Production planning in a batch oriented chemical plant in China

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Production planning in a batch oriented

chemical plant in China

A study for DSM

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B.J.J. Schiphorst

Groningen, October 12, 2011

Master’s thesis Econometrics, Operations Research and Actuarial Studies University of Groningen

Supervisor: Prof. dr. G. Sierksma

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Abstract

Jinling DSM Resins (JDR) is a chemical company in Nanjing, China. JDR produces com-posite resins, which are used together with glass fiber to build, among others, boats and windmill blades. The Chinese market is rapidly expanding, so demand is high. Therefore, JDR wants to improve the capacity of its chemical plant.

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Foreword

This is my master’s thesis which concludes my study of Econometrics, Operations Research and Actuarial Studies at the University of Groningen, The Netherlands. The study of my thesis was carried out at Jinling DSM Resins in the city of Nanjing, China, where I worked for six months as an intern in the Purchasing Department, forecasting prices of raw mate-rials, and in the Demand and Supply Chain Department, modeling the production line to optimize the production process.

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CONTENTS CONTENTS

1 Introduction

1.1 Jinling DSM Resins Co. Ltd.

ddddddddddd or in English, Jinling DSM Resins Co. Ltd. (JDR) is a chem-ical company in Nanjing, China1_. _{It is a successful joint venture between DSM}2 _and

SINOPEC3. JDR produces composite resins, which are used as raw material in the Fiber-glass Reinforced Plastics market. Composite resins are often used together with Fiber-glass fiber and its main applications include, among others, the automotive industry and the public transportation sector, pipes, boat hulls, and, in rapid development, windmill blades. JDR has over 150 dedicated employees and has an annual production capacity of circa 35 mil-lion metric tons. During 2007 the company substituted its last Dutch general manager by a new Chinese one, making the company totally Chinese-run. The Chinese market is rapidly expanding[17], so demand is high. More often than not, demand is higher than the available production capacity. Therefore, JDR continuously wants to improve the capacity of its chemical plant.

Figure 1: Wind energy is a major growth area for reinforced plastics in China. China more than doubled its total installed capacity in 2006[18]. This is a LM Glass fiber’s wind turbine blade factory. (Picture courtesy of LM Glass Fiber.)

One could argue that it is easy enough to expand the current production site to increase the capacity. However, there are two reasons why it is better to push the limits of the current facility. First, any company will always want to get the highest return on invested capital. Building a production site requires a substantial investment, which is effectively a fixed cost. Making a higher turnover without investing more will thus increase profit, which is simply good business practice. Secondly, JDR’s production site is housed in a chemical industrial area just outside Nanjing city. As not only Chinese markets but also Chinese cities are rapidly expanding, this industrial area is meant to become a residential area in the near future. All the industries in the area will likely have to move, probably

1_{www.jdr.com.cn}

2_{Dutch State Mines,}_www.dsm.com

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1.1 Jinling DSM Resins Co. Ltd. 1 INTRODUCTION

within a time period of the next five to ten years. This uncertainty about future housing keeps JDR management from making big investments in their current production site, as it would not fit in DSM’s highly valued Sustainable Development Policy4.

Figure 2: The factory of JDR in the chemical industrial area just north-east of Nanjing city, as seen from its office location.

The production line is rather complex. There are several stages, each with a number of parallel machines. Each product has a different production time on each machine. Simul-taneous arrival of multiple products at a single machine causes bottlenecks. It is the role of the production planner to plan all the jobs on the machines such that the demanded finished goods are produced within the boundaries of the production capacity. Most fin-ished goods are combinations of several semi-finfin-ished products. The planner will have to consider the production capacity and readily available stock for each of these semi-finished products. The planner has to decide what product will be made by what machine, con-sidering different production times per product per machine. For each machine, he also has to schedule the sequence in which the products are produced, taking into account the cleaning times between products and the possibility of conflicts between machines, which may cause waiting times. Conflicts arise in bottlenecks, where multiple machines flow into fewer machines and waiting times occur. The horizon for each production planning can vary from week, month, to year. Most production plans will be based on a monthly hori-zon, but sometimes emergency orders need to be scheduled within days and for budgeting purposes longer horizons of up to a year are needed.

The production planning is presented as a Gantt chart, in which the production sequences for every machine are depicted over a time axis. Gantt charts are a type of bar-chart that illustrate the start and finish dates of each job per machine. See figure3 for Example 1 of

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1.1 Jinling DSM Resins Co. Ltd. 1 INTRODUCTION

a Gantt chart. In the Gantt chart in figure 3, we see three stages I-III, with in total five machines on which Products A through G are being produced. The horizontal timeline ranges from Monday 00:00 AM to Wednesday 04:00 AM. There are two machines in Stage I (Machines I-1 and I-2), two in Stage II (Machine II-1 and II-2), and one machine in Stage III (Machine III). Products A and B are semi-finished products that are combined into Product A+B. There is a cleaning time between Product A and Product C in Machine I-1. Not all products need to be processed on all machines, as Product D skips Stage II. We observe a number of bottlenecks. Product B is finished on Machine I-2 on Monday 8 AM, but has to wait four hours until Product A is finished on Machine II-1 before it can flow into Machine II-2. This creates idle time for Machine I-2. Similarly, Product G has to wait four hours on Machine II-2 before it can flow onto Machine III.

Figure 3: Gantt chart corresponding to Example 1.

