We consider the problem of scheduling n jobs to minimize the total earliness and tardiness penalty. We review the literature on this topic, providing a framework to show how results have been generalized starting with a basic model that contains symmetric penalties, one machine and a common due date. To this base we add such features as parallel machines, complex penalty functions and distinct due dates. We also consolidate many of the existing results by proving general forms of two key properties of earliness/tardiness models.

Sequencing with Earliness and Tardiness Penalties: A Review

The objective of the berth-scheduling problem is to determine the berthing times and positions of containerships in port container terminals. Every vessel requires a specific amount of space in a wharf for a predetermined length of time to unload and load containers. In this study, a mixed-integer-linear-programming (MIP) model was formulated for the berth-scheduling problem. The simulated annealing algorithm was applied to the berth-scheduling problem to find near-optimal solutions. Experimental results showed that the simulated annealing algorithm obtains solutions that are similar to the optimal solutions found by the MIP model.

Berth scheduling by simulated annealing

Assignment problems deal with the question how to assign n items (eg jobs) to n machines (or workers) in the best possible way They consist of two components: the assignment as underlying combinatorial structure and an objective function modeling the ”best way”

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Linear Assignment Problems and Extensions

This paper considers the gap between scheduling theory and scheduling practice. The development and the main results of classical scheduling theory are reviewed and presented in an easily accessible way. Recent trends in scheduling research which attempt to make it more relevant and applicable are described. The nature of the gap between theory and practice is discussed. The failure of classical scheduling theory to address the total environment within which the scheduling function operates is noted. However, scheduling research in operations management and manufacturing systems tends to ignore the rich vein of methods, techniques and results in the classical theory. The need for an integrated scheduling research effort, containing elements of both approaches, is stressed.

Addressing the gap in scheduling research: a review of optimization and heuristic methods in production scheduling

A survey of scheduling with controllable processing times

This paper presents a procedure to minimize the total penalty when jobs are scheduled on a single machine subject to earliness and tardiness penalties This performance criterion has been shown to be non-regular thus, requiring a search among schedules with inserted machine idle time to find a solution A procedure to optimally insert idle time is also presented

Minimizing Weighted Absolute Deviation in Single Machine Scheduling

A bounding scheme for deriving the minimal cycle time of a single-transporter N-stage process with time-window constraints

Minimizing the fleet size with dependent time-window and single-track constraints

This paper presents a new dual network simplex algorithm for the minimum cost network flow problem. The algorithm works directly on the original capacitated network and runs in O(mn(m +n logn) logn) time for the network withn nodes andm arcs. This complexity is better than the complexity of Orlin, Plotkin and Tardos’ (1993) dual network simplex algorithm by a factor ofm/n.

Ronald D. Armstrong

Papers

Minimizing Weighted Absolute Deviation in Single Machine Scheduling

A bounding scheme for deriving the minimal cycle time of a single-transporter N-stage process with time-window constraints

Minimizing the fleet size with dependent time-window and single-track constraints

A new strongly polynomial dual network simplex algorithm

Single machine scheduling to minimize mean absolute lateness: a heuristic solution