Teaching Operation Management with GeoGebra. An example of Make-to-stock Problem Solving

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1 Teaching Operation Management with GeoGebra. An example of Make-to-stock Problem Solving Calona Z 1, Santos J 2, Arcelus M 3 Abstract Improving classroom effectiveness is a major challenge for professors. Students abilities need to be nurtured, and integrating dynamic mathematics into teaching can enhance both professor and student performance. This paper presents GeoGebra as an alternative to solving make-to-stock problems in inventory management. This model has the advantage of being interactive and user-friendly, allowing students to experiment with different values and draw conclusions on their own. Keywords: Teaching Innovation, Operation Management, Inventory Management, Geogebra, Make-to-stock 1 Introduction Professors are facing a major challenge when it comes to improving classroom effectiveness, such as creating situations that will foster students mental abilities and making students interact with the instructor and each other to solve a problem (McKeachie, 1999). The main tools developed to create these situations (puzzles, cognitive analogies, case studies, role-playing, problem-based learning) are called Active Learning Techniques (McCarthy and Anderson, 2000). 1 Zeyda Calona Tecnun Universidad de Navarra. Pº Manuel Lardizábal 13, San Sebastián 2 Javier Santos García ( jsantos@tecnun.es) Tecnun Universidad de Navarra. Pº Manuel Lardizábal 13, San Sebastián 3 Mikel Arcelus Alonso Tecnun Universidad de Navarra. Pº Manuel Lardizábal 13, San Sebastián 903

2 One of the new challenges in Active Learning Techniques consists of integrating the use of technology, especially when a technology allows students to dynamically interact in the proposing and solving of problems. Using these new techniques, which are usually based on computer software, students can understand topics better and learn faster, thereby improving their overall academic success. Active Learning Techniques are useful in recapturing students attention when dealing with topics where what-if scenarios can be used to analyze the impact of certain variables on the results of the problems under study or when the concept explained is complex, as is the case with mathematical concepts. At the university level, integrating dynamic mathematics into teaching can enhance the performance of both professors and students. Moreover, professors are encouraged to use and assess technology and interactive mathematics, which contributes to overall classroom effectiveness. Dynamic Mathematics Software (DMS), which supports constructions with points, lines and all conic sections, could be used as an Active Learning Technique (Hohenwarter and Preiner, 2007) that provides the typical features of a Computer Algebra System (CAS), such as function plotting, root finding, derivatives and integrals. The ability to represent functions dynamically is used by teachers of mathematics to propose a bottom up approach (Llobet, 2011). This approach does not use a formal and structured methodology; instead, it proposes a visual and interactive environment where students experiment before learning the concepts. Many DMS applications like Capri, Sketchpad, Microsoft Mathematics and GeoGebra are becoming popular among high school teachers, but they have not been deployed in management and engineering education (Soman, 2012) except for in the teaching of mathematics (Velichova, 2011), (Wurnig, 2008) or linear programming. Soman demonstrates the pedagogical use of GeoGebra in Operation Management, reporting that it helps students feel the implication of the decision they take. This paper presents a practical case that applies GeoGebra, a free software, to Operation Management (more specifically in production planning and scheduling problems), particularly to make-to-stock strategies. In make-to-stock problems, decisions regarding the manufacturing period affect the management total cost. GeoGebra contributes to the dynamic analysis of the effect and helps determine the optimum value for the manufacturing period. 2 GeoGebra GeoGebra emerged in 2001 as Markus Hohenwarter s Master s thesis (Hohenwarter and Borcherds, 2012), and since then it has become increasingly popular with teachers and researchers around the world because of its easy-to-use dynamic 904

3 mathematics software that combines many aspects of various mathematical packages. In addition, GeoGebra is free, and due to its open-source nature an extensive user community has developed around it. Designed specifically for educational purposes, GeoGebra can help students grasp experimental, problem-oriented and research-oriented learning in mathematics, both in the classroom and at home. Therefore, GeoGebra can be used as a tool to better explain concepts and to help students understand and learn faster. 2.1 GeoGebra Applications Although GeoGebra has been designed to solve algebraic and geometric problems, it offers a wide range of applications. For example, nowadays it is being used in various approaches to solving and explaining engineering problems such as Mohr s Circle (Figure 1) and standard deviation (Figure 2). Fig. 1 Example of the dynamic calculation of Mohr s Cycle in GeoGebra (GeoGebra, 2013) Fig. 2 Example of the dynamic study of standard deviation (GeoGebra, 2012) 905

4 3 Make-to-stock Problems In the Make-to-stock (MTS) strategy, a family of products must be manufactured based on demand forecasts. It can be considered push-type production, and the main objective is to determine the lot size for each product and consequently the production period for the family. Traditional inventory management systems can be used to solve make-to-stock problems (Stevenson, 1998). According to inventory theory, the yearly demand for a product (D) can be produced in optimum batches (Q*), taking into account the resource production rate (P), production costs (p), setup costs (C) and inventory costs (H). Figure 3 summarizes the equations required to determine optimal cycle time (T*) and, consequently, optimal total cost (CT*). I Q Q M -D P - D Q* 2CD H(1 ) Q * T* D D P 2C HD(1 ) t p T t D QM CT* D p C H Q * 2 Fig. 3 Optimum cycle time according to traditional inventory problem The difference between the production cycle (T) and the production time for the product (tp) is known as idle time, and it must be minimized in order to increase resource effectiveness. Normally, more than one product is produced with the same set of resources, and according to the above formulas, T* will be different for each product. The challenge for Make-to-Stock strategies is to set the best cycle time for the family of products. One of the approaches to solving this problem is known as the Common Cycle Approach, where the same cycle time is set for the family (Figure 4). I Qi Di T tpi Pi Pi i T t p i T Fig. 4 Optimum cycle time according to the Common Cycle Approach t t CT n i 1 n n 1 T Di pi Ci Hi Di 1 T 2 i 1 CT = 0 T* T n i 1 i 1 2C Hi D(1 i i) i 906

