Published Research
Adelman, D. and Barz, C. "A PriceDirected Dynamic Heuristic for the Economic Lot Scheduling Problem." To appear in IIE Transactions
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We formulate the wellknown economic lot scheduling problem (ELSP) with sequence dependent setup times and costs as a semiMarkov decision process. Using an ane approximation of the bias function, we obtain a semiinnite linear program determining a lower bound for the minimum average total cost rate. The solution of this problem is directly used in a pricedirected dynamic heuristic to determine a good cyclic schedule. As the state space of the ELSP is nontrivial for the multiproduct setting with setup times, we further illustrate how a lookahead version of the pricedirected dynamic heuristic can be used to construct and dynamically improve an approximation of the state space. Numerical results show that the resulting heuristic performs competitively.

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Adelman, D. and Barz, C. "A Unifying Approximate Dynamic Programming Model for the Economic Lot Scheduling Problem." To appear in Mathematics of Operations Research.
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We formulate the wellknown economic lot scheduling problem (ELSP) with sequence dependent setup times and costs as a semiMarkov decision process. Using an affine approximation of the bias function, we obtain a semiinfinite linear program determining a lower bound for the minimum average cost rate. Under a very mild condition, we can reduce this problem to a relatively small convex quadratically constrained linear problem by exploiting the structure of the objective function and the state space. This problem is equivalent to the lower bound problem derived by Dobson (1992) and reduces to the wellknown lower bound problem introduced in Bomberger (1966) for sequencedependent setups. We thus provide a framework that unifies previous work, and opens new paths for future research on tighter lower bounds and dynamic heuristics.

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Adelman, D. and Mersereau, A. "Dynamic Capacity Allocation to Customers Who Remember Past Service." Management Science. 59(3), March 2013, 592612.
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We study the problem faced by a supplier deciding how to dynamically allocate limited capacity among a portfolio of customers who remember the ll rates provided to them in the past. A customer's order quantity is positively correlated with past ll rates. Customers dier from one another in their contribution margins, in their sensitivities to the past, and in their demand volatilities. By analyzing and comparing policies that ignore goodwill with ones that account for it, we investigate when and how customer memory eects
impact supplier profits. We develop an approximate dynamic programming (ADP) policy that dynamically rationalizes the ll rates the rm provides to each customer. This policy achieves higher rewards than margingreedy and Lagrangian policies and yields insights into how a supplier can eectively manage customer memories to its advantage.

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Adelman, D and Klabjan, D. "Computing Near Optimal Policies in Generalized Joint Replenishment." INFORMS. 24(1), Winter 2012, 148164.
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We provide a practical methodology for solving the generalized joint replenishment (GJR) problem, based on a mathematical programming approach to approximate dynamic programming. We show how to automatically generate a value function approximation basis built upon piecewiselinear ridge functions, by developing and exploiting a theoretical connection with the problem of finding optimal cyclic schedules. We provide a variant of the algorithm that is effective in practice, and exploit the special structure of the GJR problem to provide a coherent, implementable framework.

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Zhang, D. and Adelman, D. "An Approximate Dynamic Programming Approach to Network Revenue Management with Customer Choice." Transportation Science, 43, 381394, 2009.
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We consider a network revenue management problem where customers choose among open fare products according to some prespecified choice model. Starting with a Markov decision process (MDP) formulation, we approximate the value function with an affine function of the state vector. We show that the resulting problem provides a tighter bound for the MDP value than the choicebased linear program proposed by Gallego et al. (2004) and van Ryzin and Liu (2004). We develop a column generation algorithm to solve the problem for a multinomial logit choice model with disjoint consideration sets. We also provide new results on the wellknown decomposition heuristic. Our numerical study shows the policies from our solution approach can significantly outperform heuristics from the choicebased linear program.

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Adelman, D. "A Simple Algebraic Approximation to the Erlang Loss System." Operations Research Letters, 36, 484491, 2008.
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We use Palm calculus to derive a simple, intuitive system of two linearquadratic equations and two unknowns, whose algebraic solution yields Harel's (1988) upper bound to the Erlang loss probability. We then derive a sequence of progressively stronger systems of equations, which eventually become exact. These algebraic relations provide a parsimonious, new metaphor for modeling Erlang loss behaviour within optimization models. We illustrate our framework using two example applications.

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Adelman, D. and Mersereau, A. "Relaxations of Weakly Coupled Stochastic Dynamic Programs." Operations Research, 56(3), 712727, 2008.
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We consider a broad class of stochastic dynamic programming problems that are amenable to relaxation via decomposition. These problems comprise multiple subproblems that are independent of each other except for a collection of coupling constraints on the action space. We fit an additively separable value function approximation using two techniques, namely Lagrangian relaxation and the linear programming (LP) approach to approximate dynamic programming. We prove various results comparing the relaxations to each other and to the optimal problem value. We also provide a column generation algorithm for solving the LPbased relaxation to any desired optimality tolerance, and we report on numerical experiments on banditlike problems. Our results provide insight into the complexity versus quality tradeoff when choosing which of these relaxations to implement.

