**(3). ****OPTIMIZATION AND LOGISTICS**

Questions about the topics within the subject area of *Optimization and Logistics *should be directed to Ole B. Olesen, Department of Business and Economics, e-mail: ole@sam.sdu.dk

The first part of topics (3.1-3.4c) is of interest for both Oecon and Math.Oecon students

The second part of topics (3.5) is of interest only (mainly) for Math.Oecon students

All topics in the first part can be written in English or Danish

All topics in the second part can only be written in English if the supervisor cannot read Danish.

**3.1 ****Supply Chain Management**

**3.1.a Aggregated Planning**

When a company sets up an aggregated plan, it, among other things, tries to get an overall picture of its future need for labor over the next 4-12 months based on forecasts of the total demand for its products. The plan furthermore specifies the link between the necessary inventory throughout the period and the extent of any subcontracting that may have been planned. Different strategies can be pursued in the forming of an optimal plan. Furthermore, special problems are linked with the choice of how to implement an aggregated plan in a specification of actual production plans (when what is produced and in which sequences).

Literature:

C. C. Bozarth and R. B. Handfield: "Introduction to Operations and Supply Chain Management", (2005), chapter 12.

Chopra and Meindl: ”Supply Chain Management. Strategy, Planning and Operation”, chapters 8-9.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.1.b Aggregated Planning for a small manufacturing company**

Students are asked to draw up various suggestions for an aggregated plan for the next 12 months based on historic data about demand and technical issues linked to the production. Disaggregated data are available for 27 item numbers, which are to be aggregated to a standard product (top-down analysis). The average consumption of labor for each item number will be provided. The company’s products are characterized by being perishable, and therefore the storage costs have to be modelled in a somewhat untraditional way.

Furthermore, the company is located in an area where it is difficult to attract qualified labor, but at the moment the company has a well-educated labor force.

Literature:

C. C. Bozarth and R. B. Handfield: "Introduction to Operations and Supply Chain Management", (2005), chapter 12.

Chopra and Meindl: ”Supply Chain Management. Strategy, Planning and Operation”, chapters 8-9.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.1.c Optimal Inventory planning**

This topic is relatively broad, and models and methods from production and inventory planning can be used. One possibility is to work with dynamic, deterministic stock management problems. Another possibility is to look at stochastic, static inventory problems. A third possibility is to look at variations of the EOQ formula. Finally, it is also a possibility to look at what optimal stock management means for the entire or parts of the supply chain which the company/organization is part of. It is also possible to use software for these analyses, for example Excel/VBA, Arena or other software.

Literature: C. C. Bozarth and R. B. Handfield: "Introduction to Operations and Supply Chain Management", (2005), chapter 13.

Chopra and Meindl: ”Supply Chain Management. Strategy, Planning and Operation”, chapter 10.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.1.d Material Requirement Planning**

MRP deals with the tools which a company can use for production planning when the manufacturing process is dependent on deliveries from supply chain partners. These deliveries must be ordered, so that they are delivered at exactly the time when the part is needed in the manufacturing process.

Literature:

C. C. Bozarth and R. B. Handfield: "Introduction to Operations and Supply Chain Management", (2005), chapter 14.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.1.e Forecasting**

Every single day, businesses make decisions about future undertakings, without knowing exactly what the future brings. For example, businesses have to order supplies for their inventories without precise knowledge of future demand. Likewise, investments are made by the businesses without exact knowledge about how large the resulting profits will potentially be. There are many ways of forecasting the future. Some businesses use subjective processes, such as experience and intuition, while the approach of others is based on quantitative forecasting. Some of the more quantitative methods are moving average models, trend projections and regression, to mention but a few. It is of course possible to use IT for these estimations.

Literature:

C. C. Bozarth and R. B. Handfield: "Introduction to Operations and Supply Chain Management", (2005), chapter 9.

Chopra and Meindl: ”Supply Chain Management. Strategy, Planning and Operation”, chapter 7. John E. Hanke and D. W. Wichern ”Business Forecasting” (2005).

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.1.f Forecast of the demand for product from a small manufacturing company**

Day-to-day demand data for three years disaggregated on 27 item numbers will be provided. Students are asked to make a forecast analysis based on the first two years and validated on data from the third year. The demand is influenced by seasonal variations and campaign offers. Students are asked to make both a forecast analysis based on the individual item numbers but also based on “aggregated products”. Information about which item numbers refer to products with high substitutability will be provided.

