Common operation scheduling with general processing times: A branch-and-cut algorithm to minimize the weighted number of tardy jobs

Common operation scheduling (COS) problems arise in real-world applications, such as industrial processes of material cutting or component dismantling. In COS, distinct jobs may share operations, and when an operation is done, it is done for all the jobs that share it. We here propose a 0-1 LP formulation with exponentially many inequalities to minimize the weighted number of tardy jobs. Separation of inequalities is in NP, provided that an ordinary min Lmax scheduling problem is in P. We develop a branch-and-cut algorithm for two cases: one machine with precedence relation; identical parallel machines with unit operation times. In these cases separation is the constrained maximization of a submodular set function. A previous method is modified to tackle the two cases, and compared to our algorithm. We report on tests conducted on both industrial and artificial instances. For single machine and general processing times the new method definitely outperforms the other, extending in this way the range of COS applications

Real-time Emergency Response through Performant IoT Architectures

International audienceThis paper describes the design of an Internet of Things (IoT) system for building evacuation. There are two main design decisions for such systems: i) specifying the platform on which the IoT intelligent components should be located; and ii) establishing the level of collaboration among the components. For safety-critical systems, such as evacuation, real-time performance and evacuation time are critical. The approach aims to minimize computational and evacuation delays and uses Queuing Network (QN) models. The approach was tested, by computer simulation, on a real exhibition venue in Alan Turing Building, Italy, that has 34 sets of IoT sensors and actuators. Experiments were performed that tested the effect of segmenting the physical space into different sized virtual cubes. Experiments were also conducted concerning the distribution of the software architecture. The results show that using centralized architectural pattern with a segmentation of the space into large cubes is the only practical solution

Maximum lateness minimization in one-dimensional Bin Packing problems

In the One-dimensional Bin Packing problem (1-BP) items of different lengths must be assigned to a minimum number of bins of unit length. Regarding each item as a job that requires unit time and some resource amount, and each bin as the total (discrete) resource available per time unit, the minimization of the number of bins corresponds to the minimization of the makespan. We here generalize the problem to the case in which each item is due by some date: our objective is to minimize a convex combination of makespan and maximum lateness. We propose a time indexed ILP formulation to solve the problem. The formulation can be decomposed and solved by column generation, in which case single-bin packing is relegated to a pricing problem: therefore, extensions to s-dimensional problems can be dealt with independently. We show how to couple the formulation with quite simple bounds to (individual terms of) the objective function, so as to get very good gaps with instances that are considered difficult for the 1-BP

Integrating Process Optimization and Inventory Planning in Cutting-Stock with Skiving Option: an Optimization Model and its Application

We consider a two-stage flow line where the first stage produces components for the downstream assembly stage. An integer programming model which integrates decisions at both the planning and the operation level is proposed, with the aim of minimizing production, holding and transportation costs. The model is tested on instances built on the basis of a real cutting process with skiving option, i.e., with the possibility of recombining components to obtain required parts. The implementation of the proposed methodology allows the integration of two hierarchical decision levels (short-term operations vs. mid-term planning) and functional areas (production vs. purchase of materials) within a single planning model, and provides an example of how an element of an Advanced Planning System (APS) could be designed. Moreover, the use of suitable cost figures in the model allows to correctly manage the insertion of hot orders of finite parts

Bin Packing with due dates

In the Bin Packing problem (BP), items of different sizes must be assigned to a minimum number of bins. In the k-dimensional problem (kBP), items and bins are closed k-intervals. Regarding each item as a job that requires unit time and some resource amount, and each bin as the total (discrete) resource available per time unit, the kBP objective is the minimization of the makespan. We generalize the kBP problem to Bin Packing and Scheduling (kBPS) by changing the objective to any (even non-regular) function of the completion time of the jobs. Interesting applications are those in which each part (= job) is to be produced within a specific due date. Typical examples of regular functions are maximum lateness, weighted sum of jobs tardiness, etc. In practice, a convex combination of such functions is often considered. When the scheduling term in the objective function is the weighted sum of jobs tardiness or of tardy jobs, one can specialize an exact formulation for the Cutting Stock Problem with Due Dates (Arbib and Marinelli, 2014). An alternative, more general and perhaps more effective approach is to use an ad-hoc time-indexed formulation. This approach, which can encompass Dantzig-Wolfe decomposition and, consequently, column generation, is close to that described by van den Akker et al. (2005) for general time-indexed formulations applied to parallel scheduling. When column generation is used, the difficulty of k-dimensional packing is relegated to the pricing problem. To find a lower bound for the 2BPS one can then solve a relaxed 2-dimensional pricing problem by the arc-flow formulation (Macedo, Alves and V. de Carvalho, 2010). In alternative, one can implement conservative scales (Belov et al., 2013) via a time-indexed formulation for 1BPS. In this talk we just discuss a preliminary computational experience carried out for 1BPS with Lmax as scheduling term of the objective function