Optimization-based auctions and stochastic assembly replenishment policies for industrial procurement

Abstract

This thesis describes two applications of Operations Research to the field of industrial procurement, addressing problems encountered in supplier selection and supplier control, respectively. The first part addresses the problem of designing multi-item procurement auctions in capacity-constrained environments. Using insights from classical auction theory, we construct an optimization based auction mechanism ("Smart Market") relying on the dynamic resolution of a linear program minimizing the buyer's cost under the suppliers' capacity constraints. Based on the optimal allocation corresponding to each set of bids, suppliers can respond by modifying their offers, giving rise to a dynamic competitive bidding process. A first contribution of our work is the solution we develop to assist suppliers, a bidding suggestion device based on a myopic best response (MBR) calculation solving an inverse optimization problem. The second main contribution is the analytical study of the bid profile sequences arising in this smart market within a game-theoretic framework assuming linear costs for the suppliers. Under a particularly weak behavioral assumption and some symmetry requirements, we establish an explicit upper bound for the winning bids when the auction terminates as a function of the market environment parameters. This bound constitutes a performance guarantee from the buyer's perspective, and provides insights on how capacity constraints affect relative market power. We then formulate a complete behavioral model and solution methodology based on the MBR rationale and the concept of local Nash Equilibrium, and argue its realism. We derive analytically some structural and convergence properties of the MBR dynamics in the simplest non-trivial market environment, suggesting further possible design improvements, and obtain insights on market behavior, efficiency and incentive compatibility issues through numerical simulations. In particular, experiments tend to show that suppliers might be relied upon to provide their own capacity information when procurement contracts are properly designed. The second part is motivated by a strategic challenge faced in particular by electronic goods manufacturing companies. Because most of their assembly operations are highly automated, procurement delays typically account for most of the total production lead-time, and have a major impact on inventory costs. However, in an increasingly global outsourcing environment, these delays can be both long and uncertain. This leads us to examine the problem of optimally procuring components in a single-product stochastic assembly system. We consider a model where product demand follows a stationary Poisson process, assembly is instantaneous, and unsatisfied demand is backordered. The suppliers are uncapacitated and the components have independent but non-identically distributed stochastic procurement delays. The following class of policies is considered: The finished goods inventory is initially filled to its base stock level, and each customer order triggers a replenishment order for a component after a component-dependent postponement lead time. The objective is to minimize the sum of holding and backorder costs in steady-state over this class of replenishment policies. To keep the analysis tractable, we assume that no mixing occurs between component orders (synchronization assumption). Combining classical queueing network theory with original results concerning a distributional property we call closure under maximization and translation (CMT), we obtain a near-optimal solution in closed-form. We then demonstrate through simulation, using industrial data from a Hewlett-Packard facility, that the policy we derived significantly outperforms other policies commonly used in practice. In addition, we show that it is quite robust with respect to various model assumptions, except the synchronization one. We thus conclude that this work is potentially amenable to implementation in the settings where this assumption is not exceedingly demanding. Moreover, we believe that the CMT distributions we introduce could also prove useful in a variety of applications beyond the context of supply chains, such as project management, reliability analysis, and the study of natural extreme phenomena.