Anantaram Balakrishnan

A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design

The fixed-charge network design problem arises in a variety of problem contexts including transportation, communication, and production scheduling. We develop a family of dual-ascent algorithms for this problem. This approach generalizes known ascent procedures for solving shortest path, plant location, Steiner network and directed spanning tree problems. Our computational results for several classes of test problems with up to 500 integer and 1.98 million continuous variables and constraints show that the dual-ascent procedure and an associated drop-add heuristic generate solutions that, in almost all cases, are guaranteed to be within 1 to 4% of optimality. Moreover, the procedure requires no more than 150 seconds on an IBM 3083 computer. The test problems correspond to dense and sparse networks, including some models that arise in freight transport.

An Integrated Inventory Allocation and Vehicle Routing Problem

We address the problem of distributing a limited amount of inventory among customers using a fleet of vehicles so as to maximize profit. Both the inventory allocation and the vehicle routing problems are important logistical decisions. In many practical situations, these two decisions are closely interrelated, and therefore, require a systematic approach to take into account both activities jointly. We formulate the integrated problem as a mixed integer program and develop a Lagrangian-based procedure to generate both good upper bounds and heuristic solutions. Computational results show that the procedure is able to generate solutions with small gaps between the upper and lower bounds for a wide range of cost structures.

Models for planning capacity expansion in local access telecommunication networks

The rapid progress of communications technology has created new opportunities for modeling and optimizing the design of local telecommunication systems. The complexity, diversity, and continuous evolution of these networks pose several modeling challenges. In this paper, we present an overview of the local telephone network environment, and discuss possible modeling approaches. In particular, we (i) discuss the engineering characteristics of the network, and introduce terminology that is commonly used in the communications industry and literature; (ii) describe a general local access network planning model and framework, and motivate different possible modeling assumptions; (iii) summarize various existing planning models in the context of this framework; and (iv) describe some new modeling approaches. The discussion in this paper is directed both to researchers interested in modeling local telecommunications systems and to planners interested in using such models. Our goal is to present relevant aspects of the engineering environment for local access telecommunication networks, and to discuss the relationship between engineering issues and the formulation of economic decision models. We indicate how changes in the underlying switching and transmission technology affect the modeling of the local telephone network. We also review various planning issues and discuss possible optimization approaches for treating them.

Stack Them High, Let 'em Fly: Lot-Sizing Policies When Inventories Stimulate Demand

In some retail contexts, stocking large quantities of inventory may not only improve service levels, but can also stimulate demand. For products having demand rates that increase with inventory levels, we analyze the effect of stocking decisions on firm profitability to develop managerial insights regarding the structure of the optimal inventory policy, and to understand how this policy differs from traditional approaches. When inventories stimulate demand, iteratively applying the standard economic order quantity (EOQ) model--by setting the demand rate parameter equal to the observed average demand rate in prior cycles--yields an equilibrium order quantity that is robust to demand parameter misestimation, but is suboptimal. The profit-maximizing policy orders larger quantities, and can replenish inventory even before on-hand stock fully depletes. Using an extension of a standard inventory-dependent demand model from the literature, we first provide a convenient characterization of products that require early replenishment. We demonstrate that the optimal cycle time is largely governed by the conventional trade-off between ordering and holding costs, whereas the reorder point relates to a promotions-oriented cost-benefit perspective. We show that the optimal policy yields significantly higher profits than cost-based inventory policies, underscoring the importance of profit-driven inventory management.

A Decomposition Algorithm for Local Access Telecommunications Network Expansion Planning

Growing demand, increasing diversity of services, and advances in transmission and switching technologies are prompting telecommunication companies to rapidly expand and modernize their networks. This paper develops and tests a decomposition methodology to generate cost-effective expansion plans, with performance guarantees, for one major component of the network hierarchy-the local access network. The model captures economies of scale in facility costs and tradeoffs between installing concentrators and expanding cables to accommodate demand growth. Our solution method exploits the special tree and routing structure of the expansion planning problem to incorporate valid inequalities, obtained by studying the problems polyhedral structure, in a dynamic program which solves an uncapacitated version of the problem. Computational results for three realistic test networks demonstrate that our enhanced dynamic programming algorithm, when embedded in a Lagrangian relaxation scheme with problem preprocessing and local improvement, is very effective in generating good upper and lower bounds: Implemented on a personal computer, the method generates solutions within 1.2-7.0% of optimality. In addition to developing a successful solution methodology for a practical problem, this paper illustrates the possibility of effectively combining decomposition methods and polyhedral approaches.