5 3.1 Make-to-Stock in Excel and GeoGebra This section describes how to implement the Common Cycle Approach using GeoGebra. For a better understanding, an example is explained and solved using Microsoft Excel and GeoGebra GeoGebra vs Microsoft Excel Microsoft Excel is the tool that is usually employed by professors to explain mathematics or operation management. It allows them to solve formulas, interact with cell values, and combine columns. In order to add some dynamism to the worksheet, it is necessary to program using Visual Basic. Furthermore, the dynamic graphical representation in Excel is limited to charts. GeoGebra has a reduced range of formulas and spreadsheets, a clearly limited number compared to Excel. In GeoGebra it is not simple to include new rows maintaining the formula structure and looses information when detecting or moving values. As a result is necessary to know in advance how to arrange tables, values and formulas in the template. Fig. 5 GeoGebra s Interface However, GeoGebra offers a dynamic worksheet (Figure 5) that is more userfriendly and an easy-to-use interface. The combination of algebra, spreadsheets and graphics allows values, points and graphs to be changed dynamically. It s as simple as dragging and dropping a variable and checking the behavior of its various values and its impact on spreadsheet cells. As a consequence it is easy to prepare a template to help student understanding and play dynamically with problem values and answer what-if questions in a simple way. 907

6 3.2 A practical example A company produces three different products in the same facility. The company works 250 days a year, 5 days a week. Currently, it produces yearly one cycle of each product to satisfy the demand shown below. The table also provides information about the production, set up and inventory cost. The task is to calculate the total cost based on the Common Cycle Approach. Table 1 Example data Product Di (u/year) pi( /u) Pi(u/day) Hi( /u year) Ci( ) A B C Microsoft Excel solution Figure 7 shows the solution using Microsoft Excel, where each cell includes a formula for solving the problem dynamically. Fig. 7 Case study solution in Microsoft Excel 908

7 Students can interact with the Excel model, but they are limited to changing numbers or formulas. In addition, it is not possible to plot inventory levels for the products GeoGebra solution With GeoGebra (Figure 8), the user can play with the results by changing values and analyzing how they affect the final solution, an approach that is clearly more dynamic. Fig. 8 Case study solution in GeoGebra The GeoGebra model allows interaction without programming by directly moving the variable to the graphics. It is also possible to combine a variable value with the value of a cell in the spreadsheet. However, the spreadsheet in GeoGebra is more limited compared to Microsoft Excel. Figures 7 and 8 show the formula for the calculation of the optimum cycle (T*) using Excel and GeoGebra, respectively. By using GeoGebra, different what-if scenarios can be easily analyzed without changing the model. Furthermore, it is possible to study the impact of an increase 909

8 in demand, a change in production rate, the economic impact of any change in working cycle, etc. 4 Conclusions In this paper, a new proposal for teaching Operation Management based on Geo- Gebra is presented. The suggested alternative for Make-to-Stock problems helps students learn more efficiently by allowing them to manipulate values via a dynamic interface. The paper s main contributions are: (1) the integration of the new software GeoGebra in the field of operations management, not only for solving inventory problems but also for dealing with continuous improvements activities; (2) the presentation of a valuable free tool for professors, thereby improving classroom efficiency; and (3) the presentation of a valuable training methodology for students to better understand inventory concepts. 5 References GeoGebra (2012) GeoGebra (2013) Hohenwarter M., Preiner J. (2007). Multiple Representations. The Journal of Online Mathematics and Its Applications, (7). Available online. Hohenwarter, M. & Borcherds, M. (2012). Geogebra software (version 4) [software]. Available from Llobet, JC. (2011). Mathematization platform in a GeoGebra environment within a didactic approach from bottom to top. Enseñanza de las ciencias, Vol 29 (1). pp McKeachie, W. J. (1999). Teaching tips: Strategies, research, and theory for college and university teachers. Boston: Houghton Mifflin. Patrick, J. Anderson, L. (2000). Active Learning Techniques Versus Traditional Teaching Styles: Two Experiments from History and Political Science. Innovative Higher Education, 24 (4) Soman, CA. (2012). GeoGebra: A tool for improving operations management teaching at MBA level. Proceedings of the 4 th World Conference P&OM Stevenson, WJ. (1998). Production Operations Management. 6th edition. Irwin Professional Publishing Velichova, D. (2011). Dynamic Tool in Mathematical Education. 14 th International Conference on Interactive Collaborative Learning (ICL). pp Wurnig O. (2008), Some Problem Solving examples of Multiple solutions using cas and dgs, Proceedings of the Discussing Group 9 : Promoting Creativity for All Students in Mathematics Education, The 11th International Congress on Mathematical Education, Monterrey, Mexico. 910