# Special Issue on Algorithms for Scheduling Problems
## 2 Special Issue  
In response to the call for papers, we selected eleven submissions for this special issue, all of which are of high quality, reflecting the stable and growing interest in the area of effective and efficient algorithms to solve problems for real-world production planning and scheduling. All submissions have been reviewed by at least three experts in the operations research area. Next, we survey all published papers in increasing order of their publication dates for this special issue. The paper [1] was the first one accepted for this special issue, where the authors wrote that, to improve energy efficiency and maintain the stability of the power grid, time-of-use (TOU) electricity tariffs have been widely used around the world, which bring both opportunities and challenges to energy-efficient scheduling problems. Although methods based on discrete-time or continuous-time models have been suggested for addressing these problems, they are deficient in solution quality or time complexity, especially when dealing with large-size instances. For such problems, a new greedy insertion heuristic algorithm with a multi-stage filtering mechanism including coarse granularityand fine granularity filtering is developed in this paper. To show the effectiveness of the proposed algorithm, a real case study is provided and detailed computational results are given. The paper [2] is devoted to a graph model of hierarchical supply chains. The goal is to measure the complexity of the links between different components of the chain, e.g., between the principal equipment manufacturer and its suppliers. The information entropy is used as a measure of knowledge about the complexity of shortages and pitfalls in relationship to the supply chain components under uncertainty. The concept of conditional entropy is introduced as a generalization of the conventional entropy. An entropy-based algorithm is developed providing an efficient assessment of the supply chain complexity as a function of the supply chain size. In the paper [3], the maximization of the number of just-in-time jobs in a permutation flow shop scheduling problem is considered. A mixed integer linear programming model to represent the problem as well as solution approaches based on enumerative and constructive heuristics are proposed and computationally implemented. The 10 constructive heuristics proposed produce good-quality results, especially for large-scale instances in reasonable time. The two best heuristics obtain near-optimal solutions, and they are better than adaptations of the classic NEH heuristic. The paper [4] is devoted to a formalization of the resource-constrained project scheduling problem (RCPSP) in terms of combinatorial optimization theory. The transformation of the original RCPSP into a combinatorial setting is based on interpreting each operation as an atomic entity that has a defined duration and has to reside on the continuous time axis meeting additional restrictions. The simplest case of continuous-time scheduling assumes a one-to-one correspondence between the resources and operations and corresponds to a linear programming problem setting. However, real scheduling problems include many-to-one relations that lead to an additional combinatorial component in the formulation of the RCPSP due to the competition of the operations. The authors investigate how to apply several typical algorithms to solve the resulting combinatorial optimization problem: an enumerative algorithm including a branch-and-bound method, a gradient algorithm, or a random search technique. The paper [5] considers a number of markets, geographically separated, with different demand characteristics for different products that share a common component. This common component can either be manufactured locally in each of the markets or transported between the markets to fulfill the demand. However, final assemblies are localized to the respective markets. The decision-making challenge is whether to manufacture the common component centrally or locally.