The data were originally part of a master’s thesis in Economics & Business Administration, so the performance of the best forecasting model can potentially be compared to the forecasting model that was used in the master’s thesis. Data will be provided in Excel sheets, so it is possible to use IT for these estimations.

Literature:

C. C. Bozarth and R. B. Handfield: "Introduction to Operations and Supply Chain Management", (2005), chapter 9.

Chopra and Meindl: ”Supply Chain Management. Strategy, Planning and Operation”, chapter 7. John E. Hanke and D. W. Wichern ”Business Forecasting” (2005).

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.1.g Project Planning**

In many companies, ongoing projects take up the majority of a company’s resources. It is therefore important that the company keeps tabs on these projects, both with respect to time and the resources that the project consumes. There are many solution methods that the company can use for monitoring its projects – some use mathematical formulations, while others are more algorithm-oriented.

Literature:

C. C. Bozarth and R. B. Handfield: "Introduction to Operations and Supply Chain Management", (2005), chapter 5.

A. Shtub, J. F. Bard and S. Globerson: ”Project Management: Processes, Methodologies and Economics.” (2005).

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.1.h Facility Layout**

Facility Layout is, for example, how to optimize the layout of a shop or production area. In many stores, there is competition for the best shelves or display areas that will catch the attention of the customers. Likewise, it is important for manufacturing companies to design their production areas, so that, for example, transportation times between the production sites are as short as possible. This topic gives students an opportunity to work further with Jensen’s add-ins or perhaps even create their own solution routines.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.1.i Capacity Management**

This topic has to do with the problems which a business faces when the demand for its products/services is higher than expected. For example, it deals with evaluation of capacity alternatives and with identifying procedures that can increase the company’s throughput.

Students can include a discussion of the advantages and disadvantages of a classic inflexible batch production with large intermediate inventories versus a “leaner” design with a flexible technology.

Literature:

Fisher, Marshall L. 1997. “What Is the Right Supply Chain for Your Product?” Harvard Business Review, 75 (2/4), pp. 105-116.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.1.j Supply Chain Management**

This is a broad topic, and models and methods from e.g. production planning or inventory planning can be used. It may be useful to choose a specific problem as the starting point. For example, students can analyze how information and decision-making in a distribution channel can be coordinated, so that the individual decision makers act optimally from the point of view of the supply chain.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.2 ****Lean Manufacturing/Value Stream Mapping**

**3.2.a Pull versus Push – what is Lean Manufacturing?**

The advantages of Lean Manufacturing are emphasized in many contexts, but often there are different explanations of what exactly characterizes Lean. In some contexts Lean is presented as “Make to Order”, while in other cases pull production is identified as the determining characteristic. This topic invites students to discuss and clarify what actually characterizes Lean. The project can take several directions. For example, the focus can be on pull- production design, such as the Kanban system, originally used in the Toyota Production Model, or the more recent concept of CONWIP control. The link between throughput and variability is another important area. Furthermore, the focus can be on the part of a Lean implementation, which is called “Value Stream Mapping”, and which deals with identifying “imbalances” in a production design (see, e.g., the book “*Learning to See: Value Stream Mapping to create value and eliminate muda*”). Finally, the focus can be on simulation, since many of the aspects of Lean can be “tested” in simple simulation models. Access to the simulation tool ARENA will be provided. The tool is fairly easy to use, as models are formulated by setting up and connecting graphic modules, exactly as when setting up a flow chart.

Literature:

Fisher, Marshall L. ( 1997): “What Is the Right Supply Chain for Your Product?” Harvard Business Review, 75 (2/4), pp. 105-116.

W. J. Hopp (2003): Supply Chain Science, free download.

W. J. Hopp and M-.L. Spearman (2004): To Pull or Not to Pull: What is the Question? Manufacturing and Service Operations Management 6(2), pp. 133-148.

