Stochastic Production/Location Models on Networks or a Plane

Abstract

This chapter extends the analysis of stochastic production/location problems presented in chapter 5 from the line as the location space to network and planar spaces. The inclusion of parametric uncertainty in these more general spaces makes algorithmic solution of these problems, and especially analysis and characterization of optimal solutions using comparative statics methods, extremely difficult. This probably explains why so little published work exists on these types of production/location models. Although little work has appeared for either type of space, the work on stochastic network production/location problems is more extensively developed than the work on planar models, so the bulk of this chapter will focus on network models. The material in this chapter naturally builds upon the certainty models in chapters 3 and 4, and many of the methods and results extend to the stochastic case, though sometimes in altered form.