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Adelman, D. "PriceDirected Control of a Closed Logistics Queueing Network." Operations Research 55(6), 10221038, 2007.
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Motivated by one of the leading intermodal logistics suppliers in the United States, we consider an internal pricing mechanism for managing a fleet of service units (shipping containers) flowing in a closed queueing network. Nodes represent geographic locations and arcs represent travel between them. Customer requests for arcs arrive over time, and the problem is to find an accept/reject policy that maximizes the longrun time average reward rate from accepting requests.
We formulate the problem as a semiMarkov decision process, and give a simple linear program that provides an upper bound on the optimal reward rate. Using Palm calculus, we derive a nonlinear program that approximately captures queueing and stockout effects on the network. Using its optimal Lagrange multipliers, we construct a simple functional approximation to the dynamic programming value function. The resulting policy is computationally efficient and produces superior economic performance as compared with other policies. Furthermore, it provides a methodologically grounded solution to the firm's internal pricing problem.

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Klabjan, D. and Adelman, D. "A Convergent Infinite Dimensional Linear Programming Algorithm for Deterministic SemiMarkov Decision Processes on Borel Spaces." Mathematics of Operations Research, 32(3), 528550, 2007.
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We devise an algorithm for solving the infinite dimensional linear programs that arise from general deterministic semiMarkov decision processes on Borel spaces. The algorithm constructs a sequence of approximate primal/dual solutions that converge to an optimal one. The innovative idea is to approximate the dual solution with continuous piecewise linear ridge functions that naturally map functions defined on a high dimensional domain into a linear combination of such functions defined on only a single dimension. This approximation gives rise to a primal/dual pair of semiinfinite programs, for which we show strong duality. In addition, we prove various properties of the underlying ridge functions.

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Adelman, D. "Dynamic BidPrices in Revenue Management." Operations Research, 55(4), 647661, 2007.
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We formally derive the standard deterministic linear program (LP) for bidprice control by making an affine functional approximation to the optimal dynamic programming value function. This affine functional approximation gives rise to a new LP that yields tighter bounds than the standard LP. Whereas the standard LP computes static bidprices, our LP computes a time trajectory of bidprices. We show that there exist dynamic bidprices, optimal for the LP, that are individually monotone with time. We provide a column generation procedure for solving the LP within a desired optimality tolerance, and present numerical results on computational and economic performance.

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Klabjan, D. and Adelman, D. "Existence of Optimal Policies for SemiMarkov Decision Processes Using Duality for Infinite Linear Programming." SIAM Journal on Control and Optimization, 44, 21042122, 2006.
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SemiMarkov decision processes on Borel spaces with deterministic kernels have many practical applications, particularly in inventory theory. Most of the results from general semiMarkov decision processes do not carry over to a deterministic kernel since such a kernel does not provide ``smoothness." We develop infinite dimensional linear programming theory for a general stochastic semiMarkov decision process. We give conditions, general enough to allow deterministic kernels, for solvability and strong duality of the resulting linear programs. By using the developed linear programming theory we give conditions for the existence of a stationary deterministic optimal policy.

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Adelman, D. and Klabjan, D. "Duality and Existence of Optimal Policies in Generalized Joint Replenishment." Mathematics of Operations Research, 30, 2850, 2005.
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We establish a duality theory for a broad class of deterministic inventory control problems on continuous spaces that includes the classical joint replenishment problem and inventory routing. Using this theory, we establish the existence of an optimal policy, which has been an open question. We show how a primaldual pair of infinite dimensional linear programs encode both cyclic and noncyclic schedules, and provide various results regarding cyclic schedules including an example showing that they need not be optimal.

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Adelman, D. "A PriceDirected Approach to Stochastic Inventory/Routing." Operations Research, 52(4), 499514, 2004.
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We consider a new approach to stochastic inventory/routing that approximates the future costs of current actions using optimal dual prices of a linear program. We obtain two such linear programs by formulating the control problem as a Markov decision process and then replacing the optimal value function with the sum of single customer inventory value functions. The resulting approximation yields statewise lower bounds on optimal infinitehorizon discounted costs.
We present a linear program that takes into account inventory dynamics and economics in allocating transportation costs for stochastic inventory routing. On test instances we find that these allocations do not introduce any error in the value function approximations relative to the best approximations that can be achieved without them. Also, unlike other approaches we do not restrict the set of allowable vehicle itineraries in any way. Instead, we develop an efficient algorithm to both generate and eliminate itineraries during solution of the linear programs and control policy. In simulation experiments the pricedirected policy outperforms other policies from the literature.

