Correct predictions are in blue. If we detect only a subset of a labelled sentence, we highlight the caught part as blue, the missing part light blue. False positives are in green and false negatives are in red.

Problem Flow_Shop_Scheduling — Constraint detection

We consider the following scheduling problem . A set $ N = -LCB- 1 , ... , n -RCB- of $ n $ jobs has to be processed on a single machine , which can handle at most one job at a time . Each job $ j $ has a positive processing time , $ p_j > 0 $ , and a nonnegative weight , $ w_j \ ge 0 $ , and we want to find a schedule of the jobs that minimizes the weighted sum of job completion times , $ \ sum _ -LCB- j \ in N -RCB- w_j C_j -RCB- . Here , $ C_j $ denotes the time at which job $ j $ is completed in a feasible schedule . We focus on the case when the jobs have to be consistent with precedence constraints ; the precedence constraints are given in the form of a directed acyclic graph -LRB- i.e. , a partial order -RRB- G = -LRB- N , P -RRB- , where $ -LRB- i , j -RRB- \ in P$ implies that job i must be completed before job j can be started ; we assume that G is transitively closed ; i.e. , if $ -LRB- i , j -RRB- , -LRB- j , k -RRB- \ in P$ , then $ -LRB- i , k -RRB- \ in P$ .

Problem Flow_Shop_Scheduling — Detection of the decisions and objects to be modeled

We consider the following scheduling problem . A set $ N = -LCB- 1 , ... , n -RCB- of $ n $ jobs has to be processed on a single machine , which can handle at most one job at a time . Each job $ j $ has a positive processing time , $ p_j > 0 $ , and a nonnegative weight , $ w_j \ ge 0 $ , and we want to find a schedule of the jobs that minimizes the weighted sum of job completion times , $ \ sum _ -LCB- j \ in N -RCB- w_j C_j -RCB- . Here , $ C_j $ denotes the time at which job $ j $ is completed in a feasible schedule . We focus on the case when the jobs have to be consistent with precedence constraints ; the precedence constraints are given in the form of a directed acyclic graph -LRB- i.e. , a partial order -RRB- G = -LRB- N , P -RRB- , where $ -LRB- i , j -RRB- \ in P$ implies that job i must be completed before job j can be started ; we assume that G is transitively closed ; i.e. , if $ -LRB- i , j -RRB- , -LRB- j , k -RRB- \ in P$ , then $ -LRB- i , k -RRB- \ in P$ .

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