M. Rother and J. Shook: Learning to See: Value Stream Mapping to create value and eliminate muda.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.2.b Simulering af TWI’s produktionsproces af traktor komponenter før og efter en Lean implementering**

In the book “*Learning to See: Value Stream Mapping to create value and eliminate muda*” Value Stream Mapping, which is an important part of a Lean implementation, is discussed and illustrated. Specifically, the book contains information from a case dealing with TWI’s manufacturing process of tractor components. This topic invites students to carry out a closer analysis of how appropriately this manufacturing process has been organized (utilization, throughput, cycle-time, amount of work in process, etc.). Furthermore, the described manufacturing process should be analyzed by means of simulation, and the effect of different changes in the production design should be tested. The simulation tool ARENA is fairly easy to use, as models are formulated by setting up and connecting graphic modules, exactly as when setting up a flow chart. Different suggestions for a Lean implementation must be discussed and analyzed based on how the production process behaves in simulations. More theoretical aspects of what characterizes Lean can also be included in the project. Access to the simulation tool ARENA will be provided. The tool is fairly easy to use, as models are formulated by setting up and connecting graphic modules, exactly as when setting up a flow chart. Students should discuss and analyze various suggestions for a Lean implementation, according to how the manufacturing process behaves in simulations. More theoretical aspects of what characterizes Lean can also be included in the project.

Literature: Fisher, Marshall L. ( 1997). “What Is the Right Supply Chain for Your Product?” Harvard Business Review 75 (2/4), pp. 105-116.

W. J. Hopp (2003): Supply Chain Science, free download.

W. J. Hopp and M-.L. Spearman (2004): To Pull or Not to Pull: What is the Question? Manufacturing and Service Operations Management 6(2), pp. 133-148.

M. Rother and J. Shook: Learning to See: Value Stream Mapping to create value and eliminate muda.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.3** **Routing and Localization**

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**3.3.a Routing models**

The routing problem focus on how a number of customers can be serviced from a warehouse.. The demand from each customer is known. This demand has to be met using deliveries from the warehouse. This is done by letting vehicles carry the goods from the warehouse to the customers. Each vehicle has limited capacity. The problem is now how to serve the customers and minimize the transportation cost. This problem can be formulated and solved as a mathematical optimization problem. Students are asked to provide an overview and make a comparison of models for solution of one or more of these kinds of problems. The models can be implemented in GAMS/VBA, but it is also possible to make a purely theoretical project within this topic.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.3.b The Traveling Salesman Problem**

A salesman is currently in his home town, and on the next day he will be visiting a fixed number of customers. The salesman’s problem is to plan a coherent route of the shortest possible length, so that he can visit all customers exactly once on the route. This is a classical combinatorial optimization problem. For example, one could imagine that the salesman has to visit 20 customers. There are 20 possible choices for the first customer on the route, 19 for the second, etc. This means that the shortest route of the possible 20*19*...*1 routes must be identified. This can of course be done by calculating the lengths of all possible trips, but the number of trips is very high. Alternatively, the problem can be formulated as a binary optimization problem and can be solved by means of, for example, Branch & Bound. The task is to explain a number of mathematical formulations of the problem and implement one or more of these. It is possible to work on practical datasets, for instance by having the customers live in different towns.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.3.c Metaheuristics for solving combinatorial optimization problems**

A number of logistical problems, for example within the field of routing can be solved using mathematical modeling, typically by building a binary optimization model, which is subsequently solved using, for example, the Branch & Bound algorithm. But new methods for solution of these problems have been developed, and they have proved very effective in practice, e.g. Simulated Annealing and Tabu Search. Simulated Annealing and Tabu Search do not necessarily result in identifying an optimal solution to the problem at hand, but typically in a ‘good’ solution. Students are asked to make a presentation of one of these methods and its use for solution of, for example, the type of problem described above.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.3.d Planning of mail delivery routes**

In Odense, mail is delivered daily by a number of mailmen, who each deliver mail to a fixed district. A mail delivery route is a specification of the order in which the individual roads in the district are being serviced. It is possible to plan the route, so that the total distance, which the mailman travels, will be as short as possible. This can be formulated as a mathematical optimization model. Students should provide an overview of methods and models that can solve of this type of problem. It is possible to work with small datasets, but also to make a purely theoretical project within this topic.

Prerequisite: "Ressourcestyring og Supply Chain Management".

