SimSpiders

Wine Provisioning On Board

by Felisa J. Vázquez-Abad and Yanick Champoux

The Stochastic Process

As stated in the formulation of the problem, the goal is to estimate the long term profit rate of the AirLine Company, and this in order to be able to choose the optimal reordering strategy. When we simulate several flights, we see that the inventory levels of one flight depend on those of the previous flight: the mathematical description is that of a Markov Chain.

When producing computer simulations, we usually choose a fixed number of flights to simulate the process and estimate the profit. A particular outcome of the simulation gives us a trajectory of the process (inventory levels). Naturally, each time we repeat the simulation we obtain a different trajectory and a different estimate of the profit.

When you click below, 10 different replications of the simulation are performed. Each simulation represents a series of 200 flights. In the plot you shall only see the white wine inventory levels, different colors representing five different trajectories or "possible outcomes" of a simulation.

To understand the histograms below, READ FURTHER ON...

At first, all inventory levels are at full capacity and thus for the first few flights the levels, although random, will concentrate on high numbers close to the capacity of the AirCraft. When the order takes place the level jumps to capacity. As the number of flights increases, however, the level of the inventory reaches a stationary distribution, where all inventory levels are identically distributed, although not indpendent. We have included in our plot five histograms showing the empirical distributions of the inventory levels at the specified number of flights. The more replications you ask for, the better the histograms will approximate the shape of the distributions. We invite you to click several times and observe the pattern of the histograms, which should resemble each other more and more as the number of flights increases.


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© Copyright 1998 Felisa J. Vázquez-Abad and Yanick Champoux. All rights reserved.