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Adelman, D. "PriceDirected Replenishment of Subsets: Methodology and its Application to Inventory Routing." Manufacturing & Service Operations Management, 5(4), 348371, 2003.
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The idea of pricedirected control is to use an operating policy that exploits optimal dual prices from a mathematical programming relaxation of the underlying control problem. We apply it to the problem of replenishing inventory to subsets of products/locations, such as in the distribution of industrial gases, so as to minimize longrun time average replenishment costs.
Given a marginal value for each product/location, whenever there is a stockout the dispatcher compares the total value of each feasible replenishment with its cost, and chooses one that maximizes the surplus. We derive this operating policy using a linear functional approximation to the optimal value function of a semiMarkov decision process on continuous spaces. This approximation also leads to a math program whose optimal dual prices yield values and whose optimal objective value gives a lower bound on system performance. We use duality theory to show that optimal prices satisfy several structural properties and can be interpreted as estimates of lowest achievable marginal costs. On real world instances, the pricedirected policy achieves superior, near optimal performance as compared with other approaches.

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Adelman, D. and Nemhauser, G.L. "PriceDirected Control of Remnant Inventory Systems." Operations Research, 47, 889898, 1999.
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Motivated by maketoorder cable manufacturing, we describe a remnant inventory system in which orders arrive for units of raw material that are producedtostock. As orders are satisfied, the partially consumed units of material, or remnants, are either scrapped or returned to inventory for future allocation to orders. We present a linear program that minimizes the long run average scrap rate. Its dual prices exhibit many rational properties, including monotonicity and superadditivity. We use these prices in an integerprogrammingbased control scheme, which we simulate and compare with an existing control scheme previously used in practice.

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Adelman, D. Nemhauser, G.L. et al. "Allocating Fibers in Cable Manufacturing" Manufacturing & Service Operations Management, 1, 2135, 1999.
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We study the problem of allocating stocked fibers to madetoorder cables with the goals of satisfying due dates and reducing the costs of scrap, setup, and fiber circulation. These goals are achieved by generating remnant fibers either long enough to satisfy future orders or short enough to scrap with little waste. They are also achieved by manufacturing concatenations, in which multiple cable orders are satisfied by the production of a single cable that is afterwards cut into the constituent cables ordered. We use a function that values fibers according to length, and which can be viewed as an approximation to the optimal value function of an underlying dynamic programming problem. The daily policy that arises under this approximation is an integer program with a simple linear objective function that uses changes in fiber value to take into account the multiperiod consequences of decisions. We describe our successful implementation of this integer program in the factory, summarizing our computational experience as well as realized operational improvements.

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Adelman D. and Nemhauser, G.L. "PriceDirected Control of Remnant Inventory Systems." Proceedings of the 1996 Manufacturing & Service Operations Management Conference, Dartmouth College, Hanover, NH, June 1996.
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Motivated by maketoorder cable manufacturing, we describe a remnant inventory system in which orders arrive for units of raw material that are producedtostock. As orders are satisfied, the partially consumed units of material, or remnants, are either scrapped or returned to inventory for future allocation to orders. We present a linear program that minimizes the longrun average scrap rate. Its dual prices exhibit many rational properties, including monotonicity and superadditivity. We use these prices in an integerprogrammingbased control scheme, which we simulate and compare with an existing control scheme previously used in practice.

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Adelman D., Auclair, P., Goldman, D. and Swain, J. "Multinomial Selection Procedures for Use in Simulations". Proceedings of the 1993 Winter Simulation Conference. Dartmouth College, Hanover, NH, 1993.
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We describe singlestage and closed sequential procedures for selecting the most probable cell of a multinominal distribution. These procedures are then reformulated as nonparametric techniques for selecting the best one of a umber of competing simulated systems or alternatives. We discuss performance characteristics of the procedures and make recommendations concerning their use.

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Adelman D. and Young, D. "A SpreadsheetBased Prototype Enterprise System." Industrial Engineering. 26(5), 1994.
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A spreadsheetbased prototype enterprise system can serve as an effective tool for project engineers trying to sell an enterprise system to cautious managers. In some applications, it is capable of demonstrating the basic functionality of the largescale system, such as scheduling and job costing, but without a large time and financial investment. It is found that, although closedform computations, such as economic order quantity calculations, are easy to implement, the spreadsheet system computes them slowly. A system structure that can be used to construct departmental spreadsheets that change in realtime as other departments make decisions is proposed. Computational sluggishness, limited database capability and awkward userinterfaces are disadvantages that must be dealt with by an engineer seeking to build a quick prototype enterprise system using spreadsheets.

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Adelman D., Wille, L.T. et. al. "LongRange Order, and a Possible Devil's Staircase in YBa_{2}Cu_{3}o_{z}", Journal of Physics: C.M. 4, L585L592, 1992.
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It is shown that the oxygenordered superstructures observed experimentally in YBa2Cu3Oz can be understood in terms of an Ising Hamiltonian containing screened Coulomb repulsions between any two oxygen sites, augmented with a shortrange attractive covalent interaction between oxygen sites adjoined by a copper atom. Spatially modulated commensurate phases separated by smooth solitonlike domain walls are obtained through Monte Carlo simulations. These simulations indicate the existence of a complete devil's staircase of phases. It is predicted that the plateau fine structure of the Tcz curve and the bond valence sum also exhibit experimentally observable staircase behaviour.
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