The solution of multiperiod network models with bundle constraints by aggregation

Article Abstract:

A solution of a multiperiod, multicommodity network model in the presence of bundle side constraints is proposed. The constraints limit flow through a set of arcs at each point in time. This production planning and distribution problem is transformed into two single-commodity network flow formulations. The first is an aggregated problem, the solution of which gives rise to a second disaggregated problem which provides a near optimal solution to the original. A computational error and theoretical a priori and posteriori bounds are introduced. The proposed algorithm is compared with the alternative solutions MPSX/370 and NETSIDE, the latter involving a specialized solution code. The results indicate that the proposed method outperforms the others in terms of efficiency and errors.

Methods, Models, Production management, Production planning

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Priority rules for job shops with weighted tardiness costs

Article Abstract:

Priority dispatching research has mainly focused on jobs with equal delay penalties, the effect being that strategic differentiation of client orders is ruled out. Efficient dispatching rules are developed and tested for the weighted tardiness problem, including delay penalties and job-specific due dates. The approach used is based on previous 'greedy' heuristics, in which assignment priority stems from expected tardiness expense per immediate processing requirements. Results suggest that the new regulations are not only better than competing ones for minimizing weighted tardiness penalties, but are also robust for other criteria such as costs of in-process inventories and the number of tardy jobs.

Analysis, Management, Scheduling (Management), Machine shops, Production control

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A forward simplex method for staircase linear programs

Article Abstract:

A forward simplex algorithm is presented for solving the general staircase linear programming problem. The tests indicate that the solution time of the forward simplex code is linear in the number of time periods, as compared to a quadratic or cubic relationship for standard linear programming codes. The forward simplex code solved some of the largest problems nearly 16 times faster than one of the standard, efficient simplex codes. Computational decision horizons, responsible for the good performance of the algorithm, are often found.

Linear programming, Comparative analysis

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