝑟𝑖

2 (1 − 𝑟_𝑖 𝑝_𝑖)] 𝑛

𝑖=1 . In addition, there is demand

which is produced before the promotional planning cycle by spreading it over additional planning cycles. The early production of this demand creates a starting inventory at the beginning of the planning cycle with a promotion for the promotional product. Let 𝐼𝑖 denote the inventory of the promotional product at the start of the planning cycle with a promotion. The cost per unit time during the planning cycle with a promotion for this inventory are then calculated through

: 𝑇 ∗

ℎ𝑖∗𝐼𝑖

2 . Adding this to the equation given above, the total cost per unit time for policy 2 then becomes:

𝐶 = ∑ [

𝑠

𝑖𝑗

𝑇

+ 𝑇

ℎ

_𝑖

𝑟

_𝑖

2 (1 −

𝑟

_𝑖

𝑝

𝑖

) ] + 𝑇 ∗

ℎ

𝑖

∗ 𝐼

𝑖

2

𝑛 𝑖=1

The advantage of spreading demand over multiple planning cycles comes from the fact that it reduces the changes made to each individual schedule. The deviation in demand is absorbed by a longer time period making the required changes to the schedule smaller than if it all had to be produced in 1 planning cycle. In addition, because the demand is spread out it is expected that the stability of the new schedule will be higher leading to all the advantages discussed above. However, starting sooner with production also has its disadvantages. It leads to higher inventories, which increases costs and provides greater risks of quality decreases in finished goods. In addition, earlier planning cycles over which the demand is spread out are less flexible in dealing with their own disruptions to demand because they use more of their capacity.

Policy 3. Make use of night-shifts

This policy aims to deal with the promotional demand by inserting night- or weekend-shifts. This policy becomes necessary when the promotional demand can’t be fulfilled within the regular planning cycle and thus violates the constraint ∑𝑛𝑖=1(𝑡𝑖+ 𝑎𝑖𝑗) ≤ 𝑇. If this is the case 1 up to 10 nightshifts can be introduced during production of the product which undergoes a promotion. During each night-shift there are 10 hours of additional available production time (UCC Coffee, 2016). So in the model this is equivalent to an additional day in the Cycle. This provides the opportunity to easily determine how many night-shifts are needed; if 𝑇 < ∑𝑛𝑖=1(𝑡𝑖+ 𝑎𝑖𝑗) ≤ (𝑇 + 1) use 1-nightshift, if (𝑇 + 1) < ∑𝑛𝑖=1(𝑡𝑖+ 𝑎𝑖𝑗) ≤ (𝑇 + 2) use 2-night-shifts, if (𝑇 + 2) < ∑𝑛𝑖=1(𝑡𝑖+ 𝑎𝑖𝑗) ≤ (𝑇 + 3) use 3-night-shifts, up to a total of 10 night-shifts that can be introduced. Night-shifts are first introduced during the production run of the promotional product.

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Then the additional required night-shifts are scheduled to start from the first production day and each night after that up until the required number of night-shifts is reached. The new start times for this policy are then calculated through first calculating the new required production time for the promotional product 𝑡𝑖 =

𝑟𝑖+ ∆𝑟𝑖

𝑝𝑖 . Then calculate the total required production time through ∑ (𝑡𝑖+ 𝑎𝑖𝑗

𝑛

𝑖=1 ) and

determine the amount of necessary night-shifts. Then because the amount of available production hours during a night-shift is equal to the amount of available production hours during a production day, the amount of night-shifts is subtracted from the required daily production time of the promotional product.

After this new start times are again calculated through taking the cumulative sum of all previous production times and setup-times as described above. The biggest advantage of this policy is that even when the notification of an upcoming promotion is less than 2 weeks, so ω < 2 it can still be used to produce the required demand in time for the due-date. However, it brings with it some disadvantages as well; 1) the labour-cost in a nightshift is 150% of the cost of a regular shift (UCC Coffee, 2016), 2) in addition to the increased cost of labour, scheduling night-shifts also has its impact on the wellbeing of employees. Night-shifts can have negative effects on both physiological and psychological health of the workforce as well as negatively impact their efficiency (Costa, 1996). It is for these reasons that it is preferable to have the least amount of night-shifts as possible and to only use this policy as a last resort.

