**Categories:**Theory of Constraints

# Local Optimum Versus Global Optimum Part 4

**A Simple Example**

In order to illustrate the methodology for calculating T, I, and OE the authors [1] ask us to consider a small wood shop that makes a single product – desks. As discussed in previous posts, the total throughput for this shop is the sum of the throughput contribution of each desk sold. To find the throughput of a single desk that sells for $400, we need to know the cost of all of the materials used to manufacture a single desk. The authors tell us that the cost of the wood, veneer, hardware, etc., used in the desk totals $100. To calculate the throughput (t) per unit for this desk, we use the following equation:

- t = sales revenue per desk – purchased material cost per desk
- t = $400 - $100 = $300 per desk

Using this formula, we can calculate the throughput for every desk sold. The total throughput (T) for any specific period is obtained by adding the total throughput per desk of all desks sold in that period. If the shop sells a total of 50 desks in a given month, then the total throughput (T) is found by summing up the throughput per desk for all 50 desks sold as follows:

Total Throughput = throughput per desk (t) x number of desks sold (q)

T = t x q

= $300 per desk x 50 desks

= $15,000

To find the inventory in the system, we need to find the purchase value of all of the production materials currently in the shop. This includes all of the wood material in various forms such as chip cores, veneer, cut and raw lumber; plus it also includes all of the material that is either in process and in the stockrooms, as well as hardware such as drawer hangers, knobs, and hinges. Remember, using the author’s method, their definition of inventory is valued at the purchase price paid. The value of all of this inventory was $32,000. Also remember that the inventory does not include production tools such as saws, drill and router bits, sanders, etc. Nor does this inventory include other supplies such as coffee cups, paper, etc. Operating expense includes all of the costs incurred in running the shop, as follows:

**Monthly Operating Expense**

**Category Amount**

- Salaries, insurance, and payroll taxes $10,000
- Rent and utilities $ 750
- Supplies (glue, finishing chemicals, etc.) $ 200
- Payment on equipment purchases $ 1,800
- Interest on borrowed funds $ 400
- Other miscellaneous items $ 300
- Total Operating Expenses $13,450

We then end up with the following values for Throughput (T), Inventory ( I ), and Operating Expenses (OE) as follows:

T = $15,000 I = $32,000 OE = $13,450

The authors go on to explain that to make more money, a manufacturing company must generate more sales, spend less money on conversion of raw materials to finished products, and have less money tied up in inventory. The authors summarize this by the following principle:

- Operational Measures Principle: Throughput should be going up, Inventory should be going down, and Operating Expense should be going down, ideally, all at the same time. However, it is possible and maybe even desirable to have one of the measures go in the wrong direction (or remain the same) in order to improve another one.

**Next Time**

In my next post, we will use an example to see the relationship between changes in T, I, and OE and the financial performance of the wood shop company. to demonstrate how net profit changes as T, I and OE change. As always, if you have any questions or comments about any of my posts, leave me a message and I will respond.

Until next time.

Bob Sproull

**References:**

[1] L. Srikanth and Michael Umble, Synchronous Management – Profit-Based Manufacturing for the 21^{st} Century, Volume One – 1997, The Spectrum Publishing Company, Wallingford, CT

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