MGX 3771 Operations Management
Individual Assignment 1 (40 marks)
Due date: 5 September 2021 at 11.55 PM (Melbourne Local Time)
- Answer the problems according to the assigned order.
- All steps of the calculations must be shown clearly, leading to the final answer.
- Use two decimal points in your final answers (wherever applicable).
- Wherever possible, use word processing to write your answer. While handwriting can be used (particularly for diagrams and formulas), readability and good layout must be carefully maintained.
- Do not take any risk of collusion or plagiarism! Never share your work with anyone!
1. Line balancing (9 marks)
A manufacturing company sets up an assembly line that operates for 8 hours per day to produce its products. The daily demand for the products is 200 units. The tasks involved in this assembly line are listed in the table below:
|Task||Task Time (seconds)||Preceding Tasks||Task||Task Time (seconds)||Preceding Tasks|
|F||60||C||L||30||G, J, K|
Answer the following questions:
- Draw the precedence diagram of this assembly line, and calculate the workstation cycle time along with the estimated number of workstations required to achieve the demand (1 mark).
- Balance the assembly line using the largest number of following tasks as the primary priority rule and the longest-task-time as the second priority rule to achieve the demand. Use tables to show the number of following tasks and arrange the tasks into workstations. Calculate the idle time of each workstation and the efficiency of the assembly line (2 marks).
- Re-balance the assembly line using the longest-task-time as the primary priority rule and the largest number of following tasks as the second priority rule. Use a table to arrange the tasks into workstations. Calculate the idle time of each workstation and the efficiency of the assembly line; are they different from the one in sub-question b)? Why? (2 marks)
- If the demand increases by 20%, apply the two strategies below to meet the new demand:
- Use overtime to meet the new demand using the assembly line of sub-questions b) and
c). Is the overtime different between the two assembly lines? Why? (1 mark)
- Re-balance the assembly line using the longest-task-time as the primary priority rule and the largest number of following tasks as the second priority rule to achieve the new demand. Use a table to arrange the tasks into workstations. Calculate the idle time of each workstation and the efficiency of the assembly line (2 marks).
- Based on the individual task times, calculate the maximum output that the assembly line can produce within the daily working hours and the estimated number of workstations required to achieve that output (1 mark).
2. Queueing (7 marks)
A small cafeteria serves very popular drinks and operates for 8 hours, 7 days per week. It charges customers $10 per drink. The data shows that customers arrive at the café at an average of one every 5 minutes. The café employs one staff, and, on average, it takes 4 minutes for the staff to serve each customer (from taking the order and the payment and making the drink). The hourly salary of the staff is $25.
(Assume a Poisson distribution for the arrival rate of customers and exponential distribution for the service time performed by the staff).
Answer the following questions:
- Due to limited space, only 3 customers can be accommodated inside the cafe, and the rest must wait outside. What is the probability that at least one customer waiting outside the café? (1 mark)
- Assume that customers do not want to wait in a queue for more than 8 minutes. What is the average number of customers the café would lose per day? (1 mark)
- To improve the service, the management wants to reduce the probability of customers waiting outside the café down to 10%. How would that decision affect the service time and customer’s waiting time? Use trial and error to find the answer, and show the two closest figures above and below your final answer at 2 decimal points (1 mark).
- The management considers three options to reduce the customers’ waiting time:
- Employing another staff to take the order and payment while the original staff will make the drink only. This option will reduce the service time by 50%.
- Employing another staff (with a similar level of skills to the original staff) to perform the full service to customers.
- Replacing the staff with an automatic machine with an average service time of 4 minutes per serve (assume normal distribution). The automatic machine costs $20,000. Calculate the average customers’ waiting time for each of the three options (2 marks).
Compare the three options and provide your recommendation to the café. Consider other aspects than customers’ waiting time in your recommendation (2 marks).
3. Tree decision diagram (5 marks)
A company operates in one small city with an annual operating cost of $200,000 per year and an annual sales revenue of $400,000 per year. The manager considers moving to a big city to expand the business and increase the sales revenue. To relocate to the big city, the company must carry the relocation cost of $1,000,000, and the annual operating cost in the big city is 50% higher than in the small city. Based on the historical record of the big city, the company is aware that it would face four different market growth scenarios:
- high growth where annual sales revenue will increase to $1,600,000 per year.
- Medium growth where annual sales revenue will increase to $800,000 per year.
- Low growth where annual sales revenue will increase to $600,000 per year.
- Zero growth where annual sales revenue will have no increase.
The probabilities of the high, medium, and low growth of sales revenue in the big city are 15%, 20%, and 25%, respectively.