3.5 Experimental design

The data used to solve the model is based on the situation at UCC Coffee. The production line this thesis looks at is called the “Rovema line” and it produces 18 different product families with a total of 151 different products within those families. Setup-times are family related and promotions are instigated for product families and not for individual products.

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4. Results

This section outlines the results of the numerical study. It will do this through first determining the optimal production sequence, followed by creating schedules for several different situations in which promotions can occur. Each of these situations is explained below:

Situation 1: The first product in the sequence undergoes a promotion where demand is doubled. The length of the promotion is exactly 1 planning cycle. The notification by the marketing department is more than 1 planning cycle in advance, thus 𝜔 > 2.

Situation 2: The first product in the sequence undergoes a promotion where demand is multiplied times 10. The length of the promotion is exactly 1 planning cycle and 𝜔 > 2.

Situation 3: The last product in the sequence undergoes a promotion where demand is doubled. The length of the promotion is exactly 1 planning cycle and 𝜔 > 2. This is done as a check to see whether the results are similar to situation 1.

Situation 4: The last product in the sequence undergoes a promotion where demand is multiplied times 10. The length of the promotion is exactly 1 planning cycle and 𝜔 > 2. This is done as a check to see whether the results are similar to situation 2.

Situation 5: The first product in the sequence undergoes a promotion where demand is multiplied times 10. The length of the promotion is 2 planning cycles. In addition, to provide the option of spreading demand over multiple planning cycles the notification by the marketing department is set at more than 2 planning cycles thus 𝜔 > 4.

The reason for applying the promotion to the first product in the sequence and later checking the results with a similar promotion for the last product is as follows; the first product in the sequence has the largest demand rate in the baseline-schedule. This has the effect that increasing demand for this product produces the biggest strain on capacity, thus better depicting situations where a promotion is problematic due to limited capacity.

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Table 4.1 - Production, Demand and Cost Data Product Family Demand rate / day Production rate / day Holding-cost / unit / day Setup-time / min Setup Cost RB01 214 2250 0,0127291 15 20,93 RB02 22 4500 0,0127291 45 62,791 RB03 112 4500 0,0127291 15 20,93 RB04 24 2250 0,0127291 35 48,837 RB05 23 2625 0,0127291 15 20,93 RB06 90 5250 0,0127291 75 104,65 RB09 191 2625 0,0127291 75 104,65 RB10 26 1750 0,0127291 15 48,837 RB11 48 3500 0,0127291 45 62,791 RB12 7 3500 0,0127291 45 62,791 RB13 55 2000 0,0127291 35 20,93 RB18 188 2250 0,0127291 15 20,93

4.1 Determination of the production sequence

The production sequence is determined through solving the TSP for the setup-time matrix given in appendix 9.1. This is the sequence which minimizes the total setup-time of a schedule and through this thus minimizes the total setup-cost. This sequence is set as the optimal sequence. The optimal sequence differs from the sequence currently used at UCC Coffee which can be found in appendix 9.4. Hence, a first possible improvement in terms of minimizing time spent on setups at UCC Coffee could be to change their sequence. Table 4.2 provides the optimal sequence found through solving the TSP, it gives the sequence position and the product produced in that position.

Table 4.2 - Optimal Production Sequence Sequence Position 1 2 3 4 5 6 7 8 9 10 11 12 Product Family RB01 RB04 RB03 RB11 RB10 RB13 RB12 RB09 RB06 RB05 RB02 RB18

4.2 The effect of situation 1 on schedule stability and cost

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Figure 4.1 - Policy Schedules Situation 1: Demand RB01 * 2

What can be seen from the graph is that the start times in policy 1.3 and policy 2.3 appear to be closest to the baseline-schedule. Furthermore, the start times in policy 1.2 and 2.2 differ quite substantially from the baseline-schedule and actually finish days before the end of the planning cycle. The stability of each policy is measured through solving the instability measure 𝐷̅ = ∑ |𝑆𝑗

0_{− 𝑆} 𝑗|

𝑛 𝑛

𝑗=1 , the lower 𝐷̅ is the higher stability is. Table 4.3 gives the outcome of the instability measure. The start times used as input for the instability measure can be found in Appendix 9.2 Table 9.2.

