The analysis of an inventory control model using posynomial geometric programming

We consider a generalization of the well-known ‘sawtooth’ inventory control model which is used to determine optimal policies for stocking a single item under certain conditions. The case where several items are to be stocked simultaneously and subject to a number of constraints give rise to the generalization that is of interest. We show that the problem of analysing the model may he viewed as a problem in posynomial Geometric Programming. We then point out some of the advantages to be realized from viewing it this way and from using Geometric Programming techniques to solve it. These include, the ability to obtain feasible solutions with known upper bounds on the difference between their associated costs and the minimum cost, a capability for performing an analysis of the sensitivity of the values of the optimized parameters to variations in input parameters, availability of a solution method that is computationally more attractive than methods previously known and, arising out of this last benefit, an ability to deal with much more complicated problems to which the model is applied than previously seemed practical. A simple example problem is solved in detail to illustrate many of these benefits and results are presented for a much more complex case. In addition some possible extensions of the model, which can also be dealt with in this framework, are pointed out.