A general quantity discount and supplier selection mixed integer programming model

Abstract

Recently, new models and heuristics for exploiting quantity discounts have been proposed that are applicable in classical
purchasing as well as in an e-business environment and can be implemented as part of an advanced planning system. These models
can now handle both the single- and multi-item case with fixed cost to be shared among several products ordered at the same
point in time from a single supplier. Furthermore, the supplier selection problem is addressed, i.e., how to best exploit
quantity discounts over time offered by several suppliers. Last but not least, additional constraints on the buyer’s or on
the supplier’s side may be included. While so far only purpose-built heuristics have been proposed for this generalized problem,
we present a linear mixed integer programming (MIP) model, which not only represents the all-units discount but also the incremental discount
case. Furthermore, the objective function chosen resolves (former) conflicts among proponents of a purely cost oriented and
a cash flow oriented modeling approach. Computational tests show that our model yields near optimal solutions within a given
CPU time limit by making use of a standard MIP solver.