One Benders cut to rule all schedules in the neighbourhood

Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose tighter dual bounds, its application to resource-constrained scheduling remains less explored. Given a position-based Mixed-Integer Linear Programming (MILP) formulation for scheduling on unrelated parallel machines, we notice that certain $k-$OPT neighbourhoods could implicitly be explored by regular local search operators, thus allowing us to integrate Local Branching into Branch-and-Check schemes. After enumerating such neighbourhoods and obtaining their local optima - hence, proving that they are suboptimal - a local branching cut (applied as a Benders cut) eliminates all their solutions at once, thus avoiding an overload of the master problem with thousands of Benders cuts. However, to guarantee convergence to optimality, the constructed neighbourhood should be exhaustively explored, hence this time-consuming procedure must be accelerated by domination rules or selectively implemented on nodes which are more likely to reduce the optimality gap. In this study, the realisation of this idea is limited on the common 'internal (job) swaps' to construct formulation-specific $4$-OPT neighbourhoods. Nonetheless, the experimentation on two challenging scheduling problems (i.e., the minimisation of total completion times and the minimisation of total tardiness on unrelated machines with sequence-dependent and resource-constrained setups) shows that the proposed methodology offers considerable reductions of optimality gaps or faster convergence to optimality. The simplicity of our approach allows its transferability to other neighbourhoods and different sequencing optimisation problems, hence providing a promising prospect to improve Branch-and-Check methods

Weighted tardiness minimization for unrelated machines with sequence-dependent and resource-constrained setups

Motivated by the need of quick job (re-)scheduling, we examine an elaborate scheduling environment under the objective of total weighted tardiness minimization. The examined problem variant moves well beyond existing literature, as it considers unrelated machines, sequence-dependent and machine-dependent setup times and a renewable resource constraint on the number of simultaneous setups. For this variant, we provide a relaxed MILP to calculate lower bounds, thus estimating a worst-case optimality gap. As a fast exact approach appears not plausible for instances of practical importance, we extend known (meta-)heuristics to deal with the problem at hand, coupling them with a Constraint Programming (CP) component - vital to guarantee the non-violation of the problem's constraints - which optimally allocates resources with respect to tardiness minimization. The validity and versatility of employing different (meta-)heuristics exploiting a relaxed MILP as a quality measure is revealed by our extensive experimental study, which shows that the methods deployed have complementary strengths depending on the instance parameters. Since the problem description has been obtained from a textile manufacturer where jobs of diverse size arrive continuously under tight deadlines, we also discuss the practical impact of our approach in terms of both tardiness decrease and broader managerial insights

Surgical Outcomes in Syndromic Tetralogy of Fallot: A Systematic Review and Evidence Quality Assessment

Tetralogy of Fallot (ToF) is one of the most common cyanotic congenital heart defects. We sought to summarize all available data regarding the epidemiology and perioperative outcomes of syndromic ToF patients. A PRISMA-compliant systematic literature review of PubMed and Cochrane Library was performed. Twelve original studies were included. The incidence of syndromic ToF was 15.3% (n = 549/3597). The most prevalent genetic syndromes were 22q11.2 deletion (47.8%; 95% CI 43.4–52.2) and trisomy 21 (41.9%; 95% CI 37.7–46.3). Complete surgical repair was performed in 75.2% of the patients (n = 161/214; 95% CI 69.0–80.1) and staged repair in 24.8% (n = 53/214; 95 CI 19.4–30.9). Relief of RVOT obstruction was performed with transannular patch in 64.7% (n = 79/122; 95% CI 55.9–72.7) of the patients, pulmonary valve-sparing technique in 17.2% (n = 21/122; 95% CI 11.5–24.9), and RV-PA conduit in 18.0% (n = 22/122; 95% CI 12.1–25.9). Pleural effusions were the most common postoperative complications (n = 28/549; 5.1%; 95% CI 3.5–7.3). Reoperations were performed in 4.4% (n = 24/549; 95% CI 2.9–6.4) of the patients. All-cause mortality rate was 9.8% (n = 51/521; 95% CI 7.5–12.7). Genetic syndromes are seen in approximately 15% of ToF patients. Long-term survival exceeds 90%, suggesting that surgical management should be dictated by anatomy regardless of genetics

A Review of Percutaneous Transluminal Angioplasty in Hemodialysis Fistula

The number of patients in dialysis increases every year. In this review, we will evaluate the role of percutaneous transluminal angioplasty (PTA) according to patency of arteriovenous fistula and grafts. The main indication of PΤΑ is stenosis > 50% or obstruction of the vascular lumen of an arteriovenous fistula and graft. It is usually performed under local anesthesia. The infection rate is as low as the number of complications. Fistula can be used in dialysis in the same day without the need for a central venous catheter. Primary patency is >50% in the first year while primary assisted patency is 80–90% in the same time period. Repeated PTA is as durable as the primary PTA. An early PTA carries a risk of new interventions. Cutting balloon can be used as a second-line method. Stents and covered stents are kept for the management of complications and central outflow venous stenosis. PTA is the treatment of choice for stenosis or obstruction of dialysis fistulas. Repeated PTA may be needed for better patency. Drug eluting balloon may become the future in PTA of dialysis fistula, but more trials are needed