We study a primitive vehicle routing-type problem in which fleet of n unit speed robots start from point within non-obtuse triangle $$\Delta $$ , where $$n \in \{1,2,3\}$$ . The goal is to design robots’ trajectories so as visit all edges the with smallest visitation time makespan. begin our by introducing framework for subdividing into regions respect type optimal trajectory that each P admits...

The two-machine permutation flowshop scheduling problem to minimize makespan or total completion time criterion is addressed where setup times are considered to be separate from processing times. Setup times are relaxed to be random variables as opposed to the common assumption in the literature that setup times are exactly known (deterministic) in advance. The probability distributions of setu...

Due to various factors of uncertainty within production, the key performance indicators connected to production plans are difficult to fulfil. This problem becomes especially serious as emission regulations are enforced, which discourage manufacturers from high emission output and high energy consumption. Thus, this paper proposes a feedback control method for the production scheduling problem ...

The scale of data in a MapReduce system is increasing quickly. Thus how to efficiently schedule a set of production jobs has become increasingly important. For a given set of jobs, a well-designed scheduling algorithm can significantly reduce makespan and increase the utilization of clusters. However, there exists very few studies that aim to construct a scheduler that minimizes the makespan of...

We consider the scheduling problems F2 j jCmax and F2 j no-wait jCmax, i.e. makespan minimization in a two machine ow shop, with and without no wait in process. For both problems solution algorithms based on sorting with O(n logn) running time are known, where n denotes the number of jobs [Johnson 1954, Gilmore & Gomory 1964]. We prove that no asymptotically faster algorithms can solve these pr...

The permutation flow shop scheduling problem (PFSP) is one of the most well known and well studied production scheduling problems with strong industrial background. Most scheduling problems are combinatorial optimization problems which are too difficult to be solved optimally, and hence heuristics are used to obtain good solutions in a reasonable time. The specific goal of this paper is to inve...

We consider data analytics workloads on distributed architectures, in particular clusters of commodity machines. To find a job partitioning that minimizes running time, a cost model, which we more accurately refer to as makespan model, is needed. In attempting to find the simplest possible, but sufficiently accurate, such model, we explore piecewise linear functions of input, output, and comput...

Theoretical results about Johnson s problem with stochastic processing times are few. In general, just finding the expected makespan of a given sequence is already difficult, even for discrete processing time distributions. Furthermore, to obtain optimal service level we need to compute the entire distribution of the makespan. Therefore the use of heuristics and simulation is justified. We show...

For a scheduling problem on parallel machines, the power of preemption is defined as the ratio of the makespan of an optimal non-preemptive schedule over the makespan of an optimal preemptive schedule. For m uniform parallel machines, we give the necessary and sufficient conditions under which the global bound of 2 − 1/m is tight. If the makespan of the optimal preemptive schedule is defined by...

this paper presented a mixed integer programming for integrated scheduling and process planning. the presented process plan included some orders with precedence relations similar to multiple traveling salesman problem (mtsp), which was categorized as an np-hard problem. these types of problems are also called advanced planning because of simultaneously determining the appropriate sequence and m...