An activity matrix (AM) shows the activities that transform an organization's inputs into outputs. The inputs are the system targets and the materials, energy and other resources that are used to achieve these. The outputs are the system performance expressed in terms of production, quality, profit, environmental performance, waste, etc. Performance may be measured against the financial, environmental, technical, social or other system targets. A concurrent enterprise view is used to represent the manufacturing system activities and the paper examines how an AM may be used to represent and design systems. Two kinds of AM are examined; an unconstrained activity matrix and an input-output activity matrix (IOAM). With an unconstrained AM, the system designer chooses system outputs (attributes or requirements) intuitively. This provides great flexibility and allows e.g. the social and organisational implications of proposed changes to be investigated. The inputs are not formally stated. Although a systems designer normally focuses on identifying the stages of a product life cycle and analysing their impact on the system's outputs, the main emphasis of the paper is on the IOAM and its use to represent the transformation of an organization's inputs into outputs. The input-output representation developed in the paper is used to examine manufacturing and logistics systems. First, the IOAM is used to represent a manufacturing system (as one tier of a logistics chain) and its performance. Secondly, the LOAM representations may be derived for a multi-tier system to represent its production, economic and environmental performance. (C) 2011 Elsevier B.V. All rights reserved.