The literature on flow shop scheduling has extensively analyzed two classes of problems: permutation and non-permutation ones (PFS and NPFS). Most of the papers in this field have been just devoted on comparing the solutions obtained in both approaches. Our contribution consists of analyzing the structure of the critical paths determining the makespan of both kinds of schedules for the case of 2 jobs and m machines. We introduce a new characterization of the critical paths of PFS solutions as well as a decomposition procedure, yielding a representation of NPFS solutions as sequences of partial PFS ones. In structural comparisons we find cases in which NPFS solutions are dominated by PFS solutions. Numerical comparisons indicate that a wider dispersion of processing times improves the chances of obtaining optimal non-permutation schedules, in particular when this dispersion affects only a few machines.

This paper is interested in pharmaceuticals distribution which is one of the most important activities and ensures the availability of drug products to a set of customers (pharmacies). The study introduces the Disrupted Vehicle Routing problem with Soft Time Windows since pharmaceutical distributors should respond to increased demands for products to ensure timely and efficient delivery to dynamic demands. We also propose an improved multiobjective local search (IMOLS), which uses methods of neighborhood search such as large neighborhood search (LNS) and variable neighborhood search (VNS) based on a hybrid approach in the optimization of vehicle routes. The algorithm is expected to achieve competitive results compared with previously published studies.

The main purpose of this paper is to study the vehicle routing problem with hard time windows where the main challenges is to include both sources of uncertainties, namely the travel and the service time that can arise due to multiple causes. We propose a new approach for the robust problem based on the implementation of an adaptive large neighborhood search algorithm and the use of efficient mechanisms to derive the best robust solution that responds to all uncertainties with reduced running times. The computational experiments are performed and improve the objective function of a set of instances with different levels of the uncertainty polytope to obtain the best robust solutions that protect from the violation of time windows for different scenarios.

In this paper, the focus is on mechanical systems that, like a ship or a submarine, perform risky missions and that must remain operating for the whole mission time. Missions take place far from the operational base and so, in case of failures, although repairs are possible, spares parts cannot be resupplied. Hence, given space constraints, the problem is to define the optimal set of spare parts that should be taken aboard, to maximize the probability to complete the mission. To solve this problem, we propose a constructive algorithm that generates the Pareto Optimal Frontier of all the non-dominated solutions, in terms of the system’s reliability and of required space. At first, the algorithm is formulated in a generic way; next, it is contextualized to the common case of Weibull distributed failure times. In this condition, the underlying equations of the model cannot be solved in closed form and an approximated procedure is proposed and validated through extensive numerical simulation.

When operating in highly competitive business environments, contemporary manufacturing firms must persistently find ways to fulfill timely orders with quality ensured merchandise, manage the unanticipated fabrication disruptions, and minimize total operating expenses. To address the aforementioned concerns, this study explores the optimal runtime decision for a manufacturing system featuring an expedited fabrication rate, random equipment failures, and scrap. Specifically, the proposed study considers an expedited rate that is linked to higher setup and unit costs. The fabrication process is subject to random failure and scrap rates. The failure instance follows a Poisson distribution, is repaired right away, and the fabrication of interrupted batch resumes when the equipment is restored. The defective goods are identified and scrapped. Mathematical modeling and optimization method are used to find the total system cost and the optimal runtime of the problem. The applicability and sensitivity analyses of research outcome are illustrated through a numerical example. Diverse critical information regarding the individual/joint impacts of variations in stochastic time-to-failure, expedited rate, and random scrap on the optimal runtime decision, total system expenses, different cost components, and machine utilization, can now be revealed to assist in in-depth problem analyses and decision makings.

The Combinatorial Optimization Problem (COPs) is one of the branches of applied mathematics and computer sciences, which is accompanied by many problems such as Facility Layout Problem (FLP), Vehicle Routing Problem (VRP), etc. Even though the use of several mathematical formulations is employed for FLP, Quadratic Assignment Problem (QAP) is one of the most commonly used. One of the major problems of Combinatorial NP-hard Optimization Problem is QAP mathematical model. Consequently, many approaches have been introduced to solve this problem, and these approaches are classified as Approximate and Exact methods. With QAP, each facility is allocated to just one location, thereby reducing cost in terms of aggregate distances weighted by flow values. The primary aim of this study is to propose a hybrid approach which combines Discrete Differential Evolution (DDE) algorithm and Tabu Search (TS) algorithm to enhance solutions of QAP model, to reduce the distances between the locations by finding the best distribution of N facilities to N locations, and to implement hybrid approach based on discrete differential evolution (HDDETS) on many instances of QAP from the benchmark. The performance of the proposed approach has been tested on several sets of instances from the data set of QAP and the results obtained have shown the effective performance of the proposed algorithm in improving several solutions of QAP in reasonable time. Afterwards, the proposed approach is compared with other recent methods in the literature review. Based on the computation results, the proposed hybrid approach outperforms the other methods.

