Question

Wally’s Widget Warehouse takes orders from 7 a.m. to 7 p.m. The manager wants to analyze the process and has provided the following process flow diagram. There are three steps required to ship a customer order. The first step is to take the order from a customer. The second step is to pick the order for the customer, and then they have to pack the order to ready it for shipping. Wally promises that every order placed today gets shipped tomorrow. That means the picking and packing operations must finish all orders before they go home.

Wally wants to figure out the following:

1. What is the current maximum output of the process assuming that no one works overtime?

2. How long will the picking and packing operations have to work if we have a day where the order taker works at his maximum capacity?

3. Given b, what is the maximum number of orders waiting to be picked?

4. Given b, what is the maximum number of orders waiting to be packed?

5. If we double the packing capacity (from 60 to 120 orders per hour), what impact does this have on your answers in parts (b), (c), and (d)?

Please show work!

Answer 1

a) Take Order = 100 per hour * 12 hours = 1200
Pick Order = 80 per hour * 24 hours = 1920
Pack Order = 60 per hour * 24 hours = 1440

The maximum capacity of the process is limited by the bottleneck process, which in this case is order taking (1200).

b) If we take the maximum of 1200 orders then:

Pick Order = 1200 orders / 80 per hour = 15 hours

Pack Order = 1200 orders / 60 per hour = 20 hours.

c) Orders can be taken at a rate of 100/hr and can be picked at a rate of 80/hr, so they build at the rate of 20/hr. Orders are taken for 12 hours,

thus the maximum orders waiting for picking = 20/hr * 12 hrs = 240.

d) Orders can be picked at a rate of 80/hr and can be packed at a rate of 60/hr, so they build at a rate of 20/hr. Orders are picked for 15 hrs,

thus the maximum orders waiting for packing = 20/hr * 15 hrs = 300.

e) b is changed, If we take the maximum of 1200 orders then: Pick Order = 1200 orders / 80 per hour = 15 hours, Pack Order = 1200 orders / 120 per hour = 10 hours, However, packing has to wait for the orders to be picked, so it would be 15 hours.