• Management Science and Financial Engineering
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• v.17 no.2
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• pp.23-37
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• 2011

In this paper, we address a layout design problem for determining an optimal 4-class-based dedicated linear storage layout in a class of unit load storage systems. Assuming that space requirement for a class is the sum of the maximum inventory levels of products assigned to the class, and that one-way travel time is a linear function of storage index, we formulate a 4-class-based dedicated linear storage problem PTL[4] and provide an exact splitting algorithm with $O(n{\lceil}logn{\rceil})$. Our algorithms could be applied to more than a 4-class-based dedicated storage layout problem with slight modification in order to reduce computational execution time.

• Management Science and Financial Engineering
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• v.12 no.1
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• pp.79-94
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• 2006

In this paper, we readdress a layout design problem, PTL[3], for determining an optimal 3-class-based dedicated linear storage layout in a class of unit load storage systems. Based on some fundamental properties derived, we provide a converging exact algorithm with O(n[logn]), which is more efficient than that of Yang and Kim [8] and can be applied to PTL[K] with $K{\ge}4$ in order to reduce computational execution time. In addition, we prove that the necessary condition suggested by them is also a sufficient condition to PTL[3].

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.3
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• pp.222-229
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• 2003

In this paper, we address a layout design problem, PTN[2], for determining an appropriate 2-class-based dedicated storage layout in a class of unit load storage systems. Our strong conjecture is that PTNI2] is NP-hard. Restricting PTN[2], we provide three solvable cases of PTN[2] in which an optimal solution to the solvable cases is one of the partitions based on the PAI(product activity index)-nonincreasing ordering. However, we show with a counterexample that a solution based on the PAI-non increasing ordering does not always give an optimal solution to PTN[2]. Utilizing the derived properties, we construct an effective heuristic algorithm for solving PTN[2] based on a PAI-non increasing ordering with performance ratio bound. Our algorithm with O($n^2$) is effective in the sense that it guarantees a better class-based storage layout than a randomized storage layout in terms of the expected single command travel time.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.505-516
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• 2007

In this paper, we provide some fundamental properties and basic theoretical results of K-class-based dedicated storage policy in a unit load system assuming the constant-space assumption that the number of storage locations for a class is not the maximum aggregate inventory position for a class but the sum of space requirement for products assigned to the class. The main theorem is that there exists a (K+1) -class-based storage layout whose expexted single command (SC) travel time is not greater than that of a K-class-based storage layout, i.e, $E(SC^*_{K+1}){\leq}E(SC^*_K)\;for\;K=1,{\cdots}$, (n-1).

• Journal of Korean Institute of Industrial Engineers
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• v.30 no.3
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• pp.190-196
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• 2004

In this paper, we address a layout design problem, PTL[3], for determining an optimal 3-class-based dedicated linear storage layout in a class of unit load storage systems. Our objective is to minimize the expected single command travel time. We analyze PTL[3] to derive a fundamental property that an optimal solution to PTL[3] is one of the partitions based on the PAI(product activity index)-nonincreasing ordering. Using the property and partial enumeration, we construct an efficient exact algorithm with O $(n\;{\lceil}\;log\;n\;{\rceil}\;)$ for solving PTL[3].

• Journal of Korean Institute of Industrial Engineers
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• v.18 no.2
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• pp.109-121
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• 1992

In this paper, we address a layout design problem for determining a K-class-based dedicated storage layout in an automated storage retrieval system. K-class-based dedicated storage employs K zones in which lots from a class of products are stored randomly. Zones form a partition of storage locations. Our objective function is to minimize the expected single command travel time, which is expressed as a set function of space requirements for zones, average demand rates from classes, and one-way travel times from the pickup/deposit station to locations. We construct a heuristic algorithm based on analytical results and a local search method, the methodology deveolped can be used with easily-available data by warehouse planners to improve the throughput capacity of a conventional warehouse as well as an AS/RS.