Optimal solution of set covering/partitioning problems using dual heuristics

Article Abstract:

An algorithm for a mixed set covering/partitioning model that includes the set covering and set partitioning problems is presented. The algorithm employs continuous heuristics applied to the dual of the linear programming relaxation to offer lower bounds for a branch and bounds algorithm. The practical applications of the set partitioning model include: the scheduling of trucks, trains, and ships; stock cutting; and political redistricting. The algorithm performs better than the current best set covering and partitioning algorithms.

Research, Heuristic programming, Branch and bound algorithms, Partitions (Mathematics)

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A multiplier adjustment method for the generalized assignment problem

Article Abstract:

The assignment problem is generalized and covers the assignment of n jobs to m agents. The article examines a branch and bound algorithm for assignment problems that are generalized under guidelines produced from a Lagrangian relaxation when the multipliers are set according to the heuristic adjustment technique. A huge sample of small random problems and a huge group of problems generated from the vehicle routing applications are tested by the algorithm.

Analysis, Mathematical optimization, Optimization theory, Lagrangian functions

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A survey of exact algorithms for the simple assembly line balancing problem

Article Abstract:

The article examines the formulation of the simple assembly line balancing problem (SALBP). Generations and changes over the course of time are examined. The problem's alternate 0-1 programming developments and a basic integer programming formulation are evaluated. A summary is provided on the computational functions of SALBP.

Methods, Statistical decision, Statistical decision theory, Assembly-line balancing

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