Spreadsheet Models for Managers

Demonstrations for Session 2
Analysis and Synthesis

We have one demonstration (2000-4 or 2007+) for this session: Using Array Computations in Excel.

Using Array Computations in Excel (2000-4) or (2007+)

[Sheet: Furniture]

In this example, we're given an array of furniture prices (FurniturePrices), an array of furniture requirements for a range of job categories (FurnitureAnalysis), and a breakdown of the total headcount by employee category (EmployeeAnalysis). We're asked to compute the breakdown of furniture required, by type.

All we have to do to find the array of furniture we need (FurnitureAllocation) is to multiply the FurnitureAnalysis by the EmployeeAnalysis, as an array product. This has the effect of multiplying each row of FurnitureAnalysis by the number of employees of that type.

To find the cost of this amount of furniture, we use either of two approaches, which yield the same result. In the first approach, we multiply FurnitureAllocation by FurniturePrices, using array multiplication. Then we sum up the cells of this range, and the result is in C34.

In the second approach, we use matrix multiplication:

Of course, whenever we use MMULT or TRANSPOSE, we have to enter the formula as an array formula.

Here we transpose EmployeeAnalysis, because its dimensions are (Category x 1) and those of FurnitureAnalysis are (Category x ItemType). The matrix product of the result is therefore (1 x ItemType). When we matrix multiply that by FurniturePrices, which is (ItemType x 1), the result is (1 x 1), which is just a number, and the total we seek.

In the next part, we're given the hiring streams for all categories of employees, in a range called HiringAnalysis, and we're asked to compute the cash stream that pays for the furniture of new hires. We can do this in a single formula using matrix multiplication:

This forms the product of three matrices. You might be wondering why we didn't write this as

Whether you use MMMult or MMult, the units of this product, using dimensional analysis, are $/item * items/headcount * headcount = $. The matrix shapes are

The result thus has units of $ and is a single row 6 months wide.

Next, we seek the procurement schedule for the furniture items of various types. To do this, we have to figure out how to multiply the matrices together. We know the HiringAnalysis, which is a matrix of (EmployeeCategory x Month), and we know the FurnitureAnalysis, which is a matrix of (EmployeeCategory x ItemType). The procurement schedule is a matrix of (ItemType x Month). So the matrix product we seek is

This is implemented in the formula

Finally, we compute cumulative procurement as the running sum of procurement.