This paper deals with the $$1|{p-\text {batch}, s_j\le b}|\sum C_j$$1 | p - batch , s j ≤ b | ∑ C j scheduling problem, where jobs are scheduled in batches on a single machine in order to minimize the total completion time. A size is given for each job, such that the total size of each batch cannot exceed a fixed capacity b. A graph-based model is proposed for computing a very effective lower bound based on linear programming; the model, with an exponential number of variables, is solved by column generation and embedded into both a heuristic price and branch algorithm and an exact branch and price algorithm. The same model is able to handle parallel-machine problems like $$Pm|{p-\text {batch}, s_j\le b}|\sum C_j$$P m | p - batch , s j ≤ b | ∑ C j very efficiently. Computational results show that the new lower bound strongly dominates the bounds currently available in the literature, and the proposed heuristic algorithm is able to achieve high-quality solutions on large problems in a reasonable computation time. For the single-machine case, the exact branch and price algorithm is able to solve all the tested instances with 30 jobs and a good amount of 40-job examples.

Digital Contact Tracing (DCT) has been proved to be an effective tool to counteract the new SARS-CoV-2 or Covid-19. Despite this widespread effort to adopt the DCT, less attention has been paid to the organisation of the health logistics system that should support the tracing activities. Actually, the DCT poses a challenge to the logistics of the local health system in terms of number of daily tests to be collected and evaluated, especially when the spreading of the virus is soaring. In this paper we introduce a new optimisation problem called the Daily Swab Test Collection (DSTC) problem, that is the daily problem of collecting swab tests at home in such a way to guarantee a timely testing to people notified by the app to be in contact with a positive case. The problem is formulated as a variant of the team orienteering problem. The contributions of this paper are the following: (i) the new optimisation problem DSTC that complements and improves the DCT approach proposed by Ferretti et al. (Science https://doi.org/10.1126/science.abb6936, 2020), (ii) the DSCT formulation as a variant of the TOP and a literature review highlighting that this variant can have useful application in healthcare management, (iii) new realistic benchmark instances for the DSTC based on the city of Turin, (iv) two new efficient and effective hybrid algorithms capable to deal with realistic instances, (v) the managerial insights of our approach with a special regard on the fairness of the solutions. The main finding is that it possible to optimise the underlying logistics system in such a way to guarantee a timely testing to people recognised by the DCT.

Multicore architectures provide the increased performance required by modern embedded real-time systems. Most platforms exhibit a non-uniform memory access (NUMA). In NUMA, memory banks with different access time can be explicitly addressed. Such an architecture, however, is challenging predictability given the significant impact of the allocation of variables on the execution times. At software level, real-world embedded applications (e.g. automotive) are composed by thousands of functions often communicating through shared variables stored in memory, with a variable access time because of NUMA. This paper addresses the mapping of complex embedded applications onto NUMA multicore architectures. The developed problem formulation offers a solution to the following problems: (i) allocating variables (called labels in the automotive context) over memories of different characteristics, (ii) mapping functionalities (called runnables) onto CPUs, (iii) creating OS tasks from runnables, and (iv) assigning priorities to tasks. Our developed implementation is capable to handle an application composed by 1K+ runnables, all sharing 10K+ labels and finds a solution in at most 3 minutes on a standard laptop, enabling interactive design space exploration.

Parallel batch scheduling has many applications in the industrial sector, like in material and chemical treatments, mold manufacturing and so on. The number of jobs that can be processed on a machine mostly depends on the shape and size of the jobs and of the machine. This work investigates the problem of batching jobs with multiple sizes and multiple incompatible families. A flow formulation of the problem is exploited to solve it through two column generation-based heuristics. First, the column generation finds the optimal solution of the continuous relaxation, then two heuristics are proposed to move from the continuous to the integer solution of the problem: one is based on the price-and-branch heuristic, the other on a variable rounding procedure. Experiments with several combinations of parameters are provided to show the impact of the number of sizes and families on computation times and quality of solutions.

This paper extends and improves the performance of a digital reversible watermarking algorithm based on histogram shifting presented in previous works. The considered algorithm exploits the property of image histograms of some kinds of medical images which present many contiguous 0-runs, i.e., a comb structure in the gray level frequencies. In particular, radiographic images exhibit this structure after contrast enhancement during the acquisition process. The previous work suggested performing gray-level histogram shifting according to a local optimization technique. In this paper, we apply combinatorial optimization techniques to entire blocks of contiguous 0-runs using a non-linear objective function transformed to fit a linear optimization algorithm. The obtained results show a meaningful improvement in the payload capacity of the original data-hiding method. A mild Peak Signal-to-Noise Ratio (PSNR) reduction is still acceptable for a qualitative preview of the images, which can be completely restored to their original cover form thanks to the reversibility of the method.