Manufacturing Capacity

The Problem

The PrasMic Corporation is a manufacturer of metal parts for automobiles and machine tools. At the end of their production line are four machines that hone the parts, that is they refine existing holes to a precise diameter in the parts. PrasMic is concerned about their honing capacity. Occasionally the weekly demand is greater than their weekly honing capacity, a shortage occurs, and the customer�s demands are not met. The company does not run at maximum capacity the entire time because having honed product in inventory costs money. They prefer to hone and ship as necessary. However, to buy a new machine costs approximately $4 million and take 18 months to order and install.

Complicating the situation is the company�s record keeping. PrasMic receives release forms from its various customers which contain the customer�s order for the week and their predicted order for the next nine weeks. Because PrasMic prefer to hone on demand, they have always only considered the current demand when planning their production and very rarely kept the release forms to look at the predicted demand for the coming weeks. As a result, the data set is incomplete and only contains information from the release forms the company happened to keep. Regardless, PrasMic needs the existing data analyzed and a recommendation given for how to deal with their capacity shortages.

Areas of Application

Reasoning & Deduction
Basic arithmetic: averages
Algebra: rate conversion, percentages, scatterplots, line of best fit, correlation coefficient

Explanation of Alignment with Standards

Background Information

Data is provided for three of the four companies for which PrasMic manufactures parts:

Fiord and Costly are automobile manufactures.
Walabe is a machine parts manufacturer.
Unskil is a machine tool manufacturer (no data available).

There are four machines:

Two machines are dedicated to honing parts for Fiord and Costly.
One machine, affectionately called "Bing Angus", hones parts for Walabe.
One machine hones parts for Unskil (no data available).

PrasMic rarely has one hundred percent uptime:

The Fiord and Costly machines average seventy percent uptime.
Big Angus and the Unskil machine average eighty percent uptime.

PrasMic currently has two production schedule depending on demand

Their regular work schedule is five days with approximately twenty-one machine hours per day.
Their overtime work schedule is six days with approximately twenty-one machine hours for the first five days and fifteen overtime hours on the sixth day

Materials Included

Long Version:

Release form information for all twenty-one parts over an approximately forty-five week period.
Capacities for the four honing machines.

Short Version:

Release form information for six parts over an approximately forty-five week period.
Capacities for the four honing machines.

Both Versions:

List of possible questions to consider.
Suggestions on how to handle the missing data.
Sample scatterplots & graphs.
Instructions on calculating a correlation coefficient.
Suggested extensions.

Download

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Last modified: Jun 25, 2010, 14:54 UTC