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Selected papers of Duro Kurepa - download pdf or read online

By Duro Kurepa

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N, k = 1, . . , (m − 1). This constraint ensures that the first sublot begins processing on machine (k + 1) only after it has completed processing on machine k, has been transferred to machine (k + 1) and the setup on machine (k + 1) has been completed. (b) For sublots 2,. . ,nj : Ci j (k+1) − p j (k+1)si j (k+1) ≥ Ci j k + F T j + V T j si j k , ∀i = 2, . . , n i , j = 1, . . , N, k = 1, . . , (m − 1). This constraint ensures that all the sublots, excluding the first one, begin processing on the (k +1) th machine only after they have finished processing on the kth machine and have been transferred to machine (k + 1).

Both of these algorithms are based on solving relaxed mathematical formulations of the problem under consideration. Their experimental results show that a solution, which minimizes the makespan, is not necessarily optimal for the criterion of flow time minimization. Baker [2] and Vickson and Alfredsson [37] separately addressed the 2/N/C/ II/DV problem. Clearly, in the absence of setup times, transfer and removal times, and intermingling amongst sublots of different lots, unit-size sublots are optimal.

Some Generic Mathematical Models 35 Variables: si j k Sublot size of the i th sublot of lot j on machine k; a generalization of the definition of sublot sizes presented in Sect. 2 Ci j k Completion time of the i th sublot of lot j on machine k; the subscript j is omitted for problems involving a single lot 1, if lot i precedes lot j yi j = 0, otherwise. 2 m/N/{C,E,V}/{II,NI}/{CV,DV}/{Lot-Attached Setup and Removal Times, Sublot Transfer Times, No Intermingling} The lot streaming problem involving multiple lots deals with the issue of finding the sublot sizes for each lot and the sequence in which to process the lots in order to optimize a performance measure.

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