The Sequential Ordering Problem (SOP) is a version of the Asymmetric Traveling Salesman Problem (ATSP) where precedence constraints on the vertices must also be observed. The SOP has many real life applications and it has proved to be a great challenge (there are SOPs with 40-50 vertices which have not been solved optimally yet with significant computational effort). We use novel branch&bound s...

Stochastic Approach to Vehicle Routing Problem: Development and Theories Abstract In this article, a chance constrained (CCP) formulation of the Vehicle Routing Problem (VRP) is proposed. The reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. Knowing that reliable computer software...

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...

Function design of embedded real-time system introduced the problem of real-time task scheduling with precedence constraint which needs that scheduling sequence produced by algorithm satisfying not only real-time constraint of every task, but also precedence constraint among tasks. Based on parallel topological sort, this paper presents a new on-line scheduling algorithm OSA-RPC which can set p...

In this paper, a resource flow-based branch-and-bound procedure is designed to solve the well-known resource-constrained project scheduling problem under mixed uncertainty of fuzziness and randomness (FS-RCPSP). The objective minimize expected makespan subject precedence constraints. proposed can be employed obtain optimal solutions also truncated in order find promising near solutions. depth-f...

We introduce a multimode resource-constrained project scheduling problem with finish-to-start precedence relations among project activities, considering renewable and nonrenewable resource costs. We assume that renewable resources are rented and are not available in all periods of time of the project. In other words, there is a mandated ready date as well as a due date for each renewable resour...