Author

# James K. Park

Bio: James K. Park is an academic researcher from Sandia National Laboratories. The author has contributed to research in topics: Semigroup & Time complexity. The author has an hindex of 7, co-authored 10 publications receiving 499 citations.

##### Papers

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TL;DR: This paper shows that for many of these concave cost economic lot size problems, the dynamic programming formulation of the problem gives rise to a special kind of array, called a Monge array, and shows how the structure of Monge arrays can be exploited to obtain significantly faster algorithms for these economic lots size problems.

Abstract: Many problems in inventory control, production planning, and capacity planning can be formulated in terms of a simple economic lot size model proposed independently by A. S. Manne (1958) and by H. M. Wagner and T. M. Whitin (1958). The Manne-Wagner-Whitin model and its variants have been studied widely in the operations research and management science communities, and a large number of algorithms have been proposed for solving various problems expressed in terms of this model, most of which assume concave costs and rely on dynamic programming. In this paper, we show that for many of these concave cost economic lot size problems, the dynamic programming formulation of the problem gives rise to a special kind of array, called a Monge array. We then show how the structure of Monge arrays can be exploited to obtain significantly faster algorithms for these economic lot size problems. We focus on uncapacitated problems, i.e., problems without bounds on production, inventory, or backlogging; capacitated problem...

349 citations

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TL;DR: This paper identifies a subset Λ of the set of all cost arrays satisfying the Demidenko conditions, such that for any C ∈ Λ, the running time of the aforementioned dynamic-programming algorithm can be reduced to O( n ).

Abstract: The traveling-salesman problem, though in general NP-hard, possesses several special cases that can be solved in polynomial time. In particular, when the cost array C associated with an n -vertex traveling-salesman problem satisfies what are known as the Demidenko conditions, then a minimum-cost traveling-salesman tour can be computed in O( n 2 ) time using a simple dynamic-programming algorithm. In this paper, we identify a subset Λ of the set of all cost arrays satisfying the Demidenko conditions, such that for any C ∈ Λ , the running time of the aforementioned dynamic-programming algorithm can be reduced to O( n ). We obtain this speedup using recently developed techniques for on-line searching in Monge arrays.

47 citations

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TL;DR: It is shown that the natural extension of the northwest-corner-rule greedy algorithm solves an instance of the d-dimensional transportation problem if and only if the problem's cost array possesses a d- dimensional Monge property recently proposed by Aggarwal and Park in the context of their study of monotone arrays.

Abstract: In 1963, Hoffman gave necessary and sufficient conditions under which a family of O(mn)-time greedy algorithms solves the classical two-dimensional transportation problem with m sources and n sinks. One member of this family, an algorithm based on the «northwest corner rule», is of particular interest, as its running time is easily reduced to O(m+n). When restricted to this algorithm, Hoffman's result can be expressed as follows: the northwest-corner-rule greedy algorithm solves the two-dimensional transportation problem for all source and supply vectors if and only if the problem's cost array C={c[i,j]} possesses what is known as the (two-dimensional) Monge property, which requires c[i 1 ,j 1 ]+c[i 2 ,j 2 ] ≤ c[i 1 ,j 2 ]+c[i 2 ,j 1 ] for i 1

*45 citations*

*01 Jun 1989*

TL;DR: This paper proposes a class of adaptive backoff methods that do not use any extra hardware and can significantly reduce the memory traffic to synchronization variables and shows that when the number of processors participating in a barrier synchronization is small, reductions of 20 percent to over 95 percent in synchronization traffic can be achieved at no extra cost.

Abstract: : Shared-memory multiprocessors commonly use shared variables for synchronization. Our simulations of real parallel applications show that large- scale cache-coherent multiprocessors suffer significant amounts of invalidation traffic due to synchronization. Large multiprocessors that do not cache synchronization variables are often more severely impacted. If this synchronization traffic is not reduced or managed adequately, synchronization references can cause sever congestion in the network. We propose a class of adaptive backoff methods that do not use any extra hardware and can significantly reduce the memory traffic to synchronization variables. These methods use synchronization state to reduce polling of synchronization variables. Our simulations show that when the number of processors participating in a barrier synchronization is small compared to the time of arrival of the processors, reductions of 20 percent to over 95 percent in synchronization traffic can be achieved at no extra cost. In other situations adaptive backoff techniques result in a tradeoff between reduced network accesses and increased processor idle time.

