We consider the polyhedral structure of the precedence constrained knapsack (PCK) problem, also known as the partially ordered knapsack problem. A set of items N is given, along with a partial order, or set of precedence relationships, on the items, denoted by S ⊆ N × N. A precedence relationship (i, j) ∈ S exists if item i can be placed in the knapsack only if item j is in the knapsack. Each i...

In this paper, it is investigated how to sequence jobs with fuzzy processing times and predict their due dates on a single machine such that the total weighted possibilistic mean value of the weighted earliness–tardiness costs is minimized. First, an optimal polynomial time algorithm is put forward for the scheduling problem when there are no precedence constraints among jobs. Moreover, it is s...

We provide a general scheme for constructing monotone algorithms for a wide class C of scheduling problems Q|prec, rj |γ on related machines with precedence constraints and/or release dates. Our scheme works in the offline and the online setting. It takes as input two approximation/competitive algorithms for the (simpler) scheduling problems P |prec, rj |γ on identical machines and 1|prec, rj |...

We propose a stronger formulation of the precedence constraints and the station limits for the simple assembly line balancing problem. The linear relaxation of the improved integer program theoretically dominates all previous formulations using impulse variables, and produces solutions of significantly better quality in practice. The improved formulation can be used to strengthen related proble...

In this paper, a scheduling algorithm based on deadline time and precedence constraints was developed to schedule hard real-time tasks on multiprocessor systems. The real-time tasks are characterized by their arrival time, deadline time, computation time and precedence constraints. Scheduling problem for these tasks has been solved to determine the order of scheduling tasks on the processors to...

Hard and soft precedence constraints play a key role in many application domains. In telecommunications, one application is the configuration of callcontrol feature subscriptions where the task is to sequence a set of user-selected features subject to a set of hard (catalogue) precedence constraints and a set of soft (user-selected) precedence constraints. When no such consistent sequence exist...

In this paper we propose a greedy heuristic to solve the non preemptive multiprocessor static scheduling problem with precedence and strict periodicity constraints. The system of periodic tasks is described by a graph where dependent tasks are connected by precedence constraints. First, each task is repeated within the LCM of all periods of tasks (hyper-period) allowing to unroll the graph over...

We consider the problem of finding a directed acyclic graph (DAG) that optimizes a decomposable Bayesian network score. While in a favorable case an optimal DAG can be found in polynomial time, in the worst case the fastest known algorithms rely on dynamic programming across the node subsets, taking time and space 2n, to within a factor polynomial in the number of nodes n. In practice, these al...

This paper deals with a three-machine flow-shop problem in which some of the job sequences are infeasible. It is assumed that jobs are grouped into several disJoint subsets within which a job order is pre-determined. Once the first job in a group has started on a machine, then the entire group must be completed on the machine without starting a job which does not belong to the group. It is furt...

Given a set of identical capacitated bins, a set of weighted items and a set of precedences among such items, we are interested in determining the minimum number of bins that can accommodate all items and can be ordered in such a way that all precedences are satisfied. The problem, denoted as the Bin Packing Problem with Precedence Constraints (BPP-P), has a very intriguing combinatorial struct...