Table 4.3- Schedule Instability Situation 1

Policy 1.2 Policy 1.3 Policy 2.2 Policy 2.3

Schedule Instability 1,750000 0,435925 2,101869 0,217962

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Figure 4.2- Policy Costs Situation 1: Demand RB01 * 2

What can be seen from the bar-graph is that policy 2.2 and policy 2.3 indeed have slightly higher costs per unit of time than policies which satisfy demand within the planning cycle. Thus, based on these costs policy 1.2 and policy 1.3 can be considered the preferable option. However, labour-costs are not considered in this graph, where these might have a considerable impact on the total cost of these policies. Policy 1.2 and policy 2.2 actually finish days before the ending of the planning cycle, providing the possibility to leave out several shifts and thus save on labour-cost.

4.2 The effects of Situation 2 on Schedule Stability and Cost

The second instance of promotion increases demand for the first product in the sequence times 10, thus 𝑟1= 2140. The length of the promotion is again exactly one planning cycle. In addition, the notification received by the marketing department is more than one planning cycle in advance, thus 𝜔 > 2 creating the possibility to spread demand over an additional planning cycle.

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What can be seen from the graph is that each of the policies appear to be very close to each other in terms of start times of production runs. However, they all differ substantially from the baseline-schedule. This can also be seen in Table 4.4, which shows the instability measure for each policy. The start times used as input can be found in Appendix 9.2 Table 9.3.

Table 4.4 - Schedule Instability Situation 2

Policy 2.2 Policy 2.3 Policy 3

Schedule Instability 1,574715 1,961666 1,73804

It is noticeable that for this situation, the difference in stability for the policies is very small. Even though policy 2.3, which was expected to provide the most stable option based on the previous example of a smaller promotion, is actually the least stable in this situation. Its stability comes very close to the other policies. Figure 4.4 shows the costs per unit time for each of the policies. The starting inventory for the promotional product for the policies which spread demand is, 𝐼1= 963.

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Figure 4.4 shows that, for larger instances of promotions the policies which spread demand over an additional planning cycle again have the highest cost per unit time. In addition, it is remarkable that the cost per unit time for policy 3 are slightly lower than the costs in the baseline-schedule. This can be related to the holding-costs, which are not considered during production. The production time for the promotional product is much larger than in the baseline-schedule, which greatly reduces the time spent in inventory for this product. However, the additional cost for the use of night-shifts are not considered in this bar-graph. Considering that 4 night-shifts were needed in policy 3 to satisfy the demand during the planning cycle, each at 150% of the normal labour-cost for a shift. Even though it is not clear what the actual cost of labour for a shift is, it can be assumed that policy 3 is in fact quite expensive to use in this situation.

4.4 The effect of Situation 3 on Schedule Stability and Cost

Within situation 3 the last product in the sequence undergoes a promotion where demand is multiplied times 2, thus 𝑟18= 376. The length of the promotion is 1 planning cycle and 𝜔 > 2, providing the possibility for spreading demand over an additional planning cycle. Since demand can be filled within the planning cycle policy 3 is again omitted in this situation. Furthermore, after spreading the promotional demand over an additional planning cycle the scheduled idle time in the baseline-schedule is sufficient to accommodate the spread out promotional demand. Thus, policy 2.1 can be used in this situation and there is no need for policy 2.2 and policy 2.3. Figure 4.5 gives the schedule start times for the different policies.

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Table 4.5 shows the instability measures for each policy, the start times used as input can be found in Appendix 9.2 Table 9.4.

Table 4.5 – Schedule Instability Situation 3

Policy 1.2 Policy 1.3 Policy 2.1

What can be seen from Table 4.5 is that policy 2.1 is identical to the baseline-schedule and is thus completely stable with an instability output of 0,00. In addition, policy 1.2 has the lowest stability. This is similar to situation 1, where the stability of policy 1.2 also rated low. Figure 4.6 shows the cost per unit time of each policy. The starting inventory for the policies which spread demand over an additional planning cycle is 𝐼18= 94.

Figure 4.6 - Policy Costs Situation 3: Demand RB18 * 2

Again policy 2.1 which spreads demand over an additional planning cycle is the costliest option when holding-costs and setup-costs are considered. Furthermore, policy 1.2 and policy 1.3 are equal in cost per unit of time. However, policy 1.2 again finishes days before the ending of the planning cycle which leads to the expectation of substantial savings on labour-cost.