JDR currently has over nine hundred different products that they sell to over nine hundred customers. Resins may have variations in properties, such as fire retardancy, elasticity, uv-light resistance, chemical resistance, or electricity isolation. New recipes for resins are constantly developed to suit specific customer needs. These new recipes are developed by DSM research centers in Europe5 and Shanghai. DSM has global pricing schemes and strategies, thus JDR has little influence on the price. All they can control is the quantities of each resin they sell. This means that the product portfolio continuously changes and JDR wants to know how it can manage its product portfolio in order to maximize profit. The sales department has some power over the volumes of the products. As demand is often higher than capacity, some orders go forlorn. The sales team can decide on which orders to accept, based on the margins on the products. Currently, the sales department measures the margins on their finished goods per metric ton. However, doing so indicates a big gap between the sales department and the production department, since the production times of the resins can vary substantially. This means a resin with a low production time is of much more value than a resin with a high production time, if they have similar margins per ton. The problem lies in the complexity of the production process and the amount of

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1.2 Problem formulation 1 INTRODUCTION

confidential information that is necessary to bring the sales and production departments closer together. The margins are confidential information and are shared only with specific management team members and definitely not with the production team. The production times and recipes are also confidential information, but that is kept only by the production team.

1.2 Problem formulation

In this thesis we will consider ways to model the full production process in detail. Ideally we want a model that, given the demand for finished goods for the next time period, makes the production planning decisions such that the output of the plant is maximized by minimizing the bottlenecks that occur between machines as well as the various production and cleaning or switchover times, and outputs a full production planning overview, in the form of a Gantt chart.

1.3 Outline

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2 THE PRODUCTION PROCESS

2 The production process

In order to be able to model the production process, we first need to know and understand the process itself. This chapter describes the production process in detail. We will begin by describing the outlay of the production line. Then we will go into the production process through the various stages of the line. We will also discuss the cleaning process and some other issues. The details of the production process are very sensitive business information and therefore all information in this chapter is considered confidential and protected by professional secrecy. No part may be copied without written consent from DSM N.V.

2.1 Outlay of the production line

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2.1 Outlay of the production line 2 THE PRODUCTION PROCESS

Figure 4: Schematic overview of the entire production line.

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2.2 Producing in batches 2 THE PRODUCTION PROCESS

Figure 5: The entrance to JDR’s production plant.

2.2 Producing in batches

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2.3 Cleaning 2 THE PRODUCTION PROCESS

Once a batch is processed by a reactor and a blender, we have a basic resin (BR). Some basic resins are sold as such and need not be processed by a mixer. Thus, out of the blenders they will immediately be poured into drums, or into one of the storage tanks for later drumming. The basic resins which are sold without further processing are called con-densation products. Any product that is ready to be sold is called a finished good (FG). Thus, condensation products classify as finished goods.

Each storage tank can only be used for one specific basic resin at a time. If one would want to change the type of product in a storage tank, the tank has to be cleaned thoroughly, to prevent contamination between resins which would diminish the quality of the product. Therefore, the storage tanks are invariably used for the six most produced basic resins. The resins that must pass through the mixers before they are a FG are called modifi-cation products. These require the modifimodifi-cation of one or more basic resins in a mixer, sometimes even with the addition of extra raw material. Thus, FG are either condensation products or modification products. Of the basic resins that are condensation products, many are also the input for a modification product. So the inputs of the reactors are only raw materials, while the possible inputs of the mixers are raw materials, BR coming directly out of a blender, BR coming out of a storage tank, and BR coming out of drums. Similar to the reactors and the blenders, a mixer can only be filled with a new batch once the mixer is completely empty. Note that some of the blenders are bigger than the mixers. This means that not a whole batch of basic resin can immediately be processed by a mixer, once it is finished in a blender. Then, (part of) the batch will first have to be poured into drums and wait in the warehouse, or, if possible, wait in a storage tank. If the drumming lines are busy and there is no storage tank available, the product will have to wait in the blender until either a drumming line, storage tank, or mixer becomes available.

2.3 Cleaning

In between batches, reactors sometimes need to be cleaned. Whether or not cleaning is necessary depends on the contamination between the batches. As an example, consider producing black paint after producing white paint. This is possible without cleaning, as white paint does not contaminate black paint. However, to produce white paint after black, cleaning will need to be done, as the white paint will be contaminated by the black paint. Cleaning a reactor is done by running the reactor boiling with a special resin, namely P65. The cleaning time is equal to the standard batch processing time of this resin, in the specific reactor. Normally, this resin is sold as a high quality resin, but using it to clean a reactor deteriorates its quality and the resin is sold at a lower price under the product name 999A.

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re-2.4 Demand 2 THE PRODUCTION PROCESS

actor. This is because this way less of the high quality P65 resin is wasted by cleaning it, since one batch in this reactor is only 10 MT, whereas it is 20 MT in any other reactor. In between any two batches a small amount of switchover time will be necessary, but this time mainly depends on the available manpower and raw material. So these common switchover times are not dependent on the order in which products are produced.

2.4 Demand

Before the production planner can make the production planning for the next period, he must know what to produce. Most of the planning is done over time periods of one month. The demand for the various products in the next month is never exactly known. The sales department makes a monthly forecast for the demand for finished goods every two weeks, so it is a rolling forecast. Part of the total production is produced to stock (PTS), based on the demand forecasts. Part of the production is produced to order (PTO), based on direct orders for customers. Some orders may come as high priority emergency orders, where the product is demanded within a matter of days. So express orders have to be manufactured that have to be planned in as soon as possible. JDR has a customer rating system with five levels. The higher the level of a customer, the more JDR will want to accommodate them by accepting emergency orders. The sales department only communicates demand for finished goods, which the production planner then has to calculate back into demand for basic resins and modification resins, using the recipes.

