In the present paper, a new Integer Linear Programming (ILP) formulation is proposed for a general Multi-Day Container Drayage Problem (MDCDP) that consists in assigning trucks to container transportation tasks during several days. The model describes real-world problems taking their particular issues into account: different types of tasks, different types of containers, a heterogeneous fleet of trucks, the rest periods of drivers and so on. After a review of the state-of-the-art about the Container Drayage Problem (CDP), the MDCDP is presented and modeled as an integer programming problem. This new formulation is an improvement of a previously published formulation: it considers a more realistic objective function and fixed rest periods of drivers. As a consequence, the number of variables is quite reduced and so the new model can be more easily solved with standard solvers. Finally, computational tests on randomly generated instances are presented in order to illustrate the benefits of the new ILP formulation. In particular, it turns out that computational times for the new model are an order of magnitude lower than the previous formulation.

This paper presents an integrated system (IS) devoted to solve the complex scheduling problems in steel-making and casting (SMC) plants. The presented IS is composed of four modules: data base, optimization, simulation modules, and the user interface. In particular, we develop the two main components of the IS: the optimization and simulation modules. The optimization module is based on a mixed-integer linear programming formulation with the objective of minimizing the makespan, i.e., the completion time of the last job. Moreover, a discrete-event simulation module is used to validate and assess the proposed schedules. By designing the IS for a real case study, we show how it can be applied off-line to schedule the daily operations of the SMC, as well as online in order to face unpredictable events such as failures and blocks of the machines. Note to Practitioners-This paper is motivated by the necessity of solving the complex scheduling problems in steel-making and casting (SMC) plants. To this aim, the paper presents an integrated system (IS) that is devoted to help decision makers in selecting the optimal schedules of the operations also in the cases in which unpredictable events may occur. The main modules of the presented IS are an optimization module, based on a mixed-integer linear programming model, and a simulation module, able to verify and validate the proposed schedules by what if analyses and stochastic input parameters. Because of the complexity of the problem, some approximations referring to the transportation system planning are considered. However, the results show the efficiency of the proposed scheduling approach for real industrial applications. Future research aims at investigating about more efficient mathematical programming models in order to solve larger problems involving the planning of one or more weeks and a more detailed description of the plant.

This paper deals with the novel and complex problem of scheduling the internal operations in post-distribution cross docking systems (PDCDSs), i.e., a kind of cross docking terminal where the operations of good allocation are performed. More precisely, internal operations of the PDCDS consist in deconsolidating inbound cases, sorting products according to customer requests, and consolidating outbound cases. The problem is determining the optimal schedule of the internal operations with the objective of minimizing the makespan. The contribution of this paper is twofold. First, the PDCDS scheduling problem is characterized and the corresponding NP-hardness is proved. Second, in order to address the complexity of the problem, two mixed integer linear programming (MILP) models and a heuristic algorithm are presented. In particular, the mathematical programming formulations are solved by using symmetry breaking constraints and objective function perturbations. Moreover, the lower bounds of the start times of operations are evaluated in order to strengthen the formulations. A set of test results compare the formulation performances and a case study shows the effectiveness of the proposed heuristic algorithm to schedule the operations of an half work day of an Italian company of cloth retail stores.

This paper deals with the scheduling of operations in a Steelmaking and Continuous Casting (SM-CC) plant. In particular, we consider a real case study of an integrated plant located in the North of Italy. First, we describe in details the SM-CC process of the considered system by using the Unified Modeling Language. Second, we focus on the schedule of casts on the continuous casting machine that is subject to different types of setup operations. With the objective of minimizing the maximum completion time, the schedule of the continuous casting machine is modeled by a Mixed Integer Linear Programming formulation. An example enlightens how a proper scheduling of the casts is of basic importance to obtain good system performances.