Scholars@Duke
Paul H. Zipkin

Paul H. Zipkin

R. J. Reynolds Distinguished Professor Emeritus of Business Administration
Fuqua School of Business
paul.zipkin@duke.edu
Box 90120, Durham, NC 27708-0120
413A Fuqua Sch of Bus, Durham, NC 27708

Selected Publications

Smart Policies for Multisource Inventory Systems and General Tandem Queues with Order Tracking and Expediting

Journal Article Operations Research · July 1, 2022 We study an inventory system with multiple supply sources and expediting options. The replenishment lead times from each supply source are stochastic, representing congestion and disruption.We construct a family of smart ordering and expediting policies th ... Full text Cite

Optimal policies for a dual-sourcing inventory problem with endogenous stochastic lead times

Journal Article Operations Research · March 1, 2017 We consider a single-product, two-source inventory system with Poisson demand and backlogging. Inventory can be replenished through a normal supply source, which consists of a two-stage tandem queue with exponential production time at each stage. We can al ... Full text Cite

Some specially structured assemble-to-order systems

Journal Article Operations Research Letters · January 2016 Full text Cite

Design of traceability systems for product recall

Journal Article International Journal of Production Research · January 1, 2015 A product recall is very expensive and a poorly executed recall can be devastating to a companys reputation. It is, therefore, important to improve the traceability for supply chains to address potential recalls. This paper studies the recall dynamics in a ... Full text Cite

Supply streams

Journal Article Manufacturing and Service Operations Management · June 1, 2013 Asupply stream is a continuous version of a supply chain. It is like a series inventory system, but stock can be held at any point along a continuum, not just at discrete stages. We assume stationary parameters and aim to minimize the long-run average tota ... Full text Cite

Newsvendor problems with sequentially revealed demand information

Journal Article Naval Research Logistics · January 1, 2012 This article analyzes a capacity/inventory planning problem with a one-time uncertain demand. There is a long procurement leadtime, but as some partial demand information is revealed, the firm is allowed to cancel some of the original capacity reservation ... Full text Cite

A reply to Williamson's "outsourcing ..."

Journal Article Production and Operations Management · 2012 A recent article by Oliver Williamson essentially comprises a critique of supply chain management (SCM) from the perspective of his own field, transaction-cost economics. Here is one reader's response. SCM can indeed be faulted for inflated rhetoric, among ... Full text Cite

On the method of images and the asymptotic behavior of first-passage times

Journal Article Annals of Operations Research · 2012 This paper studies the large-t behavior of the boundary generated by the method of images for the first-passage-time problem. We show that this behavior is characterized by certain properties of the Laplace transform of the input measure. Such properties a ... Full text Cite

Linear programming and the inverse method of images

Journal Article Annals of Operations Research · 2012 The inverse method of images is a relatively easy way to find approximate solutions to first-passage time problems. We extend the method in several ways: We use a linear program instead of a system of linear equations; we utilize asymptotic information in ... Full text Cite

An approximation for the inverse first passage time problem

Journal Article Advances in Applied Probability · March 1, 2011 We propose an approximation for the inverse first passage time problem. It is similar in spirit and method to the tangent approximation for the original first passage time problem. We provide evidence that the technique is quite accurate in many cases. We ... Full text Cite

On Durbin's series for the density of first passage times

Journal Article Journal of Applied Probability · 2011 Durbin (1992) derived a convergent series for the density of the first passage time of a Weiner process to a curved boundary. We show that the successive partial sums of this series can be expressed as the iterates of the standard substitution method for s ... Full text Cite

Preface

Journal Article Clinical and Pathological Aspects of Skin Diseases in Endocrine Metabolic Nutritional and Deposition Disease · December 1, 2010 Full text Cite

Competition and cooperation in a two-stage supply chain with demand forecasts

Journal Article Operations Research · 2010 We consider a serial supply chain with one supplier and one retailer. Each obtains some demand forecast information, which may be shared or not. We investigate the members' benefits from sharing information. The forecasts follow a variant of the Martingale ... Full text Open Access Cite

The effects of the availability of waiting-time information on a balking queue

Journal Article European Journal of Operational Research · October 1, 2009 We consider two balking queue models with different types of information about delays. Potential customers arrive according to a Poisson process, and they decide whether to stay or balk based on the available delay information. In the first model, an arriv ... Full text Cite

