Single-machine scheduling with stepwise tardiness costs and release times

We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems

Order acceptance and scheduling in a single-machine environment: exact and heuristic algorithms.

In this paper, we develop exact and heuristic algorithms for the order acceptance and scheduling problem in a single-machine environment. We consider the case where a pool consisting of firm planned orders as well as potential orders is available from which an over-demanded company can select. The capacity available for processing the accepted orders is limited and orders are characterized by known processing times, delivery dates, revenues and the weight representing a penalty per unit-time delay beyond the delivery date promised to the customer. We prove the non-approximability of the problem and give two linear formulations that we solve with CPLEX. We devise two exact branch-and-bound procedures able to solve problem instances of practical dimensions. For the solution of large instances, we propose six heuristics. We provide a comparison and comments on the efficiency and quality of the results obtained using both the exact and heuristic algorithms, including the solution of the linear formulations using CPLEX.Order acceptance; Scheduling; Single machine; Branch-and-bound; Heuristics; Firm planned orders;

Flow shop scheduling with earliness, tardiness and intermediate inventory holding costs

We consider the problem of scheduling customer orders in a flow shop with the objective of minimizing the sum of tardiness, earliness (finished goods inventory holding) and intermediate (work-in-process) inventory holding costs. We formulate this problem as an integer program, and based on approximate solutions to two di erent, but closely related, Dantzig-Wolfe reformulations, we develop heuristics to minimize the total cost. We exploit the duality between Dantzig-Wolfe reformulation and Lagrangian relaxation to enhance our heuristics. This combined approach enables us to develop two di erent lower bounds on the optimal integer solution, together with intuitive approaches for obtaining near-optimal feasible integer solutions. To the best of our knowledge, this is the first paper that applies column generation to a scheduling problem with di erent types of strongly NP-hard pricing problems which are solved heuristically. The computational study demonstrates that our algorithms have a significant speed advantage over alternate methods, yield good lower bounds, and generate near-optimal feasible integer solutions for problem instances with many machines and a realistically large number of jobs

Minimizing value-at-risk in the single-machine total weighted tardiness problem

The vast majority of the machine scheduling literature focuses on deterministic problems, in which all data is known with certainty a priori. This may be a reasonable assumption when the variability in the problem parameters is low. However, as variability in the parameters increases incorporating this uncertainty explicitly into a scheduling model is essential to mitigate the resulting adverse effects. In this paper, we consider the celebrated single-machine total weighted tardiness (TWT) problem in the presence of uncertain problem parameters. We impose a probabilistic constraint on the random TWT and introduce a risk-averse stochastic programming model. In particular, the objective of the proposed model is to find a non-preemptive static job processing sequence that minimizes the value-at-risk (VaR) measure on the random TWT at a specified confidence level. Furthermore, we develop a lower bound on the optimal VaR that may also benefit alternate solution approaches in the future. In this study, we implement a tabu-search heuristic to obtain reasonably good feasible solutions and present results to demonstrate the effect of the risk parameter and the value of the proposed model with respect to a corresponding risk-neutral approach

A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Research on due date oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for the TWT and TWET problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm for solving the preemptive relaxation formulated as a mixed integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines, and then we exploit recent advances in solving the non-preemptive single machine TWT and TWET problems for constructing non-preemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances up to 5 machines and 200 jobs

A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Research on due date-oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time-related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for both problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm to solve the preemptive relaxation formulated as a mixed-integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines. We then exploit recent advances in solving the nonpreemptive single-machine TWT and TWET problems for constructing nonpreemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances of up to five machines and 200 jobs

Practical solutions for a dock assignment problem with trailer transportation.

We study a distribution warehouse in which trailers need to be assigned to docks for loading or unloading. A parking lot is used as a buffer zone and transportation between the parking lot and the docks is performed by auxiliary resources called terminal tractors. Each incoming trailer has a known arrival time and each outgoing trailer a desired departure time. The primary objective is to produce a docking schedule such that the weighted sum of the number of late outgoing trailers and the tardiness of these trailers is minimized; the secondary objective is to minimize the weighted completion time of all trailers, both incoming and outgoing. The purpose of this paper is to produce high-quality solutions to large instances that are comparable to a real-life case. We implement several heuristic algorithms: truncated branch and bound, beam search and tabu search. Lagrangian relaxation is embedded in the algorithms for constructing an initial solution and for computing lower bounds. The different solution frameworks are compared via extensive computational experiments.Dock assignment; Multicriteria scheduling; Branch and bound; Beam search; Lagrangian relaxation; Tabu search;