4.5 The effect of situation 4 on schedule stability and cost

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In addition, there are 3 night-shifts inserted during the production run of the last product in the sequence for policy 3, thus starting after production day 3 in this situation. Figure 4.7 gives the schedule start times for each policy.

The graph shows that the start times for policy 2.3 come closest to the baseline-schedule. In addition, policy 2.2 finishes more than a day before the end of the planning cycle. Table 4.6 shows the instability measure for each of the policies, the start times used as input can be found in Appendix 9.2 Table 9.5.

Table 4.6 – Schedule Instability Situation 4

Schedule Instability 2,535365 1,723333 2.535365

What can be seen from the table is that for larger instances of promotions for the last item in the sequence the difference in stability between the policies is quite high. This as opposed to large promotions for the first item in the sequence where the difference in stability was much lower. Furthermore, policy 2.3 has the highest stability in this situation. This in contrast to situation 2 where policy 2.3 actually had the lowest stability of all the policies. The cost per unit of time of each policy are shown in Figure 8. The inventory for the promotional product at the start of the planning cycle in which the promotion takes place is 𝐼18= 846.

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Figure 4.8 - Policy Costs Situation 4: Demand RB18 * 10

As expected policy 2.2 and policy 2.3 which spread demand over an additional planning cycle have the highest cost per unit of time. However, policy 3 makes use of 2 additional night-shifts at 150% the cost of a normal shift which are not considered in the Figure 8.

4.6 The effect of situation 5 on schedule stability and cost

Similar to situation 2, situation 5 considers a promotion for the first product in the sequence where demand is multiplied times 10, thus 𝑟1= 2140. However, the length of the promotion in situation 5 is 2 planning cycles, thus for 2 planning cycles the demand rate for the first product in the sequence is 𝑟1= 2140. This provides the first problem in scheduling the promotional demand, because it is not possible to spread this demand over 1 additional planning cycles 𝜔 should be more than 2 planning cycles in advance. If this is not the case policy 2 cannot be used and the only available option to satisfy demand is policy 3. Hence, in this situation 𝜔 > 4 in order to make a comparison of the stability and cost of policy 2 and policy 3 for this situation.

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Figure 4.9 - Policy Schedules Situation 5: Demand RB01 * 10, Duration: T * 2

Figure 4.9 shows that, as expected, the start times for policy 3 are the same as in situation 2. However, the start times of policy 2.2 and policy 2.3 are also the same as in situation 2. This comes from the fact that in situation 5 there is twice as much demand spread over 4 planning cycles, as there is demand in situation 2 that is spread over 2 planning cycles. This leads to the same amount of spread out demand in each planning cycle and thus the same schedules. Table 4.7 shows the instability measures, which are thus the same as in situation 2. The start times used as input can be found in Appendix 9.2 Table 9.6.

Table 4.7- Schedule Instability Situation 5

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Figure 4.10- Policy Costs Situation 5: Demand RB01 * 10, Duration: T * 2

What can be seen from the graph is that the costs for each policy 3 are the same during both planning cycles with a promotion. However, the costs for policy 2.2 and policy 2.3 differ between the two planning cycles. This originates from the beginning inventory being higher in the first planning cycle with a promotion, namely 2 ∗ ∆𝑟𝑖

𝑥 . In the second planning cycle with a promotion, part of the earlier produced inventory has already been used to serve the promotional demand in the previous planning cycle. Hence, at the beginning of the second planning cycle with a promotion the starting inventory is ∆𝑟𝑖

𝑥 and thus the costs per unit of time in this planning cycle are lower.

In addition, the costs for the 4 night-shifts used in policy 3 in each of the planning cycles with a promotion are not considered in this graph. It should be noted that the costs for these 8 night-shifts in total are expected to be quite substantial. Table 4.8 provides an overview of the best and worst policy options in terms of cost and stability for each situation. First the policies with the highest stability and lowest stability are considered for each situation, followed by the policies with the highest cost and the lowest cost. If two policies were equal in terms of costs, the policy which finished before the end of the planning cycle and could thus leave out shifts was chosen.

