# Flow Rate

5.1 Objective

Chapter 3 introduced the three basic building blocks of process flow namely the (average) flow time, (average) flow rate and (average) inventory. It is followed by a sequence of three chapters, 4, 5 and 6, which examine each one of these measures individually. Chapter 5 is concerned with flow rate analysis and issues of capacity. The major managerial concept discussed in the in the chapter is that of the bottleneck. We use the notion of the theoretical capacity as a practical and easy to grasp introduction to this topic.

5.2 Additional Suggested Readings

As in the case of the previous chapter, we assign Pizza Pazza (Kellogg case) as the major case for this module. (The Kristen Cookie Company, (HBR case #9-686-093) is a fine alternative; see problem 2 at end of chapter). The case is simple and accessible to most students, yet allows a rich discussion of the various factors that affect flow rate such as batch size, oven size and type, etc. In addition, the effects of product mix are introduced using the MBPF, Inc. example of building garages, (see problem 3). The example is small enough that it can be analyzed without the use of any formal optimization tools. For more complex examples, we rely on LP formulation, which are solved using the SOLVER routine of Excel.

The chapter provides an excellent opportunity to discuss the book The Goal (E.M. Goldratt and J. Cox, North River Press, 1992), which most our students find very informative and entertaining.

We assign the National Cranberry Cooperative case (HBS case # 9-675-014) which allows students to test and apply the concepts learned in a fairly complex setting.

Suggested Questions:

1. Draw a detailed process flow map of the current process at Receiving Plant #1. What is the capacity of each operation in the process?

2. What is the maximum long-term achievable throughput rate of Receiving Plant #1? What factors affect this throughput rate?

3. Currently what is (are) the major reason(s) for trucks waiting and excessive overtime?

4. On average, how long will the trucks have to wait on a busy day? Assume a 7am start of processing of berries and a continuous arrival rate of berries of 1,500bbls/hr.

5. What benefits would you expect if processing time were moved up from 11:00a.m to 7:00a.m. during the peak period? Should this be done for the entire season?

6. NCC is considering the purchase of two new dryers and the conversion of up to 10 dry berry holding bins so that they can hold water-harvested or dry berries. What are your recommendations? Assume that drivers are paid $5 per hour.

You may want to download (from http://www.prenhall.com/anupindi/) and use the Excel workbook NCC.xls to analyze this case. We have allowed the students to use the spreadsheet. In class we illustrate how one could analyze the case (without the spreadsheet) using inventory build-up diagrams.

Answer: Remained unchanged since the bottleneck capacity is unaffected.

5.3 Answers to Questions

5.1

a. At 50% product mix, the Unit load at each department is given

| |Unit Load Shopping |Unit Load |Unit Load | | |(hrs per contract) |Medical |Mix | | | |(hours per contract) |(hours per contract | |Paralegal |4 |6 |5 | |Tax lawyer |1 |3 |2 | |Senior partner |1 |1 |1 |

The capacity of the various departments is :

| |Unit Load (hrs per...

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