One might wonder what the effects on the market are as JDR is changing its product portfolio. Having some power over sold quantities but little over sales prices raises ques-tions about market power and the strategies companies use to influence the markets and increase their market share, as is the case in Cournot competition[8] and similar in price competition[5]. However, such game theoretic considerations fall outside of the scope of this thesis and we will take the markets as given in their current form.

2.5 Other production issues

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2.5 Other production issues 2 THE PRODUCTION PROCESS

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3 MODELING THE PRODUCTION LINE

3 Modeling the production line

Now that we have a clear picture of how the production line is laid out, we will seek to formulate a general model in mathematical terms. In this chapter we will seek to formulate a mathematical model of our production line with all its specific properties and constraints.

3.1 Flowshops

We propose to model the production planning problem as described in chapter two as a Hybrid Flexible Flowshop (HFFS) scheduling problem. A Flowshop (FS) scheduling prob-lem is defined as the probprob-lem where n jobs have to be scheduled on m serial machines. Each job has to go through all the machines in a fixed order. A machine can only process one job at a time. Jobs typically do not have identical processing times on every machine, and each machine typically does not have the same processing time for each job. Usually the objective is to minimize makespan, which means to produce a given set of jobs in the least amount of time. Often in these problems there are sequence-dependent setup times between the processing of two jobs on a machine. These are cleaning times or machine setup times that are dependent on both the previously finished job as well as the job next to be produced. There can also be machine-dependent setup times.

A Hybrid Flowshop (HFS) is a generalized version of the original flowshop, that con-sists of several serial production stages, where every stage has one or multiple parallel machines. Some stages may have only one machine, but at least one stage must have mul-tiple machines. Every job has to go through the stages in the same order. So a flowshop is a specific case of a hybrid flowshop with only one machine in every production stage. Machines within each stage can be identical or unrelated. Finally, a Hybrid Flexible Flow-shop is a further generalization of the HFS in which some jobs may skip a stage.

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3.2 Objective function 3 MODELING THE PRODUCTION LINE

3.2 Objective function

Other objective functions for scheduling problems have also been considered in the liter-ature, such as minimizing tardiness or weighted tardiness, and scheduling with earliness and tardiness penalties. One can imagine that each job has a due date, by which time it needs to be finished, otherwise the customers will become dissatisfied. Jobs that are not completed before their due date are tardy. If the due date of each job i ∈ N is defined as Di and the completion time of each job as Ci, we can define the tardiness of job i as Ti := max(0, Ci − Di) and total tardiness as ¯T =

Pn

i=1Ti, where n denotes the total number of jobs. Minimizing total tardiness would then be a way to maximize customer satisfaction. Weights Wi can be assigned to each job, depending on the profitability of the job and/or the importance of the customer. Now total weighted tardiness can be defined as ¯TW ₌Pn

i=1WiTi, and minimizing the weighted tardiness gives the production planner the flexibility to prioritize certain jobs. One can also imagine that if a job is finished before its due date, it will invoke a cost to the company, e.g. when it has to be stored in a ware-house. These jobs are called early. The earliness Ei of a job can be defined in a similar way as the tardiness by Ei := max(0, Di− Ci). If storage is expensive, early completion of a job will be unwanted, and earliness weights can be assigned to each job depending on the cost of storage. This way one may want to use a combined earliness/tardiness objective which relates the value of customer satisfaction to the cost of storage. The notion of us-ing earliness/tardiness objective functions is know as just-in-time modelus-ing. The weighted just-in-time objective function is defined as J ITW ₌Pn

i=1(αiEi+ βiTi), where αi and βi are appropriate weights for earliness and tardiness, respectively.

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3.3 Scheduling constraints and assumptions3 MODELING THE PRODUCTION LINE

recipe of a number of basic resins, and given the complexity of the production line with the different production times per machine and the arising bottlenecks, there is no clear way how to calculate these. So we will continue with the makespan objective, bearing in mind that it is useful to run sensitivities on the overall profit per hour that different sets of jobs can generate. We also note that for a more advanced study, the involvement of multiple objectives should be considered.

3.3 Scheduling constraints and assumptions

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to a different job, and finish processing the first job at a later time. Thus, the machine will still only be processing at most one job at any given time. We will set the produc-tion time for a job in our combinaproduc-tion machine equal to the producproduc-tion time of the job in the reactor, and define a lag variable to make the job wait such amount of time as is required by the blender. Note that this modeling trick only works as long as the longest processing time in the blenders is shorter than the shortest processing time in its reactor. Only then will the blender always be empty when a job is finished in the reactor, so it can immediately flow through into the blender, and the blender will never create a bottleneck.

Figure 6: Reactors and Blenders in Gantt chart.

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be fixed in the model by assuming a number of identical parallel storage tanks, effectively increasing the volume capacity.Another general aspect of such storage could be that jobs can only be held temporary before they go bad, as can be imagined for perishable goods. Resins also have a finite ’shelf lifetime’, as it is called. This could be accounted for by assuming earliness penalties on the production or completion time of jobs, and modeling a minimal weighted earliness objective. As the shelf lifetime of most resins is quite high, we will leave this outside the scope of this paper. So we assume resins can be stored indefinitely. Between any two jobs in the first stage there are sequence dependent non-anticipatory setup times. These are needed for the cleaning which was described in section 2.3. Note that the storage tanks in the second stage will not suffer cleaning times because each stor-age tank only services one type of product, which is accounted for through the eligibility of the tanks. The mixers and drumming lines also do not require sequence dependent setup times, other than a small amount of switchover time, which occurs between any two jobs regardless the sequence.