Using a Hop-Constrained Model to Generate Alternative Communication Network Design

Designing the link topology and selecting capacities in a backbone network of a communication system involve complex tradeoffs between investment and operating costs and service considerations such as network reliability and vulnerability, delays, and blocking. Incorporating all these design criteria simultaneously in a comprehensive model results in a large-scale, nonlinear, discrete optimization problem that is intractable. This paper proposes an alternate optimization-based methodology to generate several cost-effective backbone network designs with varying cost and performance characteristics. Network planners can use this method together with detailed performance evaluation techniques to select a design that achieves the proper balance between conflicting objectives. To generate different configurations, the method parametrically varies a set of hop constraints that restrict the number of links over which messages can be transmitted. Reducing the maximum number of hops increases the number of alterna...

Integrated Facility Location and Vehicle Routing Models: Recent Work and Future Prospects

SYNOPTIC ABSTRACTFacility location and vehicle routing are two widely used and studied management science resource planning models. According to the 1986 Statistical Abstract of the United States, freight transportation outlays for local trucking totaled 80.9 billion dollars in 1983. Thus, location/routing decisions have considerable economic importance in domains such as distribution systems planning. Since location and routing decisions are closely related, integrated models that consider the two aspects simultaneously offer the promise of more effective and economical decisions. However, such integrated models are complex and their design poses challenges in combining the short-term operational considerations of vehicle routing with the medium/long-term strategic issues of facility location. This paper discusses recent research related to various modeling approaches for location/routing problems, including comprehensive mathematical programming formulations, analytical approximations, and modified faci...

Requirements Planning with Substitutions: Exploiting Bill-of-Materials Flexibility in Production Planning

Designing product lines with substitutable components and subassemblies permits companies to offer a broader variety of products while continuing to exploit economies of scale in production and inventory costs. Past research on models incorporating component substitutions focuses on the benefits from reduced safety-stock requirements. This paper addresses a dynamic requirements-planning problem for two-stage multi product manufacturing systems with bill-of-materials flexibility, i.e., with options to use substitute components or subassemblies produced by an upstream stage to meet demand in each period at the downstream stage. We model the problem as an integer program, and describe a dynamic-programming solution method to find the production and substitution quantities that satisfy given multi period downstream demands at minimum total setup, production, conversion, and holding cost. This methodology can serve as a module in requirements-planning systems to plan opportunistic component substitutions based on relative future demands and production costs. Computational results using real data from an aluminum-tube manufacturer show that substitution can save, on average, 8.7% of manufacturing cost. We also apply the model to random problems with a simple product structure to develop insights regarding substitution behavior and impacts.

Manufacturing in the Digital Age: Exploiting Information Technologies for Product Realization

Information technology (IT) is both the key enabler for future manufacturing enterprises and a transformer of organizations and markets. By reducing barriers to collaboration, compressing lead time, eliminating physical movement, and enriching decision-making, IT helps manufacturers achieve their goal of meeting customer needs better, quicker, and cheaper. By providing global reach and easy connectivity, information technology has fostered cooperation while increasing market competition, and heightened customer expectations. Advances in computer and communication technologies combined with rapid changes in organizations have created new opportunities for exploiting information technologies in the entire product realization process. This paper explores these opportunities, and identifies promising directions for both basic and applied research. We first review important trends in organizations, markets, and information technologies—from increasing customer involvement and opportunistic organizational alliances to global reach and connectivity, enterprise integration, and virtualization. Adopting a process viewpoint of the product realization cycle, we translate these trends into high-impact IT applications in design and operations that offer rich potential for applied research and development. Underlying these applications are four broad classes of intelligent information processes—intelligent search, diagnosis and prognosis, collaboration, coordination, and negotiation, and understanding and learning. And, software agents provide an ideal platform to implement these processes. We briefly review developments in these basic research fields, and identify necessary scientific advances that are most important from the manufacturing perspective. Our goal is to synthesize streams of thought from many related disciplines in engineering, science, and management, and develop a framework for examining how information technologies can facilitate and influence manufacturing.

Designing Hierarchical Survivable Networks

As the computer, communication, and entertainment industries begin to integrate phone, cable, and video services and to invest in new technologies such as fiber-optic cables, interruptions in service can cause considerable customer dissatisfaction and even be catastrophic. In this environment, network providers want to offer high levels of service-in both serviceability (e.g., high bandwidth) and survivability (failure protection)-and to segment their markets, providing better technology and more robust configurations to certain key customers. We study core models with three types of customers (primary, primary but critical, and secondary) and two types of services/technologies (primary and secondary). The network must connect all primary customers using primary (high bandwidth) services and, additionally, contain a back-up path connecting the critical primary customers. Secondary customers require only single connectivity to other customers and can use either primary or secondary facilities. We propose a general multi-tier survivable network design model to configure cost effective networks for this type of market segmentation. When costs are triangular, we show how to optimally solve single-tier subproblems, with two critical customers, as a matroid intersection problem. We also propose and analyze the worst-case performance of tailored heuristics for several special cases of the two-tier model. Depending upon the particular problem setting, the heuristics have worst-case performance ratios ranging between 1.25 and 2.6. We also provide examples to show that the performance ratios for these heuristics are the best possible.