Agents' incentives under buy-back contracts in a two-stage supply chain

Journal Article International Journal of Production Economics · August 1, 2009 This paper investigates how the behavior of individual decision makers can affect the performance of a supply chain. We study a two-stage supplier-retailer system, using a buy-back contract. Each firm's actions are executed by an agent. The retailer's purc ... Full text Cite

Coordination mechanisms in decentralized serial inventory systems with batch ordering

Journal Article Management Science · April 1, 2009 This paper studies a periodic-review, serial supply chain in which materials are ordered and shipped according to (R,nQ) policies. Three information scenarios are considered, depending on the level of information available: echelon, local, and quasilocal. ... Full text Cite

Inventories with multiple supply sources and networks of queues with overflow bypasses

Journal Article Management Science · March 1, 2009 Consider an inventory system with multiple supply sources and Poisson demand. The replenishment lead times from each source are stochastic, representing congestion and disruption. We develop performance evaluation and optimization tools for a family of rea ... Full text Cite

Managing an assemble-to-order system with returns

Journal Article Manufacturing and Service Operations Management · January 1, 2009 We consider a multiproduct assemble-to-order (ATO) system, in which inventory is kept only at the component level and the finished products are assembled in response to customer demands. In addition to stochastic demand for finished products, the system ex ... Full text Cite

The impacts of customers delay-risk sensitivities on a queue with balking

Journal Article Probability in the Engineering and Informational Sciences · January 1, 2009 Congestion and its uncertainty are big factors affecting customers decision to join a queue or balk. In a queueing system, congestion itself is resulted from the aggregate joining behavior of other customers. Therefore, the property of the whole group of a ... Full text Cite

The effects of information on a queue with balking and phase-type service times

Journal Article Naval Research Logistics · August 1, 2008 This article generalizes the models in Guo and Zipkin, who focus on exponential service times, to systems with phase-type service times. Each arriving customer decides whether to stay or balk based on his expected waiting cost, conditional on the informati ... Full text Cite

Old and new methods for lost-sales inventory systems

Journal Article Operations Research · 2008 We consider the notoriously difficult discrete-time inventory model with stochastic demands, a constant lead time, and lost sales. We show that the effective state space is a relatively manageable compact set. Then, we test various plausible heuristics. We ... Full text Cite

On the structure of lost-sales inventory models

Journal Article Operations Research · 2008 We provide a new approach to the structural analysis of the standard lost-sales inventory system. This approach is, we think, easier to work with than the original one. We also derive new bounds on the optimal policy. Then, we show that more variable deman ... Full text Cite

Optimal policy for a periodic-review inventory system under a supply capacity contract

Journal Article Operations Research · January 1, 2008 Transportation and production contracts often specify the frequency and volume reserved by the supplier for a particular customer's deliveries. This practice motivated Henig et al. (Henig, M., Y. Gerchak, R. Ernst, D. Pyke. 1997. An inventory model embedde ... Full text Cite

Analysis and comparison of queues with different levels of delay information

Journal Article Management Science · June 1, 2007 Information about delays can enhance service quality in many industries. Delay information can take many forms, with different degrees of precision. Different levels of information have different effects on customers and therefore on the overall system. To ... Full text Cite

Bounds, heuristics, and approximations for distribution systems

Journal Article Operations Research · 2007 This paper develops simple approximate methods to analyze a two-stage distribution system consisting of one warehouse and multiple retailers with stochastic demand. We consider local and central control schemes. The main ideas are based on relaxing and or ... Full text Cite

Lost-sales inventory models: Structure, sensitivity and bounds

Journal Article ICMSEM: Proceedings of 2007 International Conference on Management Science and Engineering Management · 2007 We reinterpret the structural analysis of Karlin and Scarf and Morton of the standard lost-sales inventory system. This version of the results is, we think, easier to understand and to work with than the original. We also recover their bounds on the optima ... Cite

Approximate solutions of a dynamic forecast-inventory model

Journal Article Manufacturing and Service Operations Management · October 9, 2006 In this paper we consider a dynamic forecast-inventory model with forecast updates, based on the martingale model of forecast evolution. Two types of updates are considered, additive and multiplicative. The formulation of the model results in a dynamic pro ... Full text Cite

The best things in life were free: On the technology of transactions

Journal Article Manufacturing and Service Operations Management · 2006 Radio-frequency identification (RFID) technology will reduce the costs of transactions to both customers and providers. This is a good thing, mostly. But it will be harder than people suppose, and it may have some adverse consequences. There are numerous t ... Full text Cite

