On the Complexity of Scheduling Problems for Parallel/Pipelined Machines
IEEE Transactions on Computers
UET-scheduling with constrained processor allocations
Computers and Operations Research
Analysis of scheduling problems with typed task systems
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Makespan Minimization in Job Shops: A Linear Time Approximation Scheme
SIAM Journal on Discrete Mathematics
Partially ordered knapsack and applications to scheduling
Discrete Applied Mathematics
(Acyclic) Job Shops are Hard to Approximate
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Balanced coloring of bipartite graphs
Journal of Graph Theory
Scheduling cross docking operations under full, partial and no information on inbound arrivals
Computers and Operations Research
Scheduling jobs with equal processing times subject to machine eligibility constraints
Journal of Scheduling
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We consider in this article the Two-Machine Cross-Docking Flow Shop Problem, which is a special case of scheduling with typed tasks, where we have two types of tasks and one machine per type. Precedence constraints exist between tasks, but only from a task of the first type to a task of the second type. The precedence relation is thus a directed bipartite graph. Minimizing the makespan is strongly NP-hard even with unit processing times, but any greedy method yields a 2-approximation solution. In this paper, we are interested in establishing new approximability results for this problem. More specifically, we investigate three directions: list scheduling algorithms based on the relaxation of the resources, the decomposition of the problem according to the connected components of the precedence graph, and finally the search of the induced balanced subgraph with a bounded degree.