Stage three of the flowshop then, would be the mixers, which have machine eligibility. Not each mixer can produce every modification product. In the first stage there is, in the-ory, no machine eligibility. In practice, however, certain reactors have never been used to produce certain products, for reasons described in the aforementioned section on cleaning. Some products are always produced on a specific reactor, even though in theory any reactor can produce any basic resin, and we therefore do not have to assume machine eligibility in the first stage for the type of product. The drumming lines also have machine eligibility. In some cases this depends on the type of product (in the case of gelcoats and LPA resins), while in others this depends on the type and size of drum required. With the drumming lines as fourth stage, we have our complete production line.

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3.4 Formulation of a Hybrid Flexible Flowshop model3 MODELING THE PRODUCTION LINE

one in a similar fashion as we proposed for the storage tanks. We would then model seven reactors instead of the actual four, and each large 20MT reactor would be represented by two smaller 10MT ones. This poses an issue because we then require constraints such that each virtual reactor pair produces everything exactly synchronous. We choose to define per job the size of the batch as well as the packaging. We then have that each small job (10MT) can be processed on any of the four reactors, but big jobs (20MT) can only be handled by the three big reactors. Note that this represents a shortcoming of the model vs. reality. In reality, it is possible to split jobs. One can produce a batch of 20MT in one of the three big reactors, then flow 10MT of that batch into a storage tank, 5MT into a mixer and 5MT into drums via the drumming lines. Such a situation is impossible in our model. Also, the modeling of the storage tank will be suboptimal. We have three big storage tanks with a capacity of 400MT and three small storage tanks with a capacity of 200MT. If we model our virtual parallel storage tanks to be of 20MT size, we will ’lose’ storage capacity for each small 10MT batch we store. Such a small batch will use 20MT of storage capacity in our model, while in reality it only occupies 10MT. Unfortunately, we see no better way to address this issue, and we will therefore model the storage tanks in parallel machines of 20MT capacity, resulting in 90 virtual parallel machines.

3.4 Formulation of a Hybrid Flexible Flowshop model

Flowshops scheduling problems of any kind can be defined using the 3-field problem classi-fication α |β| γ, which was introduced by Graham et al. in 1979 [12], and further extended to encompass Hybrid Flowshops by Vignier et al. in 1999 [43]. In this notation, the α field denotes the layout of the shop, including the number of stages and the number and type of machines. It is composed o four parameters α1,α2,α3, and α4. α1 indicates the general configuration, in our case a hybrid flowshop. α2 notes the number of stages in the shop. α3 and α4 describe the machines in the shop, with α3 ∈ {∅, P, Q, R} indicating the type of machines in each stage and α4 the number. α3 = P means identical parallel machines, α3 = Q indicates uniform parallel machines and α3 = R represents unrelated parallel machines. α3 = ∅ is the case where there is only one single machine in the stage. Thus, a simple number m would denote a number of identical serial machines, indicating a classic flowshop problem, while P m1, Rn2 would denote m identical parallel machines in stage one, and n unrelated parallel machines in stage two. The second field β denotes the job characteristics, including all constraints and assumptions. The last field γ denotes the objective function. In our case, we want to minimize the total completion time of all jobs, which corresponds to minimizing the maximum completion time, which is the com-pletion time of the last job. Let Ci denote the completion time of job i. We then have Cmax:=maxi∈{1,..,n}{Ci}.

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3.4 Formulation of a Hybrid Flexible Flowshop model3 MODELING THE PRODUCTION LINE

might skip stages, but they move unidirectionally. Each job j, j ∈ N , has to visit a set of stages Fj, Fj ⊆ M (Fj 6= ∅). Let the processing time of job j on machine l, l ∈ Mi in stage i be denoted pilj. These processing times are dependent on the machine and the job as we have unrelated machines. If a given job j skips stage i (i /∈ Fj), then pilj = 0, ∀l ∈ Mi. Note that this is not sufficient to tackle the issue of flexibility. Suppose we model in such a way that jobs have to be virtually processed in stages they could (and should) skip, with a corresponding processing time of zero in this stage. It may not take any time to process such a job, but a machine in that stage will still need to be available to process it. This means a job may need to wait for a machine to become available, thereby inducing an idle time in the machine it is occupying. This is not desirable, as in real life the job will pass over this stage without caring about the availability of its machines because it has no business with them. The job may however have to wait for a machine in the next stage to become available. We further consider the following constraints for our hybrid flexible flowshop, also treated in Ruiz et al. (2007 and 2008)[41],[42].

• Rmil is the release time for machine l, l ∈ Mi in stage i, i ∈ M . No jobs can be scheduled on machine l before Rmil.

• Eij ⊆ Mi is the set of eligible machines that can process job j in stage i. We define pilj = 0 if l /∈ Eij. Note that we must have Eij 6= ∅ if i ∈ Fj.

• Pj ⊂ N indicates the set of predecessors of job j. We cannot start processing job j before all jobs in Pj are finished. This relates to the fact that we need combination of basic resins to produce some finished goods. Note that all precedence constraints define a directed, a-cyclical graph between jobs. Otherwise we enter the situation where job j needs to be finished before job k, which in turn needs to be finished before job j.