**3.3.e Localization of a business**

** **A business manufactures goods for a reasonably fixed group of customers. At present, the business is for example located in the Triangle Region (Kolding, Vejle, Fredericia), but in recent years more and more of the customers have been based on Zealand. This means that an increasing part of the goods have to be transported from Jutland to Zealand, which entails quite high transport costs. The business is therefore considering whether it should move to another location. Problems of this type can be solved using optimization methods. The project involves a presentation of some of these methods and an implementation of one or more of them in, for example, Excel/VBA or other software. Prerequisite: "Ressourcestyring og Supply Chain Management".

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**3.4 ****Benchmarking/Productivity Analysis**

**3****.4.a Productivity and Efficiency Measurement**

A financial institution considers a redistribution of resources, for example in connection with the staffing of its branches. Students are therefore asked to indicate whether a given branch currently has too many or too few resources in relation to its revenue and the amount of services it has delivered. This question can be answered by performing a productivity analysis. There are several methods available for performing a productivity analysis. The DEA method is based on the use of linear programming. This topic is well suited for the use of DEA for productivity evaluation based on real-life datasets. The practical uses can for example be based on datasets from the library sector, police districts, ambulance/fire stations and chief administrative authorities (statsamter), but students may also choose their own area for analysis.

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**3.4.b Benchmarking of Danish state schools (folkeskoler)**

Which Danish state schools/private schools perform best in the much debated OECD PISA survey of the performance of pupils? In this topic, students are asked to make an analysis of this problem based on the Danish PISA data. A starting point for such an analysis could be an estimation of the schools’ production function based on linear programming with resource consumption as input and the number of pupils taught and their performance in various PISA tests as output. It is also possible to formulate a statistical model with focus on the correlation between resource consumption and the number of students and their performance. Datasets for the Danish school sector will be provided, including various background data for the pupils in the form of data on parental background.

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**3.4.c Krevi’s benchmarking of Danish state schools (folkeskoler)**

In June 2011, Krevi published a report entitled ”Effektivisering i folkeskolen, Muligheder og metoder” [Efficiency improvement in Danish state schools, Opportunities and methods”]. The report presents analyses of the productivity in Danish schools based partly on the DEA method and partly on statistical analyses of parental background in the form of socio- economic characteristics. The report attempts to determine which influence school choice has on learning. The university has access to most of Krevi’s data, and these data can for example be used in a project, where the focus is on Danish schools in selected parts of Denmark, or where other DEA models are used to investigate whether the results change. Another angle could be to study the significance of parental background for the performance of schools.

**Part 2: Topics of interest only (mainly) for MathEcon students**

**3.5.a Dantzig-Wolfe decomposition**

A BA-project within this general area could focus on column generation and how it is related to the Danzig Wolfe decompositions.

**3.5.b Benders decomposition**

A BA-project within this general area could e.g. focus on how to use a Bender decomposition to solve a Mixed Integer Linear Programming problems using a sequence of LP-relaxations.

Alternatively, a BA-project could e.g. focus on the relationship between Dantzig-Wolfe decompositions and Benders decompositions in LP using duality results.

Examples of application of Benders decomposition is presented in the paper:

R. Rahmaniani, T. G. Crainic, M. Gendreau and W. Rei, “The Bender Decomposition Algorithm: a Literature Review”, June 2016, CIRRELT-2016-30. These areas include e.g. Production Planning, Production Routing, Facility Layout, Project Scheduling, Water Resource Management, Logistics Network Design, Airline scheduling, Vehicle Routing, Distribution planning, Inventory Control, Traveling Salesman,

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**3.5.c Lagrangian Relaxation**

A BA-project within this general area could e.g. focus on the use of Lagrange relaxations of Travelling Salesman problems

Alternatively, a BA-project within this general area could e.g. focus on the applications mentioned in the paper: “An Applications Oriented Guide to Lagrangian Relaxation”, M. L. Fisher, (1985) Interfaces, vol. 15, pp 10-21.

**3.5.d Benchmarking and Data Envelopment Analysis (DEA)**

A BA-project within this general area could e.g. focus on the use of convex polyhedral theory to analyze a convex hull estimator of the production possibility set in DEA. What is an appropriate facet structure of the convex hull? How is the facet structure related to alternative optimal solutions and degeneracy in LPs characterizing each of the DEA problems?

A BA-project within this general area could e.g alternatively focus on an application of DEA using various data sets (e.g. primary and secondary schools in Denmark, see topic 4.4c). A combination of these two areas is of course also a possibility.