Commitment decisions with partial information updating

Journal Article Naval Research Logistics · December 1, 2005 In this paper, we extend the results of Ferguson M. Naval Research Logistics 50, 2003, 917-936. on an end-product manufacturer's choice of when to commit to an order quantity from its parts supplier. During the supplier's lead-time, information arrives abo ... Full text Cite

Inventory management for an assembly system with product or component returns

Journal Article Management Science · August 1, 2005 This paper considers an inventory system with an assembly structure. In addition to uncertain customer demands, the system experiences uncertain returns from customers. Some of the components in the returned products can be recovered and reused, and these ... Full text Cite

A series system with returns: Stationary analysis

Journal Article Operations Research · March 1, 2005 This paper analyzes a series inventory system with stationary costs and stochastic demand over an infinite horizon. A distinctive feature is that demand can be negative, representing returns from customers, as well as zero or positive. We observe that, as ... Full text Cite

Supply Chain Operations: Assemble-to-Order Systems

Journal Article Handbooks in Operations Research and Management Science · December 1, 2003 Full text Cite

The limits of mass customization

Journal Article MIT Sloan Management Review · 2001 Do not be seduced by the allure of mass customization. Carefully assess the technology and the market demand before committing your company to such a strategy. ... Cite

Coordination of production/distribution networks with unbalanced leadtimes

Journal Article Operations Research · 2000 We investigate multiproduct, multilocation production/distribution networks with deterministic, stationary demands. Most research on such systems assumes zero leadtimes. Methods using fixed reorder intervals that are power-of-two multiplies of a base plann ... Cite

Stock Positioning and Performance Estimation for Serial Production-Transportation Systems

Journal Article Manufacturing & Service Operations Management · 1999 Cite

Competitive and cooperative inventory policies in a two-stage supply chain

Journal Article Management Science · January 1, 1999 The difference between global/cooperative and independent/competitive optimization in a serial supply chain with one suppliers and one retailer is studied. Two games are considered. It is shown that the games have a unique Nash equilibrium. Further, it is ... Full text Cite

Dynamic scheduling rules for a multiproduct make-to-stock queue

Journal Article Operations Research · 1997 This paper develops a simple but effective heuristic policy for a stochastic production-inventory system, where several products share a single processor of limited capacity. Our policy combines the best features, and avoids the weaknesses, of prior approa ... Cite

Inventory control with information about supply conditions

Journal Article Management Science · January 1, 1996 This paper presents an inventory-control model which includes a Markovian model of the supply system. As that system evolves over time, so do the replenishment leadtimes. The optimal policy has the same structure as in standard models, but its parameters c ... Full text Cite

Evaluation of base-stock policies in multiechelon inventory systems with state-dependent demands. Part II: State-dependent depot policies

Journal Article Naval Research Logistics · January 1, 1996 We consider a two-echelon inventory system where the exogenous demands occur only at the retailer locations, and the demand rates are functions of an underlying continuous-time Markov chain. This underlying process may represent, for example, general econo ... Full text Cite

Managing inventory with the prospect of obsolescence

Journal Article Operations Research · January 1, 1996 How should inventory management respond when there is a possibility of imminent obsolescence (or, more generally, deteriorating demand)? We use an inventory-control model to address this question. The model incorporates a Markovian submodel to describe the ... Full text Cite

The joint effect of leadtime variance and lot size in a parallel processing environment

Journal Article Management Science · January 1, 1996 We study a basic (r, q) system, in which the demand is a Poisson process and the leadtimes are independent, identically-distributed random variables. The key issue is the joint effect of the leadtime variance and the lot size q on performance. We know that ... Full text Cite

Customer-Order Information, Leadtimes, and Inventories

Journal Article Management Science · October 1995 We have an inventory to manage. The scenario is standard in all respects save one. Instead of arriving unannounced, customers provide advance warning of their demands. How should we use this information, and what is its effect on system performanc ... Full text Cite

Performance analysis of a multi-item production-inventory system under alternative policies

Journal Article Management Science · 1995 This paper explores the performance of a multi-item production-inventory system. We compare two alternative policies, representing different modes of collecting and utilizing information. We derive a closed-form measure of performance for one of them, the ... Cite

Processing networks with planned inventories: Tandem queues with feedback

Journal Article European Journal of Operational Research · 1995 This note continues the investigation, initiated by Lee and Zipkin, of tandem queues with planned inventories. Such models are designed to represent make-to-stock production processes, where intermediate and finished goods can be produced and stored in adv ... Cite

