Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximating the Throughput of Multiple Machines in Real-Time Scheduling
SIAM Journal on Computing
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem
SIAM Journal on Computing
Parameterized approximation scheme for the multiple knapsack problem
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Production and delivery scheduling problem with time windows
Computers and Industrial Engineering - Special issue: Selected papers from the 30th international conference on computers; industrial engineering
Integrated production and delivery scheduling with disjoint windows
Discrete Applied Mathematics
Hi-index | 5.23 |
This paper addresses the problem of coordinated scheduling of production and delivery subject to the production window constraint and the delivery capacity constraint. We have a planning horizon consisting of one or more delivery times each with a unique delivery capacity. There is a set of jobs each with a committed delivery time, processing time, production window, and profit. The company can earn the profit only if the job is processed in its production window and delivered before its committed delivery time. From the company point of view, we are interested in selecting a subset of jobs to process and deliver so as to maximize the total profit subject to the delivery capacity constraint. We consider both the single delivery time case and the multiple delivery time case. In both cases, the problem is strongly NP-hard since the subproblems at the production stage and at the delivery stage are both strongly NP-hard. Our goal is to design approximation algorithms. Suppose the jobs are k-disjoint, that is, the jobs can be partitioned into k lists of jobs such that the jobs in each list have disjoint production windows. When k is a constant, we developed the first PTAS for the single delivery case. For multiple delivery time case, we also develop a PTAS when the number of delivery times is a constant as well.