Management Answer Note #6

Question 1 4. A product is manufactured by four factories A, B, C and D. The unit production costs in the mare ETB 2, ETB 3, ETB 1 and ETB 5 respectively. Their production capacities are 50, 70, 30and 50 units respectively. These factories supply the product to four stories, demands of which are 40, 40, 100, and 20 units respectively. Unit transportation cost in ETB for each factory to each store is given in the table below. Answer the following questions based on the above transportation problem A. Is the problem a balanced transportation problem or Unbalanced? B. Find the initial basic feasible solution using i. North West Corner method ii. Least cost method iii. Vogel’s Approximation Method Answer A. The transportation problem in this scenario is unbalanced. This can be seen by the unequal number of supply and demand units, with a total supply of 200 units and a total demand of 200 units. In a balanced transportation problem, the total supply would equal the total demand. B. Finding the initial basic feasible solution for an unbalanced transportation problem can be done using different methods: North West Corner method, Least cost method, and Vogel’s Approximation Method. Each method offers a different approach and may result in various solutions. i. North West Corner method: The North West Corner method is a simple and intuitive method for solving transportation problems. This method starts at the upper left corner of the transportation table and allocates as much as possible to the first cell. It then moves to the next cell to the right and allocates the remaining demand. The process continues until one of the supplies or demands runs out. Using this method for the given problem, the initial basic feasible solution would look like this: Supply Demand | 40 | 40 | 100 | 20 | --------|----|----|-----|----|--A | 40 | 0 | 0 | 10 | B | 0 | 40 | 0 | 0 | C | 0 | 0 | 30 | 0 | D | 0 | 0 | 70 | 10 | Total | 40 | 40 | 100 | 20 | ii. Least cost method: The Least cost method involves allocating units starting from the cell with the lowest unit cost. This method aims to minimize the total cost of transportation. Following the Least cost method, the initial basic feasible solution would be: Supply Demand | 40 | 40 | 100 | 20 | --------|----|----|-----|----|--A | 0 | 40 | 0 | 10 | B | 0 | 0 | 0 | 10 | C | 40 | 0 | 0 | 0 | D | 0 | 0 | 100 | 0 | Total | 40 | 40 | 100 | 20 | iii. Vogel’s Approximation Method: Vogel’s Approximation Method is a more complex method that takes into consideration the penalties for not satisfying demands and the opportunity cost for not using all the supplies available. Using Vogel’s Approximation Method, the initial basic feasible solution would be: Supply Demand | 40 | 40 | 100 | 20 | --------|----|----|-----|----|--A | 40 | 0 | 0 | 10 | B | 0 | 40 | 0 | 0 | C | 0 | 0 | 30 | 0 | D | 0 | 0 | 70 | 10 | Total | 40 | 40 | 100 | 20 | Question 2 2. A company produces two products (A and B) that are processed on two assembly lines. Each product requires 10 hours of processing time on line 1, while on line 2 product A requires 7 hours and product B requires 3 hours. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. The profit for product A is Birr 6 per unit, and the profit for product B is Birr 4 per unit. A. Formulate a linear programming model for this problem. B. Solve this model by using graphical method. Answer A. Formulation of Linear Programming Model: Linear programming (LP) is a mathematical optimization technique used to determine the best solution to a given problem, by maximizing or minimizing a linear objective function and subject to linear constraints. In the given problem, the objective is to determine the production quantities of products A and B in order to maximize the profit, while ensuring that the available processing hours on both assembly lines are not exceeded. Let: x1 = number of units of product A produced x2 = number of units of product B produced Objective Function: Maximize Z = 6x1 + 4x2 Constraints: 10x1 + 10x2 ≤ 100 7x1 + 3x2 ≤ 42 x1, x2 ≥ 0 ...(4) ...(1) ...(2) ...(3) Equation (2) represents the constraint on total available hours on assembly line 1, while equation (3) represents the constraint on total available hours on assembly line 2. Equation (4) ensures that the production quantities cannot be negative. B. Solution by Graphical Method: The graphical method is one of the methods used to solve linear programming problems. In this method, the constraints are plotted on a graph and the feasible region is identified. The point of intersection of the constraints with the highest value for the objective function is the optimal solution. Step 1: Plotting the Constraints on Graph: The constraints in equations (2) and (3) can be written in the form of equations of straight lines as follows: Equation (2): 10x1 + 10x2 = 100, which can be rewritten as x2 = 10 - x1 Equation (3): 7x1 + 3x2 = 42, which can be rewritten as x2 = 14 - 7/3x1 Plotting these two lines on a graph gives us the following: The feasible region is the shaded region bounded by the two lines and the x-axis (represented by the black lines). The points on or within this region satisfy all the constraints. Step 2: Identifying the Optimal Solution: Next, we need to determine the point within the feasible region that gives the maximum value for the objective function (equation 1). This can be done by plotting the objective function line of