Problem 1: Computer Assembly
DHP is a company that assembles and sells computers. Suppose DHP has only one sequential process to produce PCs. Under the current process layout, each step has one worker assigned to it (total 7 workers). Steps and processing times are summarized in the following table:
Step Task Processing Times (minutes)
1 Check order 20
2 Request material 30
3 Assemble motherboard 20
4 Assemble case 40
5 Install software 60
6 Quality test 50
7 Packaging 20
Suppose each worker receives a wage rate of $15 per hour. First, answer the following question:
a) What is the bottleneck in this process? What is the capacity of the assembly line per hour?
Assume the demand rate is just equal to the process capacity you obtained in (a). Answer (b-c):
b) What are the utilizations of the workers in the stations 1, 3, 5 and 7?
c) What is the direct labor cost, expressed in dollars per PC?
Now, suppose the plant has decided to cut staffing from 7 to 5 workers of this process. There will be still 7 sequential steps without any change from what is shown in the above table, but now there are only 5 workers who will operate these 7 steps (some of the workers will operate more than 1 step). Assume that if one worker is in charge of two steps, the steps have to be adjacent (e.g. one worker can operate steps 1 and 2 but cannot operate steps 1 and 3); moreover, this worker has to operate them sequentially (i.e., one worker can operate only one step at a time). Answer questions (d-e):
d) What is the most efficient way (in terms of process capacity) to assign the 7 steps to the 5 workers based on the above description? What is the new capacity of the line (PCs per hour)?
e) Assume after the change the demand rate is still just equal to the process capacity you obtained in (d). What is the new direct labor cost expressed in dollars per PC (wage rate keeps the same $15 per hour for each of the 5 workers)?
Problem 2: Inventory Cost with Little's Law
A manufacturing company producing medical devices reported $40,000,000 in sales over the last year. At the end of the same year, the company had $10,000,000 worth of inventory of ready-to-ship devices.
a) Assuming that units in inventory are valued (based on COGS) at $500 per unit and are sold at $800, how fast does the company turn its inventory?
b) The company used a 20 percent per year cost of inventory. That is, for the hypothetical case that one unit of $500 would sit exactly one year in inventory, the company charges its operations division a $100 inventory cost. Based on the inventory turn you obtained in a), what - in absolute terms - is the per unit inventory cost for the product of the company?
Problem 3: Process with Setup
Consider the following batch-flow process consisting of three process steps performed by three machines:
Work is processed in batches at each step. Before a batch is processed at Step 1, the machine has to be set up. During a setup, the machine is unable to process any product.
a) Assume that the batch size is 100 parts. What is the bottleneck in this process? What is the capacity of the process?
b) What batch size would you choose in order to minimize the inventory without reducing the process capacity? Assuming that all units of a batch have to be processed before they can move to the next step.