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Operations Research Models and Methods
Computation Section
Subunit Continuous-Time Markov Chain
 - The Economic Analysis

The Economics worksheet is automatically constructed when a rate matrix is defined. It allows the specification of values associated with residing in a state and moving to a new state. The State Cost Rate is the cost expended per unit time residing in the state. The Transition Cost Matrix holds the cost expended whenever a transition is made, independent of time. Assuming each customer experiences a cost proportional to the time spent in the foyer, we select a cost per minute equal to the number in the system. The time dimension of the cost rates are the same as the dimension used for rates in the rate matrix, minutes for the example.

The Combined Cost Rate is a computed quantity, adding the state cost rate to the transition costs divided by the expected time to make a transition. The Combined Cost per Step is the expected cost for each step of the embedded Markov Chain.

We provide a cell to hold the Economic Measure. Here it is cost, but it can also be profit or any measure implied by the entries in the data arrays. Another holds the discount rate for problems in which the net present value is a relevant measure. Present value computations use continuous compounding. Again the discount rate has the same time dimension as the transition rates.

The buttons on the worksheet recalculate the worksheet or return the focus to the Matrix worksheet. The latter button is included on all worksheets created by the add-in.



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Operations Research Models and Methods
by Paul A. Jensen
Copyright 2004 - All rights reserved