A Mathematical Programming Approach for Online Hierarchical Scheduling
نویسندگان
چکیده
This paper considers an online hierarchical scheduling problem on parallel identical machines. We are given a set of m machines and a sequence of jobs. Each machine has a different hierarchy, and each job also has a hierarchy associated with it. A job can be assigned to a machine only if its hierarchy is no less than that of the machine. The objective is to minimize makespan. Two models are studied in the paper. For the fractional model, we present an improved algorithm and lower bounds. Both algorithm and lower bounds are based on solutions of mathematical programming. For any given m, our algorithm is optimal by numerical calculation. For the integral model, we present both a general algorithm for any m, and an improved algorithm with better competitive ratios of 2.333 and 2.610 for m = 4 and 5, respectively.
منابع مشابه
A fuzzy multi-objective linear programming approach for solving a new multi-objective job shop scheduling with sequence-dependent setup times
This paper presents a new mathematical model for a bi-objective job shop scheduling problem with sequence-dependent setup times that minimizes the weighted mean completion time and the weighted mean tardiness time. For solving this multi-objective model, we develop a fuzzy multi-objective linear programming (FMOLP) model. In this problem, a proposed FMOLP method is applied with respect to the o...
متن کاملMathematical solution of multilevel fractional programming problem with fuzzy goal programming approach
In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision ...
متن کاملExact Mixed Integer Programming for Integrated Scheduling and Process Planning in Flexible Environment
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...
متن کاملA bi-level programming approach to coordinating pricing and ordering decisions in a multi-channel supply chain
This paper investigates the Stackelberg equilibrium for pricing and ordering decisions in a multi-channel supply chain. We study a situation where a manufacturer is going to open a direct online channel in addition to n existing traditional retail channels. It is assumed that the manufacturer is the leader and the retailers are the followers. The situation has a hierarchical nature and...
متن کاملFuzzy Programming for Parallel Machines Scheduling: Minimizing Weighted Tardiness/Earliness and Flow Time through Genetic Algorithm
Appropriate scheduling and sequencing of tasks on machines is one of the basic and significant problems that a shop or a factory manager encounters; this is why in recent decades extensive studies have been done on scheduling issues. One type of scheduling problems is just-in-time (JIT) scheduling and in this area, motivated by JIT manufacturing, this study investigates a mathematical model for...
متن کاملFuzzy Programming for Parallel Machines Scheduling: Minimizing Weighted Tardiness/Earliness and Flowtime through Genetic Algorithm
Appropriate scheduling and sequencing of tasks on machines is one of the basic and significant problems that a shop or a factory manager encounters with it, this is why in recent decades extensive researches have been done on scheduling issues. A type of scheduling problems is just-in-time (JIT) scheduling and in this area, motivated by JIT manufacturing, this study investigates a mathematical ...
متن کامل