Remarks on: "Some extensions of the Discrete Lotsizing and Scheduling Problem."

Article Abstract:

Computational complexity results furnish guideposts toward fruitful directions in algorithmic research and are important in algorithm design. Therefore, complexity analysis is considered within the context of W. Bruggemann's and H. Jahnke's study on discrete lotsizing and scheduling problems. This particular analysis is prompted by a rapidly increasing amount of research on issues combining lotsizing and scheduling and two other pertinent reasons. Bruggemann et al dispute the correctness of two theorems, namely T1 and T3, that are found in a numerical model developed by four researchers that proves complexity results for variants of the discrete lotsizing and scheduling problem. The proof of T1 is corrected and the validity of both the proof of T3 and the arguments raised by Bruggemann et al is confirmed.

Inventory Control, Econometrics & Model Building, Production Planning & Control, Case studies, Econometrics, Algorithms, Production control, Business models

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Remarks on: "Some extensions of the discrete lotsizing and scheduling problem." (response to M. Salomon et al., Management Science, 1991, vol. 37, p. 801)

Article Abstract:

Salomon et al. argued in a 1991 issue of Management Science the NP-completeness of an array of variants of the discrete lot-sizing and scheduling problem (DLSP) which is differentiated through the use of a six-field notation. Their assertion is flawed because a number of the proofs they provided are wrong. Their transformations mapped some data values of the pre-image problem to the number of data in the obtained instance and are therefore not polynomial. This is evident in such examples as the 1/*/SI/G/A-optimization problem and 1/*/A/G/SI-DLSP. Salomon et al. focused on the two-item/single-period DLSP with an increasing number of machines, making their arguments untenable.

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New bounds for the identical parallel processor weighted flow time problem

Article Abstract:

The work of Eastmann, Even and Isaacs (EEI) on the identical parallel processor problem is extended using a general bound that incorporates the polynomial time lower bound first presented by EEI in 1964. The general bound can be used to generate four new bounds that can also be applied to the identical processor problem. The general bound can be analyzed to generate new insights into the link between problem characteristics and bound quality.

Parallel processing

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