Composite-variable modeling for service parts logistics

Service parts logistics focuses on providing repair parts for computer, medical, and other high-cost equipment, typically in a very short period of time. Problems within this domain are often challenging to solve, due to the complexity of the network, tight constraints on time and warehouse capacity, and the high costs of inventory and transportation resources. Mathematical modeling can be critical in solving such difficult problems, but basic modeling approaches often suffer from complicating factors such as large numbers of constraints and integer variables, non-linearities, and weak linear programming relaxations. To address some of these difficulties, we present a modeling framework based on composite variables – variables that encompass multiple decisions. We begin by considering the problem of how to stock those repair parts which are both high cost and very low demand. We then discuss how this relatively simple problem can become much more computationally challenging when we expand the scope to consider a more global view of the system. As an example, we consider what happens when warehouse capacity constraints are added. We show that a basic modeling approach to this new problem is intractable for many instances of realistic size. We then present a composite-variable model and show how it enables us to improve tractability significantly. Our experience suggests potential opportunities to be found in modeling other SPL problems within a composite-variable framework as well. We conclude by presenting modeling approaches to address a broad class of problems within this challenging and important arena.