Question

The Yum and Yee food truck near the business school serves customers during lunch hour by taking orders and making fresh batches of stir-fry. Customers have only one choice during the lunch hour so that Y&Y can maximize the number of customers served. Assume that each customer places just one lunch order, and all lunch orders are the same size: one unit of stir-fry. The stir-fry cooking works in this manner. First, one person cooks a batch of orders in a wok. The cooking depends upon the number of orders in the batch. The time to cook just one order is 3.4 minutes. For each additional order in the batch, it takes 0.4 minute more to cook. Thus, cooking two orders in a batch takes 3.8 minutes, cooking three orders takes 4.2 minutes, and so on. The other process is bagging and accepting payments (done by a separate person), which takes 0.7 minute per order.

a.What is the Setup time

b.If Y&Y operates with bath sizes of 7 units, what is their process capacity (in orders per minute)?

c.If Yum an Yee operates with batch sizes of 12 units, what is the utilization of the wok?

d. Calculate the batch size (in orders) that maximizes the overall flow rat (assume there is ample demand)? Do NOT round the batch size (i.e., assume for this calculation that a noninteger batch size is possible.

Answer 1

a. Setup time is 3 mins viz. time difference between first-order and additional order cooking time in the same wok (3.4 - 0.4) mins

b. Process Capacity = Total number of Orders/Time taken to process these orders

Total numbers of orders = 7

Time taken to process 7 orders = 3.4 + 0.4 X 6 (Cooking time) + 0.7 X 7 (packaging and billing) = 10.7 mins

Process Capacity = 7/10.7 = 0.65 orders per min

c. Utilization of Wok = Total setup and cook time of wok / Total available time

Total setup and cook time ( for a batch with the size of 12 units) = 3.4 + 0.4 X 11 = 7.8 mins

Total available time = 60 mins (Lunch hour)

Utilization of Wok = 7.8 / 60 = 13%

d. In order to maximize the overall flow rate, we need to determine how much orders can be fulfilled in one-hour for continuous demand. Let's assume a unit order be 'P'

Hence total number of orders to be filled in an hour = 3.4 mins + 0.4 min X (P-1) + 0.7 min X P <= 60 min

Solving this equation we will get P = 51.81 , since we need to take integer orders hence P = 51 orders (or batch size)