Industrial utility systems offer many degrees of freedom to improve their design and operation to achieve substantial savings in capital and/ or operating costs. However, minimizing such expenditure also represents a challenging task due to the complex and highly-combinatorial nature of the optimization problem. While conventional approaches have simplified the problem by addressing operational and design (synthesis) issues in a separate or iterative way, the present work proposes a novel computational tool for both the design and operation of industrial utility systems in which their inherent flexibility is fully exploited through different operating scenarios. In order to consider the design and operational parameters of these systems as (continuous) mathematical variables to be optimised simultaneously, a new generic modelling framework for energy equipment has been developed and validated in which performance depends on both unit size and operational load. The first part of this paper describes the linear models developed to solve this problem for multi-fuel boilers, steam and gas turbines and heat recovery steam generators. These are employed to build a robust (multiperiod) MILP formulation to tackle grassroots design, retrofit or operational problems of the size and complexity commonly found in large industrial systems. © 2007 Institution of Chemical Engineers.