Production and Inventory Management
Priority rules for job shops with weighted tardiness costs
Management Science
The two-machine flowshop scheduling problem with total tardiness
Computers and Operations Research
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Selecting jobs for a heavily loaded shop with lateness penalties
Computers and Operations Research
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Inference-Based Sensitivity Analysis for Mixed Integer/Linear Programming
Operations Research
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
Scheduling shops to minimize the weighted number of late jobs
Operations Research Letters
| Hi-index | 0.98 |
We consider selecting and sequencing jobs in a two stage flowshop so that the selected jobs are completed before a specified time limit (such as the end of a shift). The objective is to maximize the weighted (reward) sum of the selected jobs. We show that the problem is NP-hard, and present two procedures to find an optimum solution. The first procedure uses dynamic programming, and the second uses mixed integer programming. The integer programming formulation exploits special properties of the problem and solves large instances of the problem. We also develop heuristics and provide worst case performance guarantees. An improvement procedure is also developed. Extensive computational testing shows that our heuristics, when used jointly with the improvement procedure, yield excellent results (providing solutions within 3% of the optimum in an average sense) for both balanced and unbalanced shops.