27 citations

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*01 Jan 1988*

19 citations

*Cited by*

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TL;DR: In this article, the authors consider single-level lot sizing problems, their variants and solution approaches, together with exact and heuristic approaches for their solution, and conclude with some suggestions for future research.

Abstract: Lot sizing is one of the most important and also one of the most difficult problems in production planning. This subject has been studied extensively in the literature. In this article, we consider single-level lot sizing problems, their variants and solution approaches. After introducing factors affecting formulation and the complexity of production planning problems, and introducing different variants of lot sizing and scheduling problems, we discuss single-level lot sizing problems, together with exact and heuristic approaches for their solution. We conclude with some suggestions for future research.

*670 citations*

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TL;DR: This contribution summarizes recent work in the field of lot sizing and scheduling and explains differences of formal models and provides some first readings recommendations on capacitated, dynamic, and deterministic cases.

Abstract: This contribution summarizes recent work in the field of lot sizing and scheduling. The objective is not to give a comprehensive literature survey, but to explain differences of formal models and to provide some first readings recommendations. Our focus is on capacitated, dynamic, and deterministic cases. To underscore the importance of the research efforts, current practice is described and its shortcomings are exposed. Mathematical programming models where the planning horizon is subdivided into several discrete periods are given for both approaches that are well-established and approaches which may represent tomorrow's state of the art. Two research directions are discussed in more detail: continuous time models and multi-level lot sizing and scheduling. The paper concludes with some advice for future research activities.

*606 citations*

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*01 Jan 1992-Operations Research*

TL;DR: An algorithm to solve the economic lot sizing problem in O(n log n) time is presented and it is shown how the Wagner-Whitin case can even be solved in linear time.

Abstract: We consider the n-period economic lot sizing problem, where the cost coefficients are not restricted in sign. In their seminal paper, H. M. Wagner and T. M. Whitin proposed an O(n2) algorithm for the special case of this problem, where the marginal production costs are equal in all periods and the unit holding costs are nonnegative. It is well known that their approach can also be used to solve the general problem, without affecting the complexity of the algorithm. In this paper, we present an algorithm to solve the economic lot sizing problem in O(n log n) time, and we show how the Wagner-Whitin case can even be solved in linear time. Our algorithm can easily be explained by a geometrical interpretation and the time bounds are obtained without the use of any complicated data structure. Furthermore, we show how Wagner and Whitin's and our algorithm are related to algorithms that solve the dual of the simple plant location formulation of the economic lot sizing problem.

*490 citations*

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*01 May 1993-Operations Research*

TL;DR: This paper shows that for many of these concave cost economic lot size problems, the dynamic programming formulation of the problem gives rise to a special kind of array, called a Monge array, and shows how the structure of Monge arrays can be exploited to obtain significantly faster algorithms for these economic lots size problems.

Abstract: Many problems in inventory control, production planning, and capacity planning can be formulated in terms of a simple economic lot size model proposed independently by A. S. Manne (1958) and by H. M. Wagner and T. M. Whitin (1958). The Manne-Wagner-Whitin model and its variants have been studied widely in the operations research and management science communities, and a large number of algorithms have been proposed for solving various problems expressed in terms of this model, most of which assume concave costs and rely on dynamic programming. In this paper, we show that for many of these concave cost economic lot size problems, the dynamic programming formulation of the problem gives rise to a special kind of array, called a Monge array. We then show how the structure of Monge arrays can be exploited to obtain significantly faster algorithms for these economic lot size problems. We focus on uncapacitated problems, i.e., problems without bounds on production, inventory, or backlogging; capacitated problem...

*349 citations*

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TL;DR: A state-of-the-art of a particular planning problem, the Single Item Lot Sizing Problem, is given for its uncapacitated and capacitated versions.

Abstract: A state-of-the-art of a particular planning problem, the Single Item Lot Sizing Problem (SILSP), is given for its uncapacitated and capacitated versions. First classes of lot sizing problems are briefly surveyed. Various solution methods for the Uncapacitated Single Item Lot Sizing Problem (USILSP) are reviewed. Four different mathematical programming formulations of the classical problem are presented. Different extensions for real-world applications of this problem are discussed. Complexity results of the Capacitated Single Item Lot Sizing Problem (CSILSP) are given together with its different formulations and solution techniques.

*336 citations*