• Siljk denotes the sequence dependent setup time, required if we want to process job k, k ∈ N after job j, on machine l in stage i. This sequence dependent setup time is independent of processing times. We assume only non-anticipatory setup times, so job k does not have to be at the machine for setting up. Note that Siljk = 0 when any of the following conditions apply: j = k, k ∈ Pj, i /∈ Fj, i /∈ Fk, l /∈ Eij, l /∈ Eik. • Lilj serves as a variable that models the time lag for job j at machine l between stage

i and the next stage it visits. After the reactors we have a time lag because this is the time needed by the blender to process the job. We will therefore only have Lilj > 0 for i = 1, and zero otherwise.

Our problem can now be formulated in the following way:

F H4, R41, R902, R53, R54 |skip, Rm, Ej, prec, Ssd, block, lag| Cmax.

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3.5 Computational complexity 3 MODELING THE PRODUCTION LINE

parallel machines (by the ”R” notation) in each stage. In the second field we indicate the constraints: jobs may skip stages, machines have release times, each job has a set of eligible machines, there are precedence constraints among jobs, sequence dependent setup times, jobs cannot wait between machines as there is no buffer but rather jobs block the last machine, and lag. The third and final field denotes the makespan objective.

Unfortunately, our problem at hand is much more complex than most flowshop problems. Gourgand et al. (1999) [11] showed the total number of possible solutions for a HFS with n jobs, m stages and mi machines in stage i to be n! (

Qm i=1mi)

n

, which is much larger than the n! possible solutions to a regular flowshop problem. The addition of characteristics such as precedence constraints, machine eligibility, preemptive processing, skipping stages, and sequence dependent setup times, might decrease the amount of feasible solutions, but will not simplify the problem. It may even become more difficult to find a feasible solution to start with.

3.5 Computational complexity

We say that an optimization problem is polynomially solvable or solvable in polynomial time if there exists an algorithm A which outputs the optimal solution given n problem inputs, and there exists a polynomial p such that the execution of A always takes p(n) steps. In practice we like this property because it often means we can compute the optimal solution in real-time on a computer. There are many problems for which we do not know if there is an algorithm that finds the optimal solution in polynomial time, but for which we can verify a given solution to be optimal (or not) in polynomial time. We call this class of problems the class NP (non-deterministic polynomial time). NP-hard is a class of problems that are, informally, ”at least as hard as the hardest problems in NP”. It has never been proven that NP-hard problems can be solved in polynomial time. Basically, this means there is currently no algorithm that can find the optimal solution to any problem that is NP-hard in real-time.

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3.5 Computational complexity 3 MODELING THE PRODUCTION LINE

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4 LITERATURE

4 Literature

In order to select an appropriate modeling technique that can be applied to solve our problem at hand, it is necessary to know what types of models are used for this kind of problem. In this chapter we will review the latest research that is done in the field of scheduling jobs in hybrid flowshops as the one we have just described.

4.1 Theory and practice

As mentioned in the previous chapter, substantial research has been done in the field of flowshop scheduling. Given the fact that most flowshops are NP-hard, there is no easy way to find the optimal solution to the problem. In our quest for a practical application to solve our problem, we must distinguish between research which is focused on the theory of scheduling and research done on finding practical solution systems. The more theoretic pa-pers often focus on proving the order of computational complexity of flowshops, such as the papers referred to in paragraph3.5. Others look for lower bounds on the objective function. These papers typically describe very general flowshops with identical machines and without many constraints. Koulamas and Kyparisis [24] derive the best available worst-case ratio bound for the three stage flexible flowshop with the makespan minimization objective (de-noted as F P 3 || Cmax). The result is an improvement on Soewandi and Elmaghraby [38], and is further applied to the l-stage generalization of the problem (F P l || Cmax), but only where l is odd.

Unfortunately, despite the great amount of research done in the field of flowshop schedul-ing, there is still a noticeable gap between theory and practice in this field, as was noted in [26] and [42]. Overall, the majority of the research done in this field focuses on one or several specific properties of the flowshop, or one particular constraint. Most studies are concentrated on problems with identical machines, as was noted by [20], giving a number of examples. The hybrid flowshop was introduced in 1971 by Arthanary and Ramaswamy[3], who proposed a branch and bound algorithm for a hybrid flowshop with only two stages. Many papers concern simplified cases of the HFS with only two or three stages, as was also noted by [44], who knows of only six studies regarding unrelated parallel machines with multiple stages, of which only three take into account sequence dependent setup times. The multistage HFFS has not received a great deal of attention in terms of finding a practical solution. Particularly as the number of stages increases the complexity increases. A recent survey on hybrid flowshop scheduling done by Linn and Zhang [26] only notes one paper which focuses on the three-stage situation, and only one paper that handles the multi-stage (more than three) situation with parallel non-related machines in each stage. Even though the developed heuristics for these type of problems look promising in theory, it is difficult to develop a heuristic for a practical problem. This is mainly due to the large number of constraints we encounter in practical situations as the one we face.

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fo-4.2 Exact algorithms 4 LITERATURE

cus on relatively simplified instances of the problem with a limited number of constraints. There are many researchers competing in finding ’better’ heuristics for certain flowshop problems, in the sense that these heuristics operate in a lower time complexity, generally find better solutions, or have better worst case performance bounds. Slowly but surely we do notice the gap between theory and practice becomes smaller as the focus moves more and more toward increasingly complex, multi-stage, multi-constraint models. Below we will discuss a number of practical techniques used to solve HFS problems.

