UNIT V STUDY GUIDE Programming and Transportation Course Learning Outcomes for Unit V Upon completion of this unit, students should be able to: 1. Identify the major steps in decision making for network flow problems. 2. Structure linear programming problems for the transportation, transshipment, and assignment models. 3. Determine the difference between nonlinear programming, goal programming, and integer programming. 4. Outline and solve the three types of integer programming problems. Reading Assignment Chapter 9: Transportation and Assignment Models Chapter 10: Integer Programming, Goal Programming, and Nonlinear Programming Unit Lesson In this unit, we are focusing on transportation and assignment models. It is important to see how to develop solutions to transportation problems, as the issues of supply and demand are growing due to the increase of globalization. One of these models is the \"stepping-stone\" method; this is considered an iterative technique in which a temporary solution is developed prior to moving to a solution more optimized for the situation. An iterative technique is one in which the mathematical model creates improving approximate solutions for certain problems/issues. The use of transportation models can be applied to a number of situations involving supply and demand. For example, if PEPSICO wants to build a new distribution warehouse, they might use a transportation model and linear programming to determine network flow problems, production costs, and potential costs involving shipping. It is crucially important to analyze potential issues or costs that may arise when determining distribution locations. PEPSICO would not want to place a distribution warehouse in an area that is potentially hazardous. When determining the distribution of goods, it is important to consider both supply and demand. Assignment problems can be applied as well. Thus, they are defined as a class of linear programming problems. The goal really is to minimize costs that are centered on both production and transportation that can be very costly to organizations. Think about how the increase in gas costs has impacted organizations with distribution warehouses. Let's use PEPSICO as our main example: PEPSICO contracts X amount of delivery companies to ship their goods across the southeastern region of the U.S. If the price of gas increases by 1 USD, then the operating costs of the delivery companies will increase as well. This means that PEPSICO will have to pay more to the contracted delivery companies to ship their goods. The same impact occurs if PEPSICO employs their own delivery force, as operating costs will increase. This is why it is important for companies to perform a thorough analysis of distribution sites; performing at peak efficiency is vital to absorbing any potential increase in costs due to problems in transportation. MSL 5080, Methods of Analysis for Business Operations 1 Considering that PEPSICO is such a large organization, they probably use the linear programming techniques discussed in this unit to defray any potential risks. When performing a stepping-stone method, one should focus on finding the least-cost solution with regards to the current selection system. This usually involves evaluating the current system and making any needed changes to improve the processes and costs, which will increase efficiency. As mentioned earlier, the stepping-stone method is most often used in cases of transportation problems. Consistent evaluation of potential problems and improvements is necessary to improve efficiency, drive down costs, and create a more productive environment. Integer programming It is important to understand the difference between linear programming and integer programming. There are different types of integer programming problems to tackle. You can use Microsoft Excel and QM for Windows to solve problems. It is important to keep in mind that every problem is not solvable within a linear programming model. Some business problems can be solved if the variables have integer values. With the use of integer programming, at least one decision variable takes on an integer value. This occurs in the final solution. There are three types of integer programming problems to consider. The first is what is called pure integer programming. Here, all the variables involved have integer values. Mixed integer programming is when there are some variables that have integer values but this does not include all variables. With zero-one integer programming, this involves all decision variables having integer values of 0 or 1. Goal programming With goal programming, organizations often have more than one goal. Goal programming has been developed to supplement linear programming. When setting goals, organizations often identify what are the goals that are a priority and what goals are less of a priority. We use goal programming because we often cannot address all goals. With goal programming, we are attempting to meet a number of different objectives. Goal programming is used to minimize deviations between goals. We are focused on what can be achieved under the constraints that the organization is working under. An example of goal programming that is valuable to explore is one at Johnson Electric Company. The organization feels that currently maximizing profit is not feasible or realistic. The use of goal programming is valuable in determining the best production options. The management team has identified where the profit level should be during particular periods of time. The two deviational variables that are set forth include underachievement of the profit target and overachievement of the profit target. You can state the issue at Johnson Electric Company as a single-goal programming model. What if this organization wants to achieve several goals? This would identify deviational variables and the ranking of goals with priority levels would need to occur. Most goal programming problems have one goal that is more important than another goal. With these principles, the higher-order goals are satisfied before lower-order goals. Each deviational variable is assigned a priority level to identify the most to least important goals. Thus, organizations identify priorities for their main goals, of which three-to-five goals is a good parameter to follow. When goals are ranked, you can obtain a new objective function. Goal programming can also occur with weighted goals. Sometimes, we find that a goal may be two or three times more important than another goal. One approach can be to place the goals on the same level versus different levels, but there are different weights involved for each goal. The coefficients for the deviation variables include both the priority level of the goal and its weight. Non-linear programming With the methods discussed so far, we have assumed that the objective function and constraints have been linear. There are many nonlinear relationships in organizations that must be confronted. It is recommended to use Microsoft Excel to solve nonlinear programming problems. MSL 5080, Methods of Analysis for Business Operations 2 Suggested Reading Go to http://scholar.google.com/, the myCSU Online Library, or a similar business journal website, and research up to eight separate articles involving quantitative analysis, concepts, and topics covered within this unit of Methods of Analysis for Business Operations. Each article must be at least ten pages in length and be pertinent to the topics and concepts covered in Methods of Analysis for Business Operations. This is an excellent opportunity for you to research and take notes on how quantitative analysis plays an important role in the long term forecasting of profitability and growth within an organization. Learning Activities (Non-Graded) WebQuest Using http://scholar.google.com/, the CSU Online Library, or another search engine, research articles related to the concepts within this unit. Find five articles and write a one-paragraph summary of each, relating them to the various concepts within this unit and to quantitative analysis as a whole. Link these articles to problems you may encounter within an organization. Key Terms 1. 2. 3. 4. 5. 6. 7. 8. Balanced assignment problem Dummy destination Dummy source Facility location analysis Integer programming Local optimum Opportunity costs Transportation problems MSL 5080, Methods of Analysis for Business Operations 3