The 0-1 Multidimensional Knapsack Problem (MKP) is an NP-Hard problem that has many important applications in business and industry. However, business and industrial applications typically involve large problem instances that can be time consuming to solve for a guaranteed optimal solution. There are many approximate solution approaches, heuristics and metaheuristics, for the MKP published in the literature, but these typically require the fine-tuning of several parameters. Fine-tuning parameters is not only time-consuming (especially for operations research (OR) practitioners), but also implies that solution quality can be compromised if the problem instances being solved change in nature. In this paper, we demonstrate an efficient and effective implementation of a robust population-based metaheuristic that does not require parameter fine-tuning and can easily be used by OR practitioners to solve industrial size problems. Specifically, to solve the MKP, we provide an efficient adaptation of the two-phase Teaching-Learning Based Optimization (TLBO) approach that was originally designed to solve continuous nonlinear engineering design optimization problems. Empirical results using the 270 MKP test problems available in Beasley’s OR-Library demonstrate that our implementation of TLBO for the MKP is competitive with published solution approaches without the need for time-consuming parameter fine-tuning.

This article presents a new approach to address the problem of joint planning of physical and financial flows. The main contribution of this work is that it integrates supply chain contracts and also focuses on supply chain tactical planning in an uncertain and disrupted environment, taking into account budgetary and contractual constraints. In order to minimize the effect of disturbances due to existing uncertainties, a planning model is developed and implemented on a rolling horizon basis. The goal is to seek the best compromise between the available decision-making levers linked with physical and financial flows by adopting a dynamic process that allows for data update at each planning stage. The results of the implemented approach are analysed to highlight the benefits incurred by the inter-firm collaboration in terms of operational performance and working capital (WC) of the supply chain. Our approach represents a basis for negotiation with the suppliers in order to yield a possibly shared profit.

Three simple metaphor-less optimization algorithms are developed in this paper for solving the unconstrained and constrained optimization problems. These algorithms are based on the best and worst solutions obtained during the optimization process and the random interactions between the candidate solutions. These algorithms require only the common control parameters like population size and number of iterations and do not require any algorithm-specific control parameters. The performance of the proposed algorithms is investigated by implementing these on 23 benchmark functions comprising 7 unimodal, 6 multimodal and 10 fixed-dimension multimodal functions. Additional computational experiments are conducted on 25 unconstrained and 2 constrained optimization problems. The proposed simple algorithms have shown good performance and are quite competitive. The research community may take advantage of these algorithms by adapting the same for solving different unconstrained and constrained optimization problems.

In the classical vehicle routing problem with backhauls (VRPB) the customers are divided into two sets; the linehaul and backhaul customers, so that the distribution and collection services of goods are separated into different routes. This is justified by the need to avoid the reorganization of the loads inside the vehicles, to reduce the return of the vehicles with empty load and to give greater priority to the customers of the linehaul. Many logistics companies have special responsibility to make their operations greener, and electric vehicles (EVs) can be an efficient solution. Thus, when the fleet consists of electric vehicles (EVs), the driving range is limited due to their battery capacities and, therefore, it is necessary to visit recharging stations along their route. In this paper the electric vehicle routing problem with backhauls (EVRPB) is introduced and formulated as a mixed integer linear programming model. This formulation is based on the generalization of the open vehicle routing problem considering a set of new constraints focussed on maintaining the arborescence condition of the linehaul and backhaul paths. Different charging points for the EVs are considered in order to recharge the battery at the end of the linehaul route or during the course of the backhaul route. Finally, a heuristic initialization methodology is proposed, in which an auxiliary graph is used for the efficient coding of feasible solutions to the problem. The operation and effectiveness of the proposed formulation is tested on two VRPB instance datasets of literature which have been adapted to the EVRPB.