The company can decide to relocate to the big city straight away. Alternatively, it can seek information from a marketing research company to explore the probabilities of the market growth in the big city first before making the final decision. The marketing research will cost the company $200,000. From experience, the marketing research company will produce either an optimistic report or a pessimistic report on the four market growth scenarios in the big city as outlined above. For the optimistic report, the probabilities of the high, medium, and low growth of sales revenue are 20%, 30%, and 25%, respectively. In contrast, for the pessimistic report, the probabilities of the high, medium, and low growth of sales revenue are 10%, 15%, and 30%, respectively. The probability of the company receiving an optimistic report or a pessimistic report is equal to 50%. The company still can choose not to relocate to the big city upon receiving the report.
- Analyze the above scenario using a decision tree diagram by calculating the potential profit over 5 years. Assume no discounted values over the 5 years period. Explain the calculation in every node of the tree diagram (4 marks).
- Based on your decision tree diagram analysis, recommend the company to help it make the decision. Are there any other factor(s) to consider than just the potential profit in making your decision? (1 mark)
4. Aggregate capacity planning (11 marks)
A company is setting up a production capacity plan over four seasons. The normal operating hours are 8 hours per day and 60 days per season. The demand forecasts for Autumn, Winter, Spring, and Summer are 100,000 units, 80,000 units, 70,000 units, and 90,000 units, respectively. At the beginning of Autumn, the company has 80 workers and 8,800 units of inventory. The productivity rate of each worker is 2 units per hour, and all workers work at their full capacity within the normal operations hours.
The operating costs that are applied in this company are as follows. Straight time labor costs are $40 per hour, and overtime labor costs are $60 per hour. The backorder cost is $20 per unit season, and the inventory holding cost is $30 per unit season. Hiring cost is $1,000 per worker and laying off cost is $2,000 per worker.
- Construct a production plan and the total costs over the four seasons under the following scenario. The company is only allowed to hire and lay off workers in Summer. Backorders are only allowed in Autumn, Winter, and Spring; however, overtime must be used to prevent or reduce backorders in winter and spring. The overtime is limited to 7,200 hours per season. In your production capacity plan, show the calculations of the backorder units and inventory units, the overtime hours, and the number of people hired and laid off, along with their associated costs (3 marks).
- Construct another production plan and their total costs for the four seasons using chase demand strategy where the company is allowed to hire and lay off workers in Autumn, Winter, and Spring to meet the demand of the season and the number of workers in Spring must be kept in Summer. Backorder and overtime are not allowed in all seasons, while inventory is allowed in all seasons, except in Summer (3 marks).
- The company considers using a level capacity strategy in its production plan by keeping 85 workers over the four seasons. Overtime (limited to 7,200 hours per season), inventory, and backorders are allowed in all seasons except summer. Based on this scenario, construct a complete production plan that produces the lowest total costs (3 marks). Explain clearly the logic behind your production plan (2 marks).
5. Case study analysis (8 marks)
Sunflower is a company that produces unique products sold through a retailer that opens 7 days per week. Historical data suggests that the average annual demand for the product has been relatively stable over the past few years. Interestingly, the sales data also shows that the demand has seasonality. In the first and third quarters of the year (low season), daily demand dropped to 600 units per day, while in the second and fourth quarters (high season), it jumped to 1,000 units per day. Market analysis suggests that the demand for Sunflower’s products will start to grow in two years (from Year 3). The demand projection for the next five years is presented in the table below.
|Demand units per day|
Sunflower’s current assembly line configuration for the product consists of three sequential processes, and each process uses one machine that one operator runs. The production capacity of the three machines is 125 units/hour, 150 units/hour, and 100 units/hour, respectively. The company operates 8 hours per day 7 days per week. The retailer sends its daily delivery requirements for the products to Sunflower at the end of the week. Sunflower’s Operations Manager suggests adopting a production system where products are only made after receiving the customer’s order. The manager also believes that the company should make the products and deliver them daily according to the order volume from the customer. The company uses overtime to meet peak demand during the high season. The sales record so far shows that the company has delivered the customer’s orders on time, and it has received no complaints from the customer.
Sunflower’s top management is excited with the prospect of the future growth in demand, and the Operations Manager believes that the company should start to expand its production capacity by adding new machines as soon as possible. However, the top management is not certain about taking the decision.
Based on the case study above, answer the questions below: (Word limit: 500 words)
- Discuss the competitive dimensions that apply to Sunflower’s operations and how the company performs on those dimensions (2 marks).
- Discuss the problems you can identify in Sunflower’s operations and their implications on business performance (e.g., sales, profit) (2 marks).
- Based on your analysis on sub-question b), provide recommendations to Sunflower management of potential improvements in its operations for Year 1 and Year 2 before demand starts to increase (2 marks).
- Provide analysis and recommendations for Sunflower’s operations in anticipating the growth in demand starting from Year 3 onwards (2 marks).
You can use table(s) or diagram(s) in analyzing the relevant information (including the quantitative data) presented in the case study to support your answers and demonstrate your understanding of the theories or the concepts of operations management in your answers.