Basics of modelling and simulation
The following is a practical problem which we subject to mathematical analysis and optimization, that of replacing equipment (ERP), for example replacing your car or your computer. We will analyze these problems in detail, and find the simplest closed form solutions.
On the other hand, these types of problems are easily solved by simulation, and this is the tool which should be used when the problems have enough details to make them more realistic.
So we have a choice between closed form solutions and simulation: simulations have greater accuracy in the sense that they reflect reality more closely, closed form solutions indicate functional dependence on the parameters, giving structural insights. Both are very important tools.
The replacement paradox
The replacement paradox refers to the familiar situation that one faces when equipment has aged and it may be time to replace it. At a given time two choices are available: continue using the old equipment, which has lower performance and higher maintenance cost, or buy new equipment which will have better performance and lower maintenance, but a higher initial capital expenditure. The paradox arises from the fact that if we look only a short period of time into the future the decision is always bent towards keeping the old equipment, never replacing it. The maintenance and repair costs for the immediate future are far less than the replacement cost.