4.2 Exact algorithms

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4.3 Heuristics 4 LITERATURE

point where it is realistically applicable, as they are still incapable of solving medium to large problems. We will therefore switch our attention to heuristics.

4.3 Heuristics

To find a good enough solution we will explore a number of heuristic methods. These are techniques that apply common sense or rules of thumb to quickly find a decent solution. However, optimality of the solution is in no way guaranteed. Exact algorithms will stop calculating once the optimal solution has been reached, but heuristics can always keep looking for possible improvements, as there is never a guarantee that the optimum has been found. Therefore heuristics typically have a built-in stopping criterion, be it a number of iterations, the (lack of) relative improvement in solutions obtained or simply computing time. We will describe a number of heuristic methods below.

4.3.1 Dispatching rules and constructive heuristics

The simplest type of heuristics are dispatching rules, which are typically used to find a first feasible solution from which to start, after which improvement heuristics can be ap-plied. Dispatching rules are simple rules of thumb and rank jobs in order of some property. Examples include Shortest Processing Time (SPT), in which the jobs are sequenced in non-decreasing order of the processing times, whereas the Longest Processing Time (LPT) rule orders jobs in non-increasing order. For the single machine shop, the SPT rule is proved to minimize makespan as well as mean tardiness [4]. In turn, the LPT rule is known to work better in the parallel machines environment. Other dispatching rules include Earliest Release Date first (ERD) rule, which is applicable when the jobs each have individual re-lease times and which is equivalent to the first-in-first-out rule. If jobs each have a defined due date, the Earliest Due Date first (EDD) tends to minimize total tardiness [34]. While dispatching rules have been widely applied in practice, their efficacy remains poor due to lack of a global view.

The constructive heuristic described by Nawas, Enscore and Ham (1983)[31], called the NEH algorithm, is generally regarded as one of the best for the flowshop problem. It is based on the idea that a job with a high total operating time on the machines should be placed first at an appropriate relative order in the sequence. The algorithm starts with sorting the jobs in decreasing order of their total operating time requirement, the highest of which will be the first job. The sequence is then build by at each step adding a new job from the sorted list and finding the best partial solution for this new job’s position. Thus, the relative sequence of the jobs in the previous partial solution does not change.

4.3.2 Metaheuristic techniques

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on the performance of simple deterministic heuristics. Metaheuristics take one or several candidate solutions and iteratively try to improve these. The realm of feasible solutions to a complex NP-hard problem usually contains many local optima. These are points that appear to be an optimal solution to the problem, because all directly surrounding solu-tions calculate into a lower objective function. If a heuristic is too greedy it often gets stuck in a local optimum. One can easily see the resemblance with walking through a very misty mountain range, where simply walking up the first steepest slope in no way guarantees getting to the highest peak. Standing at the top, all the land directly around you may be lower, but you cannot see any other, possibly higher peaks, and therefore you do not know if it is worthwhile to keep going in search of a higher mountain to climb. The most widely used metaheuristics are Tabu Search (TS), Simulated Annealing (SA) and Genetic Algorithms (GA). These methods all strive to avoid local optima by in some way adding a bit of randomness to the search path. Tabu search was originally developed by Glover in 1986 [10]. It needs an initial solution and searches for the best solution in its neighborhood. The algorithm allows for non-improving movements and avoiding certain improving movements that may take the search toward a point it already visited, referring to the point which is ”tabu”. Simulated Annealing also performs many local searches and allows for non-improving solutions with a probability that depends both on the difference in performance between solutions, as well as on a ”Temperature” parameter, which grad-ually decreases as the algorithm progresses. The Temperature parameter originated from metallurgy applications which Kirkpatrick et al.[22] inspired this heuristic on, and it also provides a convenient way of ultimately stopping the algorithm when Temperature reaches zero. Genetic Algorithms are based on Darwin’s evolution theory, and first applied to search problems by Holland in 1975[16]. The algorithm herds a population of solutions, each build of chromosomes which in turn consist of genes. Parent solutions within the population are combined with each other by crossing chromosomes and/or by mutating genes, to generate offspring solutions, of which the best ones (called fittest) are kept in the new population generation. This process is repeated for a fixed computation time. Other metaheuristics that have also been used in hybrid flowshops are ant colony optimization, artificial immune systems, and neural networks. The performance of metaheuristics relies heavily on the initial solution, as well as on the search parameters of the algorithm. Thus far metaheuristics appear to be the most promising way to solving a complex HFS to an acceptable solution. Amongst the multistage HFS literature, we have observed the application of SA more often in problems with identical parallel machines than in problems with unrelated machines. Also, we see it often used in problems which have alternative objective functions than the makespan minimization, such as minimizing total tardiness, cost, total flow time, or a combination of these. An example is Naderi et al., who optimize a dual objective of total tardiness and total flow time in a multistage HFS with identical parallel machines and sequence dependent setup times in [30](we denote this problem as F Hm, ((P M(k)₎m

k=1) |Ssd| _¯

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[35], who do include batch production constraints as well as skipping stages, and optimize a combination of total flowtime and cost (F Hm, ((P M(k)₎m

k=1) |batch, skip| _¯

F , Cost ). A paper by Low [28] does deal with unrelated machines and sequence dependent removal times to minimize total completion time, noting no earlier work had taken setup and re-moval times into consideration.

