The design of supply chain networks (SCNs) aims at determining the number, location, and capacity of production facilities, as well as the allocation of markets (customers) and suppliers to one or more of these facilities. This paper reviews the existing literature on the use of simulation-optimization methods in the design of resilient SCNs. From this review, we classify some of the many works in the topic according to factors such as their methodology, the approach they use to deal with uncertainty and risk, etc. The paper also identifies several research opportunities, such as the inclusion of multiple criteria (e.g., monetary, environmental, and social dimensions) during the design-optimization process and the convenience of considering hybrid approaches combining metaheuristic algorithms, simulation, and machine learning methods to account for uncertainty and dynamic conditions, respectively.

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines.

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The vehicle routing problem with backhauls integrates decisions on products delivery with decisions on collection of returnable items. In this paper we analyze the scenario in which collection is optional. Both transport costs and penalty costs for not collecting are considered. A mixed-integer linear model is proposed and solved for small instances. A metaheuristic algorithm combining biased randomization techniques with iterated local search is introduced for larger instances. This approach yields cost savings and is competitive compared to other state-ofthe-art approaches.