A. Aggarwal and J. K. Park. Improved algorithms for economic lot size problems. Operations Research, 41:549--571, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....arises very often in practice, has been studied in a variety of papers. In [9] an O(n 2 ) dynamic programming algorithm was presented for the general problem (1) 4) and certain properties of optimal solutions were presented for WW costs. Almost thirty years later Wagelmans et al. 8] see also [1, 4], showed that the running time of the dynamic programming algorithm could be reduced to O(n log n) in the general case, and to O(n) with WW costs. Barany et al. 3] presented a description of the convex hull of solutions in the general case, and Pochet and Wolsey [5] showed how an alternative ....

A. Aggarwal and J.K. Park, Improved algorithms for economic lot size problems, Operations Research 41, 549-51 (1990).

....and VLSI routing, including all farthest neighbors of convex polygons. Since the publication of their paper, several new applications of monotone matrices have been discovered, e.g. dynamic programming, largest area (or perimeter) triangle in a set of points, economic lot problems, etc. see [8, 5, 6, 7, 9, 19, 22, 26, 27, 29, 28, 35, 36] for some of these applications. 1 Most of the papers cited above, however, consider only the problem of computing the maximal or minimal elements of each row. Surprisingly, very little is known about more general selection problems for monotone matrices. There are two natural selection problems ....

A. Aggarwal and J. Park, Improved algorithm for economic lot size problems, Operations Research 41 (1993), 549--571.

....1. The first category pertains to production and inventory planning. Most of the research on production and inventory planning for nonstationary demand has concentrated either on uncapacitated models (e.g. Wagner and Whitin, 1958, Zangwill, 1966, Federgruen and Tzur, 1991, Wagelmans et al. 1992, Aggarwal and Park, 1993) or on models with given capacities (e.g. Florian and Klein, 1971, Baker et al. 1978, Florian et al. 1980, Bitran and Yanasse, 1982, Van Hoesel and Wagelmans, 1996) rather than treating capacity as a decision variable. In two case studies, Bradley and Arntzen (1999) demonstrate that firms can ....

Aggarwal, A. and Park, J. K. (1993). Improved algorithms for economic lot-size problems. Operations Research, 41:549--571.

....is more expensive than in house production (q p) As in the two other cost structures we take H(I) hI . 2.2 The n period lot sizing problem The basis for solving the on line lot sizing problem is the n period problem. For an overview of results on the n period lot sizing problem, see [Aggarwal Park, 1993] or [Bahl, Ritzman Gupta, 1987] This problem can be formulated as follows. Given demands d t 0 for the discrete time periods t = 1; n, find a production plan with lot sizes X 1 ; X n , such that the cost of that production plan, n X t=1 [P (X t ) H(I t ) is minimized, ....

AGGARWAL, A., AND J.K. PARK [1993], Improved algorithms for economic lot size problems, Operations Research 41, 549--571.

....is more expensive than inhouse production (q p) As in the two other cost structures we take H(I) hI . 2.2 The n period lot sizing problem The basis for solving the on line lot sizing problem is the n period problem. For an overview of results on the n period lot sizing problem, see Aggarwal Park [1993] or Bahl, Ritzman Gupta [1987] This problem can be formulated as follows. Given demands d t 0 for the discrete time periods 1; n, find a production plan with lot sizes X 1 ; X n , such that the cost of that production plan, n X t=1 [P (X t ) H(I t ) is minimized, where I ....

AGGARWAL, A., AND J.K. PARK [1993], Improved algorithms for economic lot size problems, Operations Research 41, 549--571.

....Whitin proposed an O(T 2 ) dynamic programming algorithm, where T is the number of time periods in the planning horizon. It lasted more than thirty years before a better algorithm was found. In the early 1990 s three groups simultaneously developed algorithms with running time O(T log T ) see [5], 24] 52] Important for the implementation of graph related algorithms is the availability of software packages. The most prominent software library is LEDA, A Library of Efficient Datatypes and Algorithms, developed by Melhorn and N aher [38] It is implemented by a C class library, and ....

