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“Replacement decision” is a classical operation research topic in the industrial engineering. The replacement theory can indicate the optimal equipment life. “Optimal life” can be defined as the period between the time when the equipment comes into service and the time when it should be replaced due economic reasons. The operating cost of an equipment or asset generally rises as their condition deteriorates over time. When the cost reaches a certain level, the long-run costs associated with investment in a new equipment become less than those if keeping the old equipment [6]. At this point, replacement is carried out. Thus, a basic replacement analysis usually examines both the trend in operating and maintenance costs (O&M) and the net cost of replacement, which is defined as the difference between the cost of the new equipment and the salvage value of the old one. In some cases, the replacement analysis also considers the resale value of the equipment at various stages of its service life. For fleet replacement, the literature suggests two kinds of models: economic engineering (EE) and operational research (OR) models[12, 16]. EE models are restricted to economic and financial aspects, with technological, management and strategic variables considered as exogenous. This limitations force management to avoid formal investment analysis and to use unstructured subjective analysis [5]. Traditional OR models focus on a single objective to be maximized/minimized by modeling multiple variables. These methodologies are complemented by a management tool used for decision-making known as conventional Life Cycle Cost Analysis (LCC)[2]. According to Nowakowski [15] and other authors [7, 18], mathematical models of life cycle costs can be classified into three basic groups: models dedicated to technical objects’ manufacturers that are • designed to minimize the costs that occurred in the early stages of its lifetime, models aimed to minimize the lifetime cost of the facilities • already in operation, models oriented to customers willing to purchase a new techni• cal object.

Time replacement optimization model: comparative analysis of urban transport fleets using Monte Carlo Simulation