H. D. Ratli# and A. S. Rosenthal #1983# Order-picking in a rectangular warehouse: a solvable case of the Traveling Salesman Problem, Operations Research 31, 507#521.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the algorithm seems to be of theoretical interest only. Our algorithm is an extension of an algorithm by Cutler #1980# for three parallel lines. #For two lines, the problem is trivial.# Cutler also considered the Traveling Salesman Path Problem. A similar but easier special case was considered by Ratli# and Rosenthal #1983#: the problem of order picking in a rectangular warehouse. These authors also used the dynamic programming paradigm for their problem and obtained a linear time algorithm. Cornu#ejols, Fonlupt, and Naddef #1985# extend the result of Ratli# and Rosenthal to the Steiner Traveling Salesman Problem ....

....only if T 2 # T 0 is a tour. This allowed us to forget al..l partial solutions except the best one in each equivalence class. With little e#ort, wehavenow been able to compute the best partial solution in each equivalence class in a systematic way. Exactly the same paradigm has been followed by Ratli# and Rosenthal #1983# in their solution of the order picking problem, and by Gilmore, Lawler, and Shmoys #1985# for the bandwidth limited problem. It is in principle not di#cult to extend this approach to the Taveling Salesman Path problem, which requires to #nd a shortest, not necessarily closed curve containing ....

H. D. Ratli# and A. S. Rosenthal #1983# Order-picking in a rectangular warehouse: a solvable case of the Traveling Salesman Problem, Operations Research 31, 507#521.

....the algorithm seems to be of theoretical interest only. Our algorithm is an extension of an algorithm by Cutler [1980] for three parallel lines. For two lines, the problem is trivial. Cutler also considered the Traveling Salesman Path Problem. A similar but easier special case was considered by Ratliff and Rosenthal [1983]: the problem of order picking in a rectangular warehouse. These authors also used the dynamic programming paradigm for their problem and obtained a linear time algorithm. Cornu ejols, Fonlupt, and Naddef [1985] extend the result of Ratliff and Rosenthal to the Steiner Traveling Salesman Problem ....

....only if T 2 [ T 0 is a tour. This allowed us to forget al..l partial solutions except the best one in each equivalence class. With little effort, we have now been able to compute the best partial solution in each equivalence class in a systematic way. Exactly the same paradigm has been followed by Ratliff and Rosenthal [1983] in their solution of the order picking problem, and by Gilmore, Lawler, and Shmoys [1985] for the bandwidth limited problem. It is in principle not difficult to extend this approach to the Taveling Salesman Path problem, which requires to find a shortest, not necessarily closed curve containing ....

H. D. Ratliff and A. S. Rosenthal [1983] Order-picking in a rectangular warehouse: a solvable case of the Traveling Salesman Problem, Operations Research 31, 507--521.

....the vertices in V n P , i.e. the Steiner points, represent the intersections of aisles and crossovers (in Figure 12, these points are denoted by ffl and ffi, respectively) The distance between any pair of vertices u and v is the length of a shortest path between u and v. Ratliff and Rosenthal [98] gave an O(m) time dynamic programming algorithm for solving the order picking problem in a rectangular warehouse, where m is the number of aisles. This problem was also solved (independently, but four years later) by Carlier and Villon [20] The graph in Figure 12 is an example of a ....

H.D. Ratliff and A.S. Rosenthal, Order-picking in a rectangular warehouse: A solvable case of the traveling salesman problem, Operations Research 31, 1983, 507--521. REFERENCES 53

....There are various modifications of the RDP. A natural one includes a given subset of the node set, where the nodes of this subset are required to be in the solution. This problem varies the problem to find a traveling salesman tour of minimal length including a given subset of the node set [3, 15]. The latter problem may also be related to a generalized Steiner problem in graphs, where a certain number of node disjoint paths have to be guaranteed between all nodes of a prespecified set of basic nodes [13, 16] Another modification of the RDP arises from the problem of connecting LAN ....

D.M. Ratliff and A.S. Rosenthal. Order picking in a rectangular warehouse: a solvable case of the travelling salesman problem. Operations Research, 31:507--521, 1983.

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