Capacitated Max-Batching with interval graph compatibilities

Capacitated max -Batching with Interval Graph Compatibilities

We consider the problem of partitioning interval graphs into cliques of bounded size. Each interval has a weight, and the cost of a clique is the maximum weight of any interval in the clique. This natural graph problem can be interpreted as a batch scheduling problem. Solving an open question from [7, 4, 5], we show NP-hardness, even if the bound on the clique sizes is constant. Moreover, we gi...

Batch processing with interval graph compatibilities between tasks

We analyze batch-scheduling problems that arise in connection with certain industrial applications. The models concern processing on a single max-batch machine with the additional feature that the tasks of the same batch have to be compatible. Compatibility is a symmetric binary relation—the compatible pairs are described with an undirected “compatibility graph”, which is often an interval grap...

(a) Batching Interval = 2min (b) Batching Interval = 5min

Online Capacitated Interval Coloring

In the online capacitated interval coloring problem, a sequence of requests arrive online. Each of the requests is an interval Ij ⊆ {1, 2, . . . , n} with bandwidth bj . Initially a vector of capacities (c1, c2, . . . , cn) is given. Each color can support a set of requests such that the total bandwidth of intervals containing i is at most ci. The goal is to color the requests using a minimum n...

The Capacitated Location-Allocation Problem with Interval Parameters

In this paper, we develop a capacitated location-covering model considering interval values for demand and service parameters. We also consider flexibility on distance standard for covering demand nodes by the servers. We use the satisfaction degree to represent the constraint of service capacity. The proposed model belongs to the class of mixed integer programming models. Our model can be redu...