**3.5.e Inventory Management**

A BA-project within this general area could e.g. focus on the Economic Order Quantity (EOQ) model. The most common inventory situation faced by manufacturers, retailers, and wholesalers is that stock levels are depleted over time and then are replenished by the arrival of a batch of new units. A simple model representing this situation is the basic economic order quantity model or, for short, the EOQ model, assuming 1) a known constant demand rate of *a *units per unit time; 2) the order quantity (*Q*) to replenish inventory arrives all at once just when desired, namely, when the inventory level drops to 0; 3) planned shortages are not allowed. However, these assumptions can be relaxed to allow for more complex situation in inventory management. Possible topics in this area could be relaxing any assumptions in the basic EOQ model to represent more complex situations of inventory management problem and finding the solution for the relaxed EOQ models. It will mainly draw on knowledge from nonlinear programming and possible stochastic programming to study the problem.

Literature:

Paul A. Jensen, Jonathan F. Bard, (2002) Operations Research Models and Methods, Wiley.

John R. Birge • Francois Louveaux (2010) Introduction to Stochastic Programming, Springer

Frederick S Hillier and Gerald J. Lieberman, Introduction to Operations Research, 7th Edition, McGraw Hill

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**3.5.f The News Vendor model. **

** **

A BA-project within this general area could e.g. focus on the classical model where a daily newspaper being sold at a newsstand. A particular day’s newspaper can be carried in inventory for only a single day before it becomes outdated and needs to be replaced by the next day’s newspaper. When the demand for the newspaper is a random variable, the owner of the newsstand needs to choose a daily order quantity that provides an appropriate trade-off between the potential cost of over-ordering (the wasted expense of ordering more news papers than can be sold) and the potential cost of under-ordering (the lost profit from ordering fewer newspapers than can be sold). Such problem common exists in inventory management for perishable goods. Students may work on any type of relaxed Newsvendor model by relaxing the assumptions used in the basic model and discuss the solutions of the relaxed model by using nonlinear or stochastic programming theories.

Literature:

Paul A. Jensen, Jonathan F. Bard, (2002) Operations Research Models and Methods, Wiley.

John R. Birge • Francois Louveaux (2010) Introduction to Stochastic Programming, Springer

Frederick S Hillier and Gerald J. Lieberman, Introduction to Operations Research, 7th Edition, McGraw Hill

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**3.5.g Dynamic Inventory models with Non-perishable Goods.**

** **

A BA-project within this general area could e.g. focus on the inventory management with problems in multiple periods. Assume that the stochastic demands in each period have the same known distribution. The retailer needs to make decisions on the order quantity at the beginning of each period to balance the cost from over-ordering and under ordering. A basic dynamic inventory model usually requires a set of strong assumptions that may be hard to satisfy in real world. It is possible for students to formulate a dynamic inventory problem by considering more real world factors and using softwares, e.g. Matlab or Mathematica, to numerically study the optimal order policy. It requires both nonlinear and stochastic programming knowledge when formulating and solving the problem.

Literature:

Paul A. Jensen, Jonathan F. Bard, (2002) Operations Research Models and Methods, Wiley.

John R. Birge • Francois Louveaux (2010) Introduction to Stochastic Programming, Springer

Frederick S Hillier and Gerald J. Lieberman, Introduction to Operations Research, 7th Edition, McGraw Hill

**3.5.h Queueing Theory. **

A BA-project within this general area could e.g. focus on Discrete and Continuous Time Markov Chain. Markov Chain is a special type of stochastic process that can be used to model a lot of phenomena in real world. The major concerns are whether there exists steady state for a chain, and most importantly, if a steady state exists, what is the performance of the chain. It usually involves calculating the steady state probability and first passage time of the chain analytically. However, if the chain is get more complex, and closed form solution is hard to obtain, we may also study the chain by simulation using software, e.g. Matlab or Mathematica. The possible topics for students in this part could be finding a problem that can be modeled by a Markov Chain, and focus the study on the performance of the chain in steady state either analytically or numerically.

Literature:

Paul A. Jensen, Jonathan F. Bard, (2002) Operations Research Models and Methods, Wiley.

Donald Gross, John F. Shortle, James M. Thompson, Carl M. Harris (2008) Fundamentals of Queueing Theory, 4th Edition, Wiley