The Simple Analytics of Matrix Accounting, Activity‐Based Costing, and Linear Programming

• Published date: 01 March 2016
• DOI: http://doi.org/10.1002/jcaf.22139
• Date: 01 March 2016

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© 2016 Wiley Periodicals, Inc.

Published online in Wiley Online Library (wileyonlinelibrary.com).

DOI 10.1002/jcaf.22139

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The Simple Analytics of Matrix

Accounting, Activity-Based Costing,

andLinear Programming

Melvin Hughes

INTRODUCTION

This article devel-

ops a matrix model

of cost account-

ing and integrates

activity-based costing

(ABC) with linear

programming. The

“analytics” are sim-

ple; one only needs

to understand the

basics of matrices in

this article. While the

“simplex” algorithm

of linear program-

ming (LP) is not so

simple, computer

programs do the mathematics.

Thus, a technical treatment

ofLP is not needed for our

purposes. Just a general intui-

tive knowledge of LP is suffi-

cient. There will be two follow-

up articles that work through

the model step by step on the

computer.

In terms of literature

review, I just treat a few matrix

accounting articles and mono-

graphs from the 1960s for those

who wish to delve deeper into

matrix accounting. For this

audience, I assume the reader is

well versed in cost and manage-

rial accounting and ABC.

In the third section, I

develop a matrix model of prices

and direct costs. While tradi-

tional managerial accounting

techniques exist already, Iwill

show that the matrix model

is very powerful for what-if

analyses. Also, matrices are

computationally

efficient, and many

keystrokes are saved,

even with computer

shortcuts on mod-

ern computers. The

fourth section devel-

ops contribution

margin and direct

margin, and, coinci-

dentally, the model

quickly calculates

variances (variances

are not developed in

detail, but introduced

to show the power of

matrices). The fifth

section discusses appli-

cations of the model in the con-

text of hotel food service. The

sixth section develops a matrix

model of overhead allocation

under the ABC paradigm, com-

pleting a stylized model of the

firm. The seventh section coor-

dinates ABC and LP, suggesting

solutions to issues that arise

using LP models. The final sec-

tion concludes with comments

on uses of the mod el and sug-

gestions for further inquiry.

In the 1960s, accounting scholars researched

matrix accounting and linear programming. The

accounting profession didn’t incorporate the

research into mainstream accounting. This is

probably because the research was too abstract

and showed no immediate use. Indeed, I built the

present model from the ground up. The material

was classroom tested for 6 years at an Asso-

ciation to Advance Collegiate Schools of Business

(AACSB) accredited business school. The material

was well received because students could use a

company’s existing activity-based costing system

to build a linear programming problem.

© 2016 Wiley Periodicals, Inc.

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