A. Aggarwal, J.K. Park (1993). Improved algorithms for economic lot size problems. Oper. Res. 41, 549-571.

....by calculating n Gamma k Gamma i 1 values of f . This gives a total time complexity of O(n 2 p) and a space complexity of O(n) to compute g(0; p) There are two basic ways that the complexity of a dynamic programming algorithm can be reduced: either by general methods such as presented in [1, 13] or by more problem dependent methods such as [12] The reader is referred to [1] and the references therein for a recent account on algorithmic improvements on dynamic programming algorithms using array searching. It should be noted that our weight function satisfies the Monge condition described ....

.... of O(n 2 p) and a space complexity of O(n) to compute g(0; p) There are two basic ways that the complexity of a dynamic programming algorithm can be reduced: either by general methods such as presented in [1, 13] or by more problem dependent methods such as [12] The reader is referred to [1] and the references therein for a recent account on algorithmic improvements on dynamic programming algorithms using array searching. It should be noted that our weight function satisfies the Monge condition described in [1] if f(i; j) is raised to a high enough power. Our result is achieved by an ....

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A. Aggarwal and J.K. Park, Improved algorithms for economic lot size problems, Operations Research, 41 (1993), pp. 549--571.

....can be divided into two categories: optimal algorithms and lot sizing heuristics. The very first optimal algorithm is the well known Wagner Whitin Algorithm which has been regarded as a slow algorithm due to its O(n 2 ) worst case running time. Recently, several researchers(Aggarwal and Park [1], Federgruen and Tzur [7] Wagelmans, Van Hoesel, and Kolen [15] have developed different types of O(n log n) optimal lot sizing algorithms. More recently, Qian and Jones [12] showed that the Wagner Whitin Algorithm itself is in fact an O(n) algorithm under very realistic assumptions. Therefore, ....

....planning systems, unit costs are generally varied to reflect the status of capacity utilization or other penalty factors. Third, since this problem contains the constant unit cost case as a special case, a study of it will enhance our understanding of the DLSP. While exact algorithms [17] 6] 7] [1] [15] can produce optimal solutions to the DLSP with variable unit costs, they typically don t possess the stability property. On the other hand, no stable heuristics are known for the general variable cost case. Whether there exists any fast and stable lot sizing heuristic that produces high ....

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Aggarwal, A.M., and J.K. Park, Improved Algorithms for Economic Lot-Size Problems, Working Paper, IBM Thomas J. Watson Research Center, Yorktown Heights, NY. 1990.

.... Recurrences of the type (22) arise in many applications e.g. in connection with the concave least weight subsequence problem (cf. Hirschberg and Larmore [73] and Wilber [133] special cases of the traveling salesman problem and of economic lot sizing problems (see Park [103] and Aggarwal and Park [12]) The last two applications will be discussed in further detail below. It can be checked that if W is Monge, then also D is Monge. Since solving (22) is an online problem, the off line SMAWK algorithm of Aggarwal et al. 8] cannot be applied. Wilber developed, however, an extension of the ....

....obtain the following recurrence: E(j) min 1i j 8 : E(i) c i (d ij ) j Gamma1 X q=i 1 h q (d qj ) 9 = where d ij = P j Gamma1 q=i d q for 1 i j n 1. Obviously E(n 1) gives the cost of an optimal production schedule for the original n period problem. Aggarwal and Park [12] deal with two special cases of the above problem. In both cases the storage costs are linear, say h i (y) h 1 i y, and the production costs are of fixed cost type, i.e. c i (x) c 0 i c 1 i x for x 0 and c i (0) 0 with c 0 i 0. In the first case it is additionally assumed that ....

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A. Aggarwal and J.K. Park, Improved algorithms for economic lot-size problems, Operations Research 41, 1993, 549--571.

....step is actually performed in linear time and the overall complexity is determined by the sorting step. 1 Introduction The early 1990 s saw the emergence of powerful techniques that reduced the time requirement of dynamic programming algorithms for the classic eco1 nomic lot sizing (ELS) problem [8, 15, 1]. It was subsequently realized that certain scheduling problems involving the sum of completion times objective and an element of batching exhibited structural properties that made them amenable to more efficient dynamic programming solutions. In some cases [7, 3] the improved schemes were ....

A Aggarwal and J K Park. Improved algorithms for economic lot size problems. Operations Research, 41(3):549--571, 1993.

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A. Aggarwal and J. K. Park. Improved algorithms for economic lot size problems. Operations Research, 41:549--571, 1993.

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