Tabu search enjoys a similar popularity to SA, and we have found some applications of TS in quite complex situations. Chen et al. [7] apply TS to the three stage hybrid flexible flowshop with unrelated parallel machines to minimize makespan, encountered in a mar-itime terminal. They include a number of constraints we also consider, namely sequence dependent setup times, blocking machines, and precedence constraints (we denote this problem as F H3, ((RM(k)₎3

k=1) |Ssd, block, prec| Cmax). They run tests on various initial solution generators on a set of twenty jobs, concluding that a good initial solution is very important for the quality and efficiency of the heuristic. On the use of Tabu search in the multi-stage setting, a recent article was produced by Alfieri [2], who also includes a number of real-life constraints, such as sequence dependent setup times and batch production, but considers identical parallel machines rather than unrelated machines. A multi-objective function is optimised, consisting of maximum tardiness and total weighted tardiness (we denote the problem as F Hm, ((RM(k))m_k=1) |Ssd, batch|Tmax, ¯Tw ). The paper is espe-cially interesting for practical cases because its primary aim was not to develop the best algorithm for the problem but to create a flexible and easily usable scheduling tool. There have recently been a number of researchers who have successfully applied Genetic Algorithms to increasingly complex HFS problems. Ruiz and Maroto [36] apply GA to the multistage HFS with unrelated machines, sequence dependent setup times and job availability constraints. The objective is to minimize makespan (we denote this problem as F Hm, ((RM(k)₎m

k=1) |Ssd, Mj| Cmax). To the best of our knowledge, they are the first to include availability constraints. Yaurima et al. [44] design a variant GA with an advanced crossover operator for the same problem, based on the GA used by Ruiz and Maroto. An-other interesting study on the performance of different parameters and crossover operators for GA in the HFS setting was done by Jungwattanakit et al. (2009)[21]. They consider a multistage HFS in the textile industry with unrelated machines, sequence dependent setup times and release dates. The objective function is a convex combination of makespan and number of tardy jobs, λCmax + (1 − λ) ¯U , where ¯U stands for the total number of tardy jobs (we denote this problem as F Hm, ((RM(k)₎m

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4.4 Literature survey 4 LITERATURE

4.4 Literature survey

Thus far we have seen that solving a complex real-life HFS is very challenging and requires cutting edge custom heuristics. In order to get a better sense of which solving methods are the most promising we will give a short summary of research done. Possibly the most state-of-the-art and comprehensive survey on hybrid flowshop scheduling research to date is done by Ruiz and Vazquez-Rodriguez (2010) [37]. Of the 225 papers reviewed in their survey, none focus specifically on the four stage HFS. 83.7% of the papers they have reviewed deal with identical parallel machines, 4.7% with uniform and 11.6% with unrelated machines in each stage. It is noted that the multi-stage problem with unrelated parallel machines is the most general case and therefore, the most likely to be found in practise, but it only apears in 7.0% of the reviewed papers. Interestingly, the review paper literally states that research on chemical engineering has been neglected in the sheduling literature, which does not bode well for our problem. Ony 15% of reviewed papers have been able to formulate a mathematical programming model, which have only proven to be useful for simplified or small problems or problems with a specific setting. Most research considers problems without any specific constraints, and the flexible case were jobs may skip stages only occurs in 21 out of 225 papers. It is noted that the best research opportunity lies in metaheuristics. The review goes further to conclude real world problems may be too dynamic for the currently developed heuristics, and that no results have ever been found regarding heuristics to be robust, i.e. heuristics that will find suitable solutions under different scenarios.

4.5 Difficulties of development

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4.5 Difficulties of development 4 LITERATURE

reactor can keep processing the second job while the blender is waiting to release the first job. As long as the blender is emptied before the reactor is finished, the reactor will no incur any idle time. Note that in the model, he reactor-blender combination is one single machine. A single machine is either idle or working, it cannot be simultaneously holding one job while processing the next. Therefore in the model the reactors will always suffer idle time if the blenders are waiting. This is unfortunate, because typical reactor process-ing time is much longer than the blender processprocess-ing time so we loose reactor capacity. In reality, this will be very inefficient and costly, because the reactors are the most expensive part of the production line and the production planner will therefore focus to keep them running at full capacity. Modeling the reactors and the blenders as two separate stages would require machine-dependent machine eligibility to account for the fixed nature of each reactor with one blender, which has never been researched to the best of our knowledge. Effectively, each mixer-blender combination represents a two-stage classic flowshop in it-self. Modeling the four parallel machines as individual flowshops within a hybrid flowshop becomes highly complex, and again, has never been researched to the best of our knowledge. Next, in our proposed hybrid flowshop we choose to model the storage tanks as a sep-arate stage. We make this decision based on a number of arguments. Another option would have been to model a buffer. This would then need to be a buffer of limited ca-pacity, of which we have found no previous research done as buffers are always defined of unlimited size. As a side note, a hybrid flowshop with unlimited buffers between stages should be much easier to solve than a no-wait flowshop, as machines in earlier stages will never have to wait for machines in a later stage, because jobs can always exit a machine to go into a buffer, irrespective whether a machine is available. Thereby the sequence of jobs becomes less relevant than assigning jobs to machines in the most efficient manner. As a general remark, there is limited research available into the routing control structure between adjacent stages. Returning to our buffers, they would have to be job-dependent, as there exist only six storage tanks and they are all dedicated to a specific product. Job-dependent buffers is another feature we have not encountered in the literature reviewed. The way we have proposed to model the storage tanks as a separate stage requires the model to have certain constraints, namely machine eligibility as well as the situation where jobs can skip stages. In our instance we already have both these features, and therefore this does not add further complexity to our model. If one encounters a scheduling problem where machine eligibility and skipping stages are not already constraints or properties of the model, it may not be practical to use this modeling technique. Also, our case does not have any buffers between any stages, and if one would be to model a HFS which already has buffers it may be more sensible to model the storage tanks in that manner as well. Note that our modeling technique does have a significant drawback in our specific case, referring to the fact that there will be jobs of a smaller size as there is a smaller reactor, and by modeling multiple parallel storage tanks we effectively loose capacity if a storage tank is used to store a smaller job.