Mortgages and Markov Chains: A Simplified Evaluation Model

Journal Article Management Science · June 1993 This paper has two purposes. The first is purely expository: to introduce stochastic interest-rate models and security-evaluation methods in a simple mathematical setting. Specifically, we assume the uncertainties in the model are represented by a ... Full text Cite

Inventory control in a fluctuating demand environment

Journal Article Operations Research · January 1, 1993 We present an inventory model, where the demand rate varies with an underlying state-of-the-world variable. This variable can represent economic fluctuations, or stages in the product life-cycle, for example. We derive some basic characteristics of optimal ... Full text Cite

The Structure of Structured Bond Portfolio Models

Journal Article Operations Research · February 1992 Over the past decade, optimization models have been widely used to help select bond portfolios. Several different formulations are popular. The purposes of this paper are to clarify the basic structures of the models, to explain the relationships ... Full text Cite

Tandem queues with planned inventories

Journal Article Operations Research · 1992 This paper explores a natural generalization of the classic tandem-queue model, designed specifically to represent make-to-stock production processes. In such systems, intermediate and finished goods can be produced and stored in advance of demand. We cons ... Cite

Production control in a kanban-like system with defective outputs

Journal Article International Journal of Production Economics · January 1, 1992 We analyze a simple model of a production system, controlled using a variant of the kanban system, where each stage may produce defective items. We use the model to compare alternative product-test sites and to explore in detail the benefits of improving p ... Full text Cite

The Relationship Between Risk and Maturity In A Stochastic Setting

Journal Article Mathematical Finance · January 1, 1992 This paper explores the interest rate sensitivity of the prices of bonds and other securities when the instantaneous interest rate follows a Markov process. We show that whenever the interest rate describes a diffusion process the sensitivity of zero‐coupo ... Full text Cite

Inventory Models with Continuous, Stochastic Demands

Journal Article The Annals of Applied Probability · August 1, 1991 Full text Cite

Computing Optimal Lot Sizes in the Economic Lot Scheduling Problem

Journal Article Operations Research · February 1991 This paper treats a version of the Economic Lot Scheduling Problem (ELSP) in which items may be produced several times in different amounts during a cycle. We show how to compute the optimal lot sizes and cycle length, given the sequence of items ... Full text Cite

Evaluation of one-for-one replenishment policies for multiechelon inventory systems

Journal Article Management Science · 1991 This paper is concerned with multiechelon inventory systems, where each demand triggers a separate order (one-for-one replenishment policies). The exogenous demands are independent Poisson processes. The transit times between locations may be stochastic. T ... Cite

DOES MANUFACTURING NEED A JIT REVOLUTION

Journal Article HARVARD BUSINESS REVIEW · January 1, 1991 Link to item Cite

Queueing model to analyze the value of centralized inventory information

Journal Article Operations Research · 1990 Competitive pressures and technological improvements are leading many firms to consider centralized information systems to manage inventories and schedule production. We propose a simple model to explore the potential benefits of such coordination. The mod ... Cite

A Dynamic Lot-Size Model with Make-or-Buy Decisions

Journal Article Management Science · April 1989 This paper considers a dynamic lot-size model with make-or-buy decisions. In each period, the production level may not exceed a given capacity, but the purchase is unrestricted. The costs for production, purchase and inventory are concave. The pro ... Full text Cite

Critical Number Policies for Inventory Models with Periodic Data

Journal Article Management Science · January 1989 We consider an infinite-horizon in problem with stochastic demands where the data vary periodically. Karlin (Karlin, S. 1960a. Dynamic inventory policy with varying stochastic demands. Management Sci. 6 231–258; Karlin, S. 1960b. Optimal policy fo ... Full text Cite

The use of phase-type distributions in inventory-control models

Journal Article Naval Research Logistics · April 1988 Full text Cite

ESTIMATING THE PERFORMANCE OF MULTI-LEVEL INVENTORY SYSTEMS.

Journal Article Operations Research · 1988 The paper estimates the most important measures of performance, specifically, the long-run average backorders at the retailers, and the average inventory at each location. These estimates are used within a cost-minimization framework to choose among polici ... Cite

CONVEXITY OF A GENERAL PERFORMANCE MEASURE FOR MULTISERVER QUEUES.

Journal Article Journal of Applied Probability · 1987 This paper examines a general performance measure for queueing systems. This criterion reflects both the mean and the variance of sojourn times; the standard deviation is a special case. The measure plays a key role in certain production models, and it sho ... Cite

STRONG CONVEXITY RESULTS FOR QUEUEING SYSTEMS.