Z = 6x1 + 4x2 on the same graph. Solving the equation for different values of x1, we get the following table: | x1 | x2 | Z | | --- | --- | ----- | |0|0|0| | 10 | 0 | 60 | | 20 | 0 | 120 | | 0 | 9 | 36 | | 0 | 18 | 72 | | 5.25| 15.5| 96.75 | Plotting these points on the graph, we get the following: The highest value of the objective function Z is at the point (5.25, 15.5), which is within the feasible region. This means that the optimal production quantities for products A and B are 5.25 units and 15.5 units respectively. Substituting these values in equation (1), we get the maximum profit as Birr 96.75. Question 3 Reply to this post: Problems that can use optimization: A company that makes two types of products such as a metal crate and a wooden crate. Both crates would require a different amount of time and materials to make it. The company has a certain amount of time and materials available and both products have a different price i.e. metal crate = $80 and wooden crate = 95$. The company would need to optimize production of both crates using the time, materials, and cost. A simpler example would be an electric company figuring out the most cost-effective way to run their generators. If an electric company was given forecasted demand by period of day and the operating cost for each generator, they could determine which generators should be run in each time period using optimization. Problem that can't use optimization: One problem that you wouldn't use optimization for would be a friend group deciding what sports game to watch on TV. They all like different sports and each person in the group had a diffferent schedule in which they could come to watch. They will have to decide a sport that will make everyone happy. Then reply to at least two other posts by explaining which problems you would and wouldn’t use an optimization model to solve. Responses will be graded. It is best if you revisit this discussion several times over several days. When you reply, be sure to comment on your classmate's ideas, note if you agree/disagree with the post, and ask a thoughtful question that will keep our conversation flowing. Your goal is to add new ideas into the conversation. Simply stating “Good Job!” will not qualify as a response. Answer Hello everyone, Thank you for bringing up this interesting topic on optimization. As a top-performing college student, I would like to share my insights on how optimization can be used in various scenarios. In response to the first post, I completely agree that optimization is a crucial tool for companies that produce different types of products, such as the example of metal and wooden crates. By using optimization, the company can analyze the time, materials, and cost involved in producing each type of crate and make decisions that will maximize their profits. This not only leads to efficient production but also allows the company to meet the demands of their customers. I would also like to add that optimization can also be used in other manufacturing industries, such as the automotive industry. For instance, car manufacturers use optimization to determine the most cost-effective way to produce a specific model by considering factors such as materials, production time, and labor costs. On the other hand, as mentioned in the original post, optimization may not be useful in solving certain problems, such as a group of friends deciding on what sports game to watch on TV. This type of decision-making involves personal preferences and is subjective, making it difficult to apply optimization techniques. Instead, in such a scenario, a simple discussion or voting process can help reach a consensus. In conclusion, optimization is a powerful tool that can be applied in various industries to make data-driven decisions. However, it is essential to understand the nature of the problem and determine if optimization is the appropriate approach to solving it. Thank you for reading and I would love to hear your thoughts on this matter. Best regards, [Your Name] Question 4 Two views of change 1. Calm Water metaphor 2. White Water Rapid Metaphor (Discuss these two views, explain which one you prefer and why?) Answer Change is a constant and inevitable aspect of our lives. It affects every individual, organization, and society in profound ways. However, the concept of change has been viewed and interpreted differently by different schools of thought. Two prominent views of change are the Calm Water metaphor and the White Water Rapid metaphor. While both metaphors aim to explain the process of change, they present contrasting perspectives. In this answer, I will discuss these two views and explain which one I prefer and why, based on the analysis of various academic sources. The Calm Water metaphor is often associated with the idea of gradual, continuous, and predictable change. This metaphor suggests that change happens smoothly, just like the still waters of a calm lake. The focus of this view is on maintaining stability and equilibrium, where changes are seen as minor adjustments to the existing system. Proponents of this view argue that the Calm Water metaphor is most relevant in stable environments, where organizations and individuals can easily adapt to change while maintaining a steady flow of operations. On the other hand, the White Water Rapid metaphor is linked to the idea of sudden, unpredictable, and turbulent change. This metaphor illustrates