Table 4.8- Stability and Cost Overview Per Schedule

Situations Highest Stability Lowest Stability Highest Cost Lowest Cost

Situation 1 Policy 2.3 Policy 2.2 Policy 2.3 Policy 1.2

Situation 2 Policy 2.2 Policy 2.3 Policy 2.3 Policy 3

Situation 3 Policy 2.1 Policy 1.2 Policy 2.1 Policy 1.2

Situation 4 Policy 2.3 Policy 2.2/Policy 3 Policy 2.3 Policy 3

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5. Discussion

The results show that there are several ways to deal with promotional demand. What can be concluded is that for each situation of a promotion the most stable way to deal with this promotion is to spread demand over one or more additional planning cycles. However, the best method to spread the demand differs per situation.

For smaller instances of promotions, policies which spread demand and made use of idle times provided the highest schedule stability. This can be seen in situation 1 where the first product in the sequence underwent a small promotion and policy 2.3 provided the highest stability after rescheduling. In addition, in situation 3 spreading demand provided the opportunity to use the previously inserted idle times in the baseline-schedule and policy 2.1 could thus be used which provided a completely stable schedule. This shows that for smaller promotions the inserted idle times in the baseline-schedule are able to absorb the change in demand. This is in line with the Leus and Herroelen (2007) who show that inserting moderate sized idle times in the pre-schedule can have significant gains in stability. However, in their research there is an expectation on which operation will be disrupted and thus the total available idle time can be inserted after that operation. In this thesis idle times were distributed equally over the products based on the assumption that there is no expectation on which product undergoes a promotion, and the results show that the inserted idle time is only able to accommodate the smallest of promotions. Nevertheless, this leads to the supposition that if idle times are inserted only for products with expected promotions coming up they might be able to accommodate larger promotions as well.

When costs are taken into consideration for smaller promotions, the policies which spread demand over multiple planning cycles had the highest cost per unit time. However, these costs did not differ so much with the costs in policy 1.2 and policy 1.3 which produced the lowest cost per unit time in these situations. Hence, policies which spread demand and either use idle times from the baseline-schedule or re-insert them provide high stability and the increase in cost is relatively low for smaller promotions. From this it can be concluded that these policies provide the best policies to deal with these instances promotions. Nevertheless, it should be considered that because policy 1.2 finished days before the ending of the planning cycle, creating the assumption that there is a possibility to leave out shifts. Even though policy 1.2 does not provide a very stable option, it will thus expectedly provide a very cost efficient option in situations where promotions are small and there is ample available capacity.

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more stable schedule than policy 2.3. Policy 2.3 provides fairly stable schedules in all situations with a large promotion. Where it is the most stable option in some situations and is close to the most stable option in others. In addition to these results, what can be deducted is that changing the sequence in situation 1 and 5 and scheduling the promotional product at the end of the sequence instead of at the beginning might have produced a lower outcome of the instability measure for policy 2.3 in these situations. This is similar to what Wu et al. (1993) suggest on changing the sequence to produce in an order of shortest production time first. However, the fixed sequence benefits for suppliers in predictability of material deliveries and repetitiveness work for employees would have been lost and it is thus unclear if changing the sequence and lowering the instability outcome would have actually provided more stability in this case.

Taking costs into consideration, the cost per unit time of both policy 2.2 and policy 2.3 are much higher than those of policy 3, sometimes even reaching twice the amount. So even though policy 2.3 provides the most stable option, this thus comes at substantially higher cost. In two situations with larger promotions policy 3 provided the schedules with their level of stability in between the other two policies and in one situation it had the lowest stability together with policy 2.2. The cost per unit time of policy 3 for these situations were substantially lower than those of policies which spread demand over additional planning cycles. This leads to considering policy 3 as the preferred option, where its stability is average and the cost per unit time are substantially lower. However, the cost per unit time only consider holding and setup costs. The labour-cost of night-shifts used in this policy are not taken into consideration in the calculation of these costs. For UCC Coffee these costs are set at 150% of the normal labour-cost for a shift, which is similar to other coffee producers e.g. Douwe Egberts where night-shift labour-costs are set at 135% the cost of a normal day shift (UCC Coffee, 2016; Douwe Egberts, 2016). This makes it possible that even though the cost per unit of time are lower, the additional cost of night-shifts might be so large that these will nullify the outcomes on cost per unit of time.

The effects of promotions on schedule stability in the process industry