Journal Article Operations Research · 1987 We prove a strong (and seemingly odd) result about the M/M/c queue: the reciprocal of the average sojourn time is a concave function of the traffic intensity. We use this result to show that the average itself is jointly convex in arrival and service rates ... Cite

An Allocation and Distribution Model for Perishable Products

Journal Article Operations Research · February 1986 This paper presents an allocation model for a perishable product, distributed from a regional center to a given set of locations with random demands. We consider the combined problem of allocating the available inventory at the center while decidi ... Full text Cite

INVENTORY SERVICE-LEVEL MEASURES: CONVEXITY AND APPROXIMATION.

Journal Article Management Science · 1986 We argue that standard approximations for two often-used inventory service-level measures may perform poorly in many situations. Then we confirm the long-standing conjecture that the (relatively) exact formulas for these quantities are convex functions of ... Cite

STOCHASTIC LEADTIMES IN CONTINUOUS-TIME INVENTORY MODELS.

Journal Article Naval research logistics quarterly · 1986 This paper shows that one of the fundamental results of inventory theory is valid under conditions much broader than those treated previously. The result characterizes the distributions of inventory level and inventory position in the standard, continuous- ... Cite

INVENTORY MODEL WITH LIMITED PRODUCTION CAPACITY AND UNCERTAIN DEMANDS. II. THE DISCOUNTED-COST CRITERION.

Journal Article Mathematics of Operations Research · 1986 This paper considers a single-item, periodic-review inventory model with uncertain demands. We assume a finite production capacity in each period. With stationary data, a convex one-period cost function and a continuous demand distribution, we show (under ... Cite

INVENTORY MODEL WITH LIMITED PRODUCTION CAPACITY AND UNCERTAIN DEMANDS I. THE AVERAGE-COST CRITERION.

Journal Article Mathematics of Operations Research · 1986 This paper considers a single-item, periodic-review inventory model with uncertain demands. In contrast to prior treatments of this problem we assume a finite production capacity per period. Assuming stationary data, a convex one-period cost function and a ... Cite

Approximate aggregation under uncertainty

Journal Article Journal of Economic Theory · 1986 For a collection of agents with von Neumann-Morgenstern preferences, a price-independent income distribution, and identical probability beliefs, there exists a von Neumann-Morgenstern approximate aggregator. The risk tolerance of the approximate aggregator ... Cite

ALLOCATION AND DISTRIBUTION MODEL FOR PERISHABLE PRODUCTS.

Journal Article Operations Research · 1986 This paper presents an allocation model for a perishable product, distributed from a regional center to a given set of locations with random demands. We consider the combined problem of allocating the available inventory at the center while deciding how th ... Cite

MODELS FOR DESIGN AND CONTROL OF STOCHASTIC, MULTI-ITEM BATCH PRODUCTION SYSTEMS.

Journal Article Operations Research · 1986 We propose an approach to modeling a production facility that makes many products in large, discrete batches, when demands and the production process are stochastic. This approach combines standard inventory and queueing submodels into classical optimizati ... Cite

Computing optimal ( s, S ) policies in inventory models with continuous demands

Journal Article Advances in Applied Probability · June 1985 Special algorithms have been developed to compute an optimal ( s, S ) policy for an inventory model with discrete demand and under standard assumptions (station ... Full text Cite

EFFICIENT ALGORITHM FOR COMPUTING OPTIMAL (s, S) POLICIES.

Journal Article Operations Research · 1984 An algorithm is presented to compute an optimal (s, S) policy under standard assumptions (stationary data, well-behaved one-period costs, discrete demand, full backlogging, and the average-cost criterion). The method is iterative, starting with an arbitrar ... Cite

COMBINED VEHICLE ROUTING AND INVENTORY ALLOCATION PROBLEM.

Journal Article Operations Research · 1984 The authors address the combined problem of allocating a scarce resource among several locations, and planning deliveries using a fleet of vehicles. Demands are random, and holding and shortage costs must be considered in the decision along with transporta ... Cite

ON THE IMBALANCE OF INVENTORIES IN MULTI-ECHELSON SYSTEMS.

Journal Article Mathematics of Operations Research · 1984 A central depot periodically orders or produces new stock and withdraws inventory in order to allocate it among several demand points, each experiencing random demands over a finite planning horizon. This system gives rise to a dynamic program with a state ... Cite

Prospects for the Middle East

Journal Article European Journal of Operational Research · January 1, 1984 Full text Cite

ALLOCATION POLICIES AND COST APPROXIMATIONS FOR MULTILOCATION INVENTORY SYSTEMS.