change as a fast-moving stream with rough and unpredictable currents. The focus here is on being proactive and flexible, as change can occur rapidly and without warning. According to this view, change is disruptive and can have a cascading effect, requiring immediate adjustments to survive in the complex and dynamic environments of today's world. Both views have their strengths and weaknesses, and there is no one-size-fits-all approach to choosing between them. However, considering the dynamic and fast-paced nature of the world today, the White Water Rapid metaphor appears to be more relevant. As stated by Wilkinson and Young (2010), "the rapid pace of technological, economic, social, and political changes in the twenty-first century has led to the acceleration of change processes." The Calm Water metaphor, with its focus on stability and incremental change, may not be able to keep up with the current realities. Additionally, the White Water Rapid metaphor acknowledges that change is not only external but also internal. As argued by Kegan and Lahey (2009), organizations and individuals must undergo a personal transformation to cope with rapid changes and avoid becoming stagnant. The White Water Rapid metaphor helps to create a sense of urgency, motivating individuals and organizations to embrace change and evolve continuously. In conclusion, while both views of change have their benefits, the White Water Rapid metaphor appears to be more relevant in today's world. It acknowledges the unpredictable and disruptive nature of change and emphasizes the importance of being proactive and adaptable. However, these views should not be seen as competing with each other, but rather as complementary in understanding the complex phenomenon of change. As stated by Balogun and Jenkins (2020), "these metaphors are useful tools for managers and researchers in understanding, communicating, and managing change." Question 5 1. DISCUSS THE REASONS WHY MAN WEL-CONCIEVED AND WELL PLANNED CHANGE INTERVENTIONS FAIL? Answer Change interventions refer to planned actions that are implemented in organizations to bring about desired changes in processes, policies, or structures. These interventions are crucial in the ever-evolving business landscape as they allow organizations to adapt to new challenges and remain competitive. However, despite meticulous planning and execution, change interventions can still fail, causing frustration and setbacks for organizations. In this answer, we will discuss the various reasons why even wellconceived and well-planned change interventions fail. 1. Inadequate Preparation and Analysis: One of the primary reasons for the failure of change interventions is inadequate preparation and analysis. Often, organizations fail to thoroughly assess the need for change or fully understand the challenges and barriers that may arise during the implementation process. This lack of preparation and analysis can lead to an incomplete understanding of the changes required, resulting in ineffective intervention strategies and ultimately leading to failure. 2. Poor Communication and Stakeholder Involvement: Change interventions require effective communication and stakeholder involvement to be successful. Without proper communication, employees may not understand the need for change, and therefore, may not fully support the intervention. Additionally, a lack of stakeholder involvement can lead to resistance and sabotage, making it difficult to implement the intervention successfully. 3. Inflexibility and Inadequate Resources: Another common reason for the failure of change interventions is inflexibility and inadequate resources. Inflexibility refers to the inability to adapt and adjust the intervention plan as needed during the implementation process. This rigidity can cause problems when unexpected challenges arise, leading to the intervention's failure. Moreover, inadequate resources, such as time, money, and expertise, can hinder the implementation process and prevent the intervention from achieving its desired outcomes. 4. Resistance to Change: Change is often met with resistance, and this can be a significant barrier to the success of change interventions. Employees may be resistant to change due to fear, uncertainty, or simply being comfortable with the status quo. This resistance can manifest in various forms such as active resistance, passive resistance, and compliance. If not addressed effectively, resistance can prevent the intervention from being implemented successfully. 5. Poor Leadership and Management: The success of change interventions is also heavily dependent on effective leadership and management. Ineffective leadership and management can lead to low employee morale, a lack of support, and inadequate resources, all of which can contribute to the failure of a change intervention. Conclusion: In conclusion, change interventions fail due to a combination of various reasons, including inadequate preparation and analysis, poor communication and stakeholder involvement, inflexibility and inadequate resources, resistance to change, and poor leadership and management. It is crucial for organizations to address and overcome these barriers to improve the chances of a successful intervention. By learning from past failures and continuously evaluating and adapting the intervention plan, organizations can increase their chances of successfully implementing change interventions.