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liq-4.5 Difficulties of development 4 LITERATURE

uid product, in reality it will be easily possible to split a 20 ton batch into smaller batches by simply opening a valve and closing it before the entire batch has passed through. This is actually something that happens frequently, as the storage tanks are not all of equal size, the mixers require inputs from several basic resins which are almost never 20 ton, and the drumming lines can split batches over several drums. In the HFS model, job splitting is not allowed, which poses a large restriction. We have noted the negative implications on the storage tanks. For the mixers it also has negative implications. Consider, for example, a modification product is demanded that requires 7 tons of basic resin A and 13 tons of basic resin B. Without job splitting, we would need two reactors with either 10 or 20 tons of capacity production less than their full amount. If job splitting were possible, the excess basic resin could be poured into drums via the drumming lines and be stored for future use or sold. Job splitting is, once again, something we have not encountered previously in the multi-stage HFS setting.

The example in the previous paragraph also illustrates a last major issue, which is that of unidirectional movement. One of the basic principles of HFS modeling is that all jobs move in a single direction, which means the stages are set in a serial order. Within JDR it happens quite often that an amount of basic resin is produced and then stored in drums until it is needed as raw material to produce a modification resin. This means a job moves through a reactor, a blender, a drumming line, then is kept in a buffer for some time, after which it is split, goes into a mixer together with others, and is once again poured in drums on a drumming line. The move from drumming line to mixer means the job is not moving in a single direction. As unidirectional movement is so engraved in the nature of HFS modeling, this may be an issue that is not solvable within this framework.

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4.5 Difficulties of development 4 LITERATURE

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5 CONCLUSION AND RECOMMENDATIONS

5 Conclusion and recommendations

The bottleneck issue, where a multitude of parallel machines flow into a lesser number of machines, is one that DSM encounters in many of its production facilities. The manufac-turing team of DSM Resins Asia has acknowledged its interest in an efficient, practical solution to this issue in many of its production plants. We have studied specifically the production line within Jinling DSM Resins Co. Ltd., which consists of a multitude of stages with unrelated parallel machines. Jobs need to be scheduled subject to a variety of sequencing constraints, such that the total completion time is minimized, to effectively maximize the output capacity of the production plant.

We found the best way to model this problem is by using the Hybrid Flowshop frame-work, and have defined a Hybrid Flexible Flowshop model for our production line in four stages. We found there is still a noticeable gap between theory and practice in this topic, as was previously observed by many researchers in this field. Although we can define our problem reasonably well in mathematical terms with it, the Hybrid Flowshop framework does not provide or specify a clear solution method. We have derived that the HFS problem is NP-hard. This means an exact algorithm that can solve the problem to optimality in real-time is highly unlikely to exist, and to solve it approximately one will have to revert to dispatching rules, constructive heuristics, or meta heuristics. Of these, genetic algorithms seem the most promising.

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5 CONCLUSION AND RECOMMENDATIONS

that can only be modeled in an imperfect fashion. These are the unique reactor-blender combination in the first stage of the production process, the dedicated limited-size storage tanks, the disability to split batches in the HFS model, and the unidirectional movement restriction. If we can split batches in the model we will be able to replicate the actual situation, which is that the liquid batches can be split into several smaller batches for different purposes. It will allow us to model the storage tanks to their full capacity, and we can use the total demanded amounts of finished goods per packaging means into a model, rather than defining each job as a product type combined with a package type. Such a model could allow for quick and easy sensitivities around uncertain demand of finished products, or could even be extended to allow for stochastic demand inputs. Recommenda-tions that we suggest for future research include the possibility of splitting jobs, as well as non-unidirectional movement through the flowshop. We have a situation where there are precedence constraints because basic resins can be mixed together to produce modification resins, but the unidirectional movement does not consider the possibility of first produc-ing and drummproduc-ing the basic resins, and much later mix the basic resins from the drums to make the modified resins. Another interesting future research topic is how to account for the double first stage, where each reactor is followed by a unique blender. We have proposed a lag variable, which is imperfect because it does not model the blenders as a separate stage. If the blenders need to wait for another machine to become available, the reactors will also have to wait, but only once they are finished processing. In our model they will go idle irrespective of whether the job in the reactor is finished and ready to be blended. Effectively each reactor-blender combination is a flowshop in itself, which then flows into the rest of the production line. It would therefore be worthwhile to investigate modeling unrelated parallel flowshops within a hybrid flowshop setting.

Ultimately, JDR’s goal as a company is to maximize profits. Therefore, JDR will want a model that allows them to input an expectation of demanded products, or even better, a distribution of demand for products. Given the production times and gross margins, the model should choose how much of each product to produce and provide a full production planning, such that the gross margin of all the products produced and realistically sold during the period is maximized. However, a model this advanced is clearly one or two bridges too far for the current state of science. All-in, we must conclude there are so many instances of flowshops imaginable and existing in real-life problems, varying in layout and constraints and objective function, that flowshop scheduling research should remain a hot topic for years to come.

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Production planning in a batch oriented chemical plant in China