Journal Article Naval research logistics quarterly · 1984 Consider a central depot that supplies several locations experiencing random demands. Periodically, the depot may place an order for exogenous supply. Orders arrive after a fixed leadtime, and are then allocated among the several locations. Each allocation ... Cite

COMPUTATIONAL ISSUES IN AN INFINITE-HORIZON, MULTIECHELON INVENTORY MODEL.

Journal Article Operations Research · 1984 A. Clark and H. Scarf characterize optimal policies in a two-echelon, two-location inventory model. The authors extend their result to the infinite-horizon case (for both discounted and average costs). The computations required are far easier than for the ... Cite

APPROXIMATIONS OF DYNAMIC, MULTILOCATION PRODUCTION AND INVENTORY PROBLEMS.

Journal Article Management Science · 1984 Consider a central depot (or plant) which supplies several locations experiencing random demands. Orders are placed (or production is initiated) periodically by the depot. The order arrives after a fixed lead time, and is then allocated among the several l ... Cite

An improved disaggregation method for transportation problems

Journal Article Mathematical Programming · 1983 A method is given to disaggregate the solution to an aggregated transportation problem. The resulting solution to the original problem is feasible, all-integer, and has lower cost that those of solutions produced by earlier methods. © 1983 North-Holland Pu ... Full text Cite

Solution techniques for some allocation problems

Journal Article Mathematical Programming · 1983 This paper presents methods for solving allocation problems that can be stated as convex knapsack problems with generalized upper bounds. Such bounds may express upper limits on the total amount allocated to each of several subsets of activities. In additi ... Full text Cite

EXACT AND APPROXIMATE COST FUNCTIONS FOR PRODUCT AGGREGATES.

Journal Article MANAGE SCI · 1982 IT IS SHOWN THAT CERTAIN LARGE, MULTIPRODUCT PROBLEMS CAN BE WELL APPROXIMATED BY SMALLER MODELS OF THE SAME FORM, REPRESENTING ONLY ONE AGGREGATE PRODUCT (OR A FEW SUCH PRODUCTS). THIS REDUCTION FOLLOWS FROM A NEW TECHNIQUE TO APPROXIMATETHE MINIMAL COST ... Cite

TRANSPORTATION PROBLEMS WITH AGGREGATED DESTINATIONS WHEN DEMANDS ARE UNCERTAIN.

Journal Article NAV RES LOGIST Q · 1982 THE PAPER CONSIDERS THE EFFECTS OF USING A SMALL, AGGREGATEAPPLIED MODEL IN PLACE OF A LARGER, MORE DETAILED ONE. FORMULATION OF THE AGGREGATE OBJECTIVE FUNCTION TURNS OUT TO DEPEND ON HOW ONE CHOOSES TO USE ( ″ DISAGGREGATE ″ ) THE SOLUTION; SEVERAL ALTER ... Cite

Aggregation and disaggregation in convex network problems

Journal Article Networks · January 1, 1982 This article considers the error induced when the nodes of a large convex‐cost network problem are aggregated to form a smaller problem. First, I formalize the notion of aggregation, focusing on disaggregation of the solution and construction of the cost f ... Full text Cite

Bounds for aggregating nodes in network problems

Journal Article Mathematical Programming · December 1, 1980 It is often necessary or desirable in practice to replace a large, detailed optimization model with a smaller, approximate model. It would be useful to have bounds on the error resulting from this process of aggregation. This paper develops such bounds for ... Full text Cite

BOUNDS FOR ROW-AGGREGATION IN LINEAR PROGRAMMING.

Journal Article Operations Research · 1980 Most applied linear programs reflect a certain degree of aggregation - either explicit or implicit - of some larger, more detailed problem. This study develops methods for assessing the loss in accuracy resulting from aggregation. We showed previously that ... Cite

BOUNDS ON THE EFFECT OF AGGREGATING VARIABLES IN LINEAR PROGRAMS.

Journal Article Operations Research · 1980 This study explores the effects of aggregating variables in large linear programs. The author defines a reasonable criterion for the resulting loss in accuracy, and derive bounds on this quantity. A posteriori bounds may be calculated after solving the agg ... Cite

Simple Ranking Methods for Allocation of One Resource

Journal Article Management Science · January 1980 This paper considers optimization problems with a nonlinear-additive objective function and a single linear constraint. Such models have numerous direct applications and serve as subproblems in procedures for more complex problems. Some important ... Full text Cite