Operations Management Problems and Solutions

College Threads T-Shirt Manufacturing Process

1. College Threads is a manufacturer of t-shirts and other license-based apparel. Below is a summary of their current t-shirt manufacturing operations.  

The purchased fabric first enters the dyeing stage.  They currently own 1 dyeing bin which takes 1 hour to complete the dyeing, but can process fabric for 400 t-shirts at a time. The dyed fabric is then immediately moved to a drying station where it takes 60 minutes to allow the dye to set. The drying station can accommodate fabric for 800 t-shirts.  

The dried fabric is then moved into cutting where 2 cutting machines can each process fabric for 100 t-shirts per hour. Once the fabric is dyed, dried and cut, it is moved into sewing where 5 employees can each sew 1 t-shirt per minute.  From there, the sewn t-shirts are fed into a single printing and packaging machine that prints college logos and packages t-shirts at a rate of 30 seconds per t-shirt.

The completed t-shirts are then moved into a warehouse where they await shipping to college bookstores and other apparel retailers.

a. What is the processing rate, in t-shirts per hour, of each work station? What is College Thread’s capacityin t-shirts per hour?  How many t-shirts could they produce in a 16-hour day?

b. Should College Threads consider reducing the number of employees they currently allocate to sewing?  

c. Assuming that College Threads has unlimited demand for its t-shirts and gains $5 in profit from each t-shirt it sells, how much would they be willing to pay per 16-hour day to rent a new printing and packaging machine?

2. Consider the following process shown in the flowchart. Even though buffers are not shown in the flowchart, assume flow units can wait between steps. The numbers in the flowchart indicate the task numbers. There are a total of seven workers, each assigned to one of the tasks. Each task is performed by one worker and for batches of 5 Flow Units. Task times for individual flow units are given as follows:

a. What is the (theoretical) flow time of a batchin this process? (The theoretical flow time disregards any waiting time). Do not just provide a number; show details.

b. The operations manager measures the average flow time of this process making use of a large number of observations and determines the average flow time to be 120 minutes/batch. The average flow time includes waits between steps. She observes variability in worker task times. What is the flow time efficiency of this process? (Simply defined as the theoretical divided by the average flow time)

c. How would you improve the flow time efficiency of this process? Answer specifically for the process shown (not generic answers) and explain why/how your proposed change will improve flow time efficiency for each suggestion.

3. In a large store of The Gap, 10 identical cashiers are located in the center of the store, where customers form one line to pay for their purchases. 60% of purchases are observed to be from the Women’s Section, 30% from the Men’s Section and 10% from the Kids Section. Customers are complaining about the long wait for the cashiers.  The Store Manager is proposing to split the cashiers, placing 6 in the Women’s Section, 3 in the Men’s Section, 1 in the Kids Section. The Manager believes that this will reduce the wait for a cashier?

Do you agree with this claim YES or NO?

Justify your answer:

4. A “call center” gets 9 calls per Currently there is one agent who can answer 10 calls per hour. Arrivals follow the Poisson distribution (ie. exponential inter-arrival times) and the service times follow the exponential distribution. Make sure to show work: parameters used, assumptions made, intermediate calculations if any, etc.  in your analysis below:

1. What is the utilization for the agent?
2. What is the average number of customers in the system?
3. The manager is considering hiring additional agents to increase customer satisfaction. The hourly salary of an agent is $10. It is estimated that one-hour of customer time spent in the system (waiting or being served) costs $25. Find the hourly agent cost and hourly cost of customer wait for the case of 2 agents and 3 agents.   Determine the optimal number of agents that minimizes total cost (agent and customer wait). Show work.

5. A super-market chain satisfies online orders for vegetables and fruits by hand-picking the customer orders from their stores. The chain has 16 stores. For a popular product like tomatoes, each store keeps 200 kg. of safety inventory. A consultant suggests moving fruits and vegetables for the online channel to a so-called darkroom. A darkroom is a warehouse where storage conditions are optimized to minimize waste of fruits and vegetables. The darkroom will keep inventory for all 16 stores.

1. 1. Assuming that demand for tomatoes at your stores are independent and identical with a Normal distribution, there are no changes in lead time, and that you are aiming for the same service level at the darkroom as at the stores, how much tomato safety inventory would you keep in the darkroom? Explain your reasoning.
      
      
   2. If demand for tomatoes at stores were negatively correlated, would you expect to keep same/more/less safety inventory in the darkroom relative to your answer in part a? Explain.