Chung-Piaw Teo

Effective Zero-Inventory-Ordering Policies for the Single-Warehouse Multiretailer Problem with Piecewise Linear Cost Structures

We analyze the problem faced by companies that rely on TL (Truckload) and LTL (Less than Truckload) carriers for the distribution of products across their supply chain. Our goal is to design simple inventory policies and transportation strategies to satisfy time varying demands over a finite horizon, while minimizing system wide cost by taking advantage of quantity discounts in the transportation cost structures. For this purpose, we study the cost effectiveness of restricting the inventory policies to the class of zero-inventory-ordering (ZIO) policies in a single-warehouse multiretailer scenario in which the warehouse serves as a cross-dock facility. In particular, we demonstrate that there exists a ZIO inventory policy whose total inventory and transportation cost is no more than 4/3 (5.6/4.6 if transportation costs are stationary) times the optimal cost. However, finding the best ZIO policy is an NP hard problem as well. Thus, we propose two algorithms to find an effective ZIO policy: An exact algorithm whose running time is polynomial for any fixed number of retailers, and a linear-programming-based heuristic whose effectiveness is demonstrated in a series of computational experiments. Finally, we extend the worst-case results developed in this paper to systems in which the warehouse does hold inventory.

Designing two-echelon supply networks

A modern distribution network design model needs to deal with the trade-offs between a variety of factors, including (1) location and associated (fixed) operating cost of distribution centers (DCs), (2) total transportation costs, and (3) storage holding and replenishment costs at DCs and retail outlets. In addition, network design models should account for factors such as (4) stockouts, by setting appropriate levels of safety stocks, or (5) capacity concerns, which may affect operating costs in the form of congestion costs. The difficulty of making such trade-offs is compounded by the fact that even finding the optimal two-echelon inventory policy in a fixed and uncapacitated distribution network is already a hard problem. In this paper, we propose a generic modeling framework to address these issues that continues and extends a recent stream of research aimed at integrating insights from modern inventory theory into the supply chain network design domain. Our approach is flexible and general enough to incorporate a variety of important side constraints into the problem.

Warehouse-Retailer Network Design Problem

In this paper, we study the distribution network design problem integrating transportation and infinite horizon multiechelon inventory cost function. We consider the trade-off between inventory cost, direct shipment cost, and facility location cost in such a system. The problem is to determine how many warehouses to set up, where to locate them, how to serve the retailers using these warehouses, and to determine the optimal inventory policies for the warehouses and retailers. The objective is to minimize the total multiechelon inventory, transportation, and facility location costs. To the best of our knowledge, none of the papers in the area of distribution network design has explicitly addressed the issues of the 2-echelon inventory cost function arising from coordination of replenishment activities between the warehouses and the retailers. We structure this problem as a set-partitioning integer-programming model and solve it using column generation. The pricing subproblem that arises from the column generation algorithm gives rise to a new class of the submodular function minimization problem. We show that this pricing subproblem can be solved inO( n?log? n) time, wheren is the number of retailers. Computational results show that the moderate size distribution network design problem can be solved efficiently via this approach.

Procurement management using option contracts: random spot price and the portfolio effect

This article considers the value of portfolio procurement in a supply chain, where a buyer can either procure parts for future demand from sellers using fixed price contracts or, option contracts or tap into the market for spot purchases. A single-period portfolio procurement problem when both the product demand and the spot price are random (and possibly correlated) is examined and the optimal portfolio procurement strategy for the buyer is constructed. A shortest-monotone path algorithm is provided for the general problem to obtain the optimal procurement solution and the resulting expected minimum procurement cost. In the event that demand and spot price are independent, the solution algorithm simplifies considerably. More interestingly, the optimal procurement cost function in this case has an intuitive geometrical interpretation that facilitates managerial insights. The portfolio effect, i.e., the benefit of portfolio contract procurement over a single contract procurement is also studied. Finally, an extension to a two-period problem to examine the impact of inventory on the portfolio procurement strategy is discussed.

The Geometry of Fractional Stable Matchings and its Applications

We study the classical stable marriage and stable roommates problems using a polyhedral approach. We propose a new LP formulation for the stable roommates problem, which has a feasible solution if and only if the underlying roommates problem has a stable matching. Furthermore, for certain special weight functions on the edges, we construct a 2-approximation algorithm for the optimal stable roommates problem. Our technique exploits features of the geometry of fractional solutions of this formulation. For the stable marriage problem, we show that a related geometry allows us to express any fractional solution in the stable marriage polytope as a convex combination of stable marriage solutions. This also leads to a genuinely simple proof of the integrality of the stable marriage polytope.

Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion

We propose a semidefinite optimization (SDP) model for the class of minimax two-stage stochastic linear optimization problems with risk aversion. The distribution of second-stage random variables belongs to a set of multivariate distributions with known first and second moments. For the minimax stochastic problem with random objective, we provide a tight SDP formulation. The problem with random right-hand side is NP-hard in general. In a special case, the problem can be solved in polynomial time. Explicit constructions of the worst-case distributions are provided. Applications in a productiontransportation problem and a single facility minimax distance problem are provided to demonstrate our approach. In our experiments, the performance of minimax solutions is close to that of data-driven solutions under the multivariate normal distribution and better under extremal distributions. The minimax solutions thus guarantee to hedge against these worst possible distributions and provide a natural distribution to stress test stochastic optimization problems under distributional ambiguity.

Models for Effective Deployment and Redistribution of Bicycles Within Public Bicycle-Sharing Systems

We develop practical operations research models to support decision making in the design and management of public bicycle-sharing systems. We develop a network flow model with proportionality constraints to estimate the flow of bicycles within the network and the number of trips supported, given an initial allocation of bicycles at each station. We also examine the effectiveness of periodic redistribution of bicycles in the network to support greater flow, and the impact on the number of docks needed.We conduct our numerical analysis using transit data from train operators in Singapore. Given that a substantial proportion of passengers in the train system commute a short distance---more than 16% of passengers alight within two stops from the origin---this forms a latent segment of demand for a bicycle-sharing program. We argue that for a bicycle-sharing system to be most effective for this customer segment, the system must deploy the right number of bicycles at the right places, because this affects the utilization rate of the bicycles and how bicycles circulate within the system. We also identify the appropriate operational environments in which periodic redistribution of bicycles will be most effective for improving system performance.

Impact on inventory costs with consolidation of distribution centers

Abstract The consolidation of Distribution Centers (DCs) is a new trend in global logistics management, with a reduction in inventory costs often being cited as one of the main benefits. This paper uses an analytical modeling approach to study the impact on facility investment and inventory costs when several DCs are consolidated into a central DC. In particular, our model suggests that consolidation leads to lower total facility investment and inventory costs if the demands are identically and independently distributed, or when they follow independent but possibly nonidentical Poisson processes. This agrees with the conclusion of the classical EOQ and newsvendor models. However, we show by an example that, for general stochastic demand processes, the total facility investment and inventory costs of a consolidated system can be infinitely worse off than that of a decentralized system. This arises mainly because the order replenishment fixed cost yields a cost component proportional to the square root of the mean value of the demand, while the demand uncertainty yields a cost component proportional to the standard deviation of the demand. Whether consolidation is cost effective or not depends on the trade-off between these two components, as indicated by an extensive numerical study. We also propose an algorithm that solves for a distribution system with the total facility investment and inventory costs within √2 of the optimal.

Design for Process Flexibility: Efficiency of the Long Chain and Sparse Structure

The concept of chaining, or in more general terms, sparse process structure, has been extremely influential in the process flexibility area, with many large automakers already making this the cornerstone of their business strategies to remain competitive in the industry. The effectiveness of the process strategy, using chains or other sparse structures, has been validated in numerous empirical studies. However, to the best of our knowledge, there have been relatively few concrete analytical results on the performance of such strategies vis-a-vis the full flexibility system, especially when the system size is large or when the demand and supply are asymmetrical. This paper is an attempt to bridge this gap. We study the problem from two angles: (1) For the symmetrical system where the (mean) demand and plant capacity are balanced and identical, we utilize the concept of a generalized random walk to evaluate the asymptotic performance of the chaining structure in this environment. We show that a simple chaining structure performs surprisingly well for a variety of realistic demand distributions, even when the system size is large. (2) For the more general problem, we identify a class of conditions under which only a sparse flexible structure is needed so that the expected performance is already within e optimality of the full flexibility system. Our approach provides a theoretical justification for the widely held maxim: In many practical situations, adding a small number of links to the process flexibility structure can significantly enhance the ability of the system to match (fixed) production capacity with (random) demand.

On dependent randomized rounding algorithms

In recent years, approximation algorithms based on randomized rounding of fractional optimal solutions have been applied to several classes of discrete optimization problems. In this paper, we describe a class of rounding methods that exploits the structure and geometry of the underlying problem to round fractional solution to 0-1 solution. This is achieved by introducing dependencies in the rounding process. We show that this technique can be used to establish the integrality of several classical polyhedra (min cut, uncapacitated lot-sizing, Boolean optimization, k-median on cycle) and produces an improved approximation bound for the min-k-sat problem.