Introduction to operations research, 4th ed.
Introduction to operations research, 4th ed.
Integer and combinatorial optimization
Integer and combinatorial optimization
A survey of algorithms for the single machine total weighted tardiness scheduling problem
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
A survey of results for sequencing problems with controllable processing times
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
Minimizing total tardiness on one machine is NP-hard
Mathematics of Operations Research
Computers and Operations Research
Single machine scheduling with a variable common due date and resource-dependent processing times
Computers and Operations Research
Computers and Operations Research
Minimizing the total weighted flow time in a single machine with controllable processing times
Computers and Operations Research
Computers and Operations Research
A survey of scheduling with controllable processing times
Discrete Applied Mathematics
Single machine scheduling with discretely controllable processing times
Operations Research Letters
Computers and Operations Research
Single-machine group scheduling with resource allocation and learning effect
Computers and Industrial Engineering
Computers and Operations Research
Computers and Industrial Engineering
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The concept of time-cost trade-off is commonly considered in PERT/CPM, but it is seldom considered in the scheduling area. Such concept implies that the processing times of jobs are controllable by increasing or decreasing the available resources, such as manpower and equipment. In this paper, we focus on the single machine total tardiness problem with controllable processing times. First, a mixed-integer programming (MIP) model is formulated to find the optimal solution. Then, we propose both a linear programming model and a net benefit of compression (NBC) algorithm to obtain a set of optimal amounts of compression for a given sequence. To solve medium- to large-size problem instances, we develop a heuristic based on the NBC algorithm. To verify the proposed heuristic, the MIP model is used as a comparison for small-size problem instances, whereas for medium- to large-size instances the variable neighborhood search, a useful local search method, is employed. Computational results show that the proposed heuristic has a good performance.