You may be responsible for inventory in a store and have to manage orders. Or you may have to contend with uncertainty over future hotel room bookings and set room rates to increase occupancy. Or perhaps you oversee a company's logistics and must allow for the uncertainties of road traffic when planning delivery routes. Whatever the case, the model you want to build falls within the realm of stochastic modeling, the term "stochastic" meaning "governed by chance."
A middle-school student's journey ----------------------
Consider a student who walks to middle school. We are interested in the journey time, which depends on whom the student meets along the way. The walk takes half an hour when the student is alone, but meeting a friend on the way adds another quarter of an hour. To understand the actual journey time, we therefore need to know the probability of such a meeting. Suppose there is a 60% chance of meeting a friend; the journey will then take three-quarters of an hour with probability 0.6 and half an hour with probability 0.4. This statistical information, which tells us which value a component of the problem will take and with what probability, is a prerequisite and an integral part of the model. If it is not known, the modeler must first carry out a statistical analysis (estimation from data).
Now suppose our middle-school student is looking for the fastest route and can choose between several modes of transportation: bicycle (in which case the journey time will depend on traffic on the bike path) or bus (in which case it will depend on whether there is a wait at the bus stop). Even for this simple "shortest" path problem—where "shortest" means fastest—standard deterministic optimization methods no longer apply directly! Optimizing without accounting for uncertainty can lead to inappropriate decisions.
For this student, even if travelling by bus takes the least time, choosing it will not necessarily get the student there fastest if the bus is slow to arrive. All these uncertainties must therefore be taken into account to determine what action to take and identify the best solution.