TITLE: Modeling and Solution of Some Multi-Period Supply Chain Optimization Problems

ABSTRACT:

This thesis consists of three parts, each of which contributes to an independent topic in the broad area of multi-period supply chain optimization, and provides modeling and solution approaches for the problem in concern.

Part I studies a strategic health workforce planning problem. Analysts predict impending shortages in the health care workforce, and wages for health care workers already account for over 50% of U.S. health expenditures. It is thus increasingly important to adequately plan to meet health workforce demand at reasonable cost. Using infinite linear programming (LP) methodology, we propose an infinite-horizon model for health workforce planning in a large health system for a single worker class, e.g. nurses. We give a series of common-sense conditions any system of this kind should satisfy, and use them to prove the optimality of a natural lookahead policy. We then use real-world data to examine how such policies perform in more complex systems; in particular, our experiments show that a natural extension of the lookahead policy performs well when incorporating stochastic demand growth.

Part II investigates an integrated inventory routing (IRP) and freight consolidation problem for perishable goods with a fixed lifetime. The problem is motivated by the status-quo of logistics in many U.S. markets, but also adapts to relevant two-echelon supply chain optimization problems e.g. combined production planning and distribution. We formulate the problem as a large-scale mixed-integer programming (MIP) model. We propose an iterative solution framework with a decomposition procedure and a local search scheme. In the decomposition, a freight consolidation subproblem is first solved to obtain crucial shipping decisions, and after fixing these a restrictive model generates the other decisions for the integrated problem. The local search aims at fast identification of good neighborhoods by solving an assignment-style MIP which matches the consolidation decision with an IRP subproblem, and gradually strengthens the incumbent solution pool when executed in an iterative fashion. Experiments with empirical demand distributions based on real data demonstrate that 1) the integration can achieve remarkable efficiency compared to a sequential approach of the subproblems; 2) both the decomposition and the local search are effective in solving moderately-sized problem instances that are already challenging in practice.

Part III examines a two-echelon distribution problem which can be viewed as a one-warehouse multi-retailer (OWMR) problem reversed in time flows. Unlike the majority of the OWMR literature, where ordering is uncapacitated and the ordering cost is fixed in each period, we assume more realistic volume-dependent cost structures which can be interpreted as multiple transportation modes with batch capacities. The resulting transportation costs are piecewise linear non-convex functions of the shipping volume. Since this breaks classical optimality properties like zero-inventory-ordering, and the LP relaxation of the natural MIP formulation can be very weak, a straightforward application of previous OWMR methods may not be effective. We first introduce a technique that converts our problem to existing OWMR models by bounding the cost functions, and derive the corresponding worst-case approximation guarantees under each type of the transportation costs. We then treat or approximate the transportation costs as concave batch costs, and propose a polynomial-time 2-approximation algorithm by recombining single-echelon lot sizing subproblem solutions for the special case of full truckload costs, where trucks have an identical capacity and each incurs a fixed cost. This improves the best-known result (i.e. a 3.6-approximation) for the same cost structure. Finally, we utilize subproblem structural properties to prove the asymptotic optimality of a decentralized approach for pertinent two-echelon problems in a wider range of settings.

*Considering the independence of each part, we will focus on the last topic at the defense.*