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Throughout its history, Operational Research has evolved to include methods, models and algorithms that have been applied to a wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first summarises the up-to-date knowledge and provides an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion and used as a point of reference by a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes. [ABSTRACT FROM AUTHOR]

This paper introduces the Twin Robot Palletising Problem (TRPP) in which two robots must be scheduled and routed to pick up and deliver products at specified locations along a rail. The robots are initially located at the opposite ends of the rail and must preserve a minimum safe distance from one another. The objective is to minimise the makespan, defined as the time required to complete all operations and for both robots to return to their starting positions. The paper presents a proof of NP-Hardness of the TRPP, as well as two mixed integer linear programming models. Local search operators are introduced, before an iterated local search and an iterated local search and a genetic algorithm are developed, in which a linear-time scheduling algorithm and dynamic programming are utilised to evaluate the quality of solutions. Extensive computational results demonstrate the limits of the mathematical models, the effectiveness of the metaheuristics, and the savings obtained using twin robots instead of a single one. [ABSTRACT FROM AUTHOR]

The Workload Allocation Problem consists of assigning a sequence of | S | operations to workers. The order of these operations is fixed. Each operation consists of a batch of B units, hence a total of | J | jobs have to be performed. Each worker is assigned to an ordered subset of consecutive jobs. Workers have different skills, and therefore jobs take a variable time to process, depending on the assigned worker. The study of this problem is rooted in the operations of Calzedonia. In this paper, we briefly introduce the application before presenting algorithms for solving the problem exactly and heuristically. Our computational results compare the performance of a stand-alone mathematical formulation solved by CPLEX, a sequential exact algorithm, and a metaheuristic, with a simple heuristic implemented in the company. [ABSTRACT FROM AUTHOR]

The single machine total weighted tardiness problem with sequence-dependent setup times (often known as problem) requires a given set of jobs to be sequenced on a single machine, where a setup time is required before the processing of each job that depends on both the preceding job and the job to be processed next. The goal is to minimise the sum of weighted tardiness, where the tardiness of a job is zero if it is completed by its due date and is equal to its completion time minus its due date otherwise. In this paper, we develop an Iterated Local Search (ILS) heuristic and compare its performance with the state-of-the-art metaheuristic algorithms from the literature. The proposed ILS algorithm obtains high-quality solutions using computation times that is comparable to its competitors. [ABSTRACT FROM AUTHOR]

HIV/AIDS test laboratories in South Africa face growing demand for high quality, timely and efficient testing of blood samples in all regions of the country, however rural. The three main tests for HIV/AIDS, namely CD4, HIV Viral Load, and Infant PCR, are provided in a hierarchy of levels: CD4 is the most frequently needed test, with most laboratory coverage needed. HIV Viral Load is less frequently called for, and Infant PCR is the rarest test to be done, with correspondingly fewest laboratories needed. The National Health Laboratory Service (NHLS) of South Africa operates an inbound hub network for collection of blood samples and transfer to laboratories equipped to carry out the required tests: test results are transmitted electronically, so there is no outbound or return transport. This paper describes the development of modelling carried out over several years of collaboration with NHLS to advise decision-makers on an appropriate and efficient hub network. We present mixed integer programs to find efficient locations for both network hubs and locations for all levels of laboratory testing. Novel features include variable or range constraints on maximum travel times to test locations. [ABSTRACT FROM AUTHOR]

This paper presents the case study of an Italian carrier, Grendi Trasporti Marittimi, which provides freight transportation services by trucks and containers. Its trucks deliver container loads from a port to import customers and collect container loads from export customers to the same port. In this case study, all import customers in a route must be serviced before all export customers, each customer can be visited more than once and containers are never unloaded or reloaded from the truck chassis along any route. We model the problem using an Integer Linear Programming formulation and propose an Adaptive Guidance metaheuristic. Our extensive computational experiments show that the adaptive guidance algorithm is capable of determining good-quality solutions in many instances of practical or potential interest for the carrier within 10 min of computing time, whereas the mathematical formulation often fails to provide the first feasible solution within 3 h of computing time. [ABSTRACT FROM AUTHOR]

A correction to the article "An adaptive guidance meta-heuristic for the vehicle routing problem with splits and clustered backhauls" is presented.