Advances and Novel Approaches in Discrete Optimization

Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

An investigation of changeover sensitive heuristics in an industrial job shop environment

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Production Scheduling

Generally speaking, scheduling is the procedure of mapping a set of tasks or jobs (studied objects) to a set of target resources efficiently. More specifically, as a part of a larger planning and scheduling process, production scheduling is essential for the proper functioning of a manufacturing enterprise. This book presents ten chapters divided into five sections. Section 1 discusses rescheduling strategies, policies, and methods for production scheduling. Section 2 presents two chapters about flow shop scheduling. Section 3 describes heuristic and metaheuristic methods for treating the scheduling problem in an efficient manner. In addition, two test cases are presented in Section 4. The first uses simulation, while the second shows a real implementation of a production scheduling system. Finally, Section 5 presents some modeling strategies for building production scheduling systems. This book will be of interest to those working in the decision-making branches of production, in various operational research areas, as well as computational methods design. People from a diverse background ranging from academia and research to those working in industry, can take advantage of this volume

A hybrid bi-objective optimization approach for joint determination of safety stock and safety time buffers in multi-item single-stage industrial supply chains

In material requirements planning (MRP) systems, safety stock and safety time are two well-known inventory buffering strategies to protect against supply and demand uncertainties. While the role of safety stocks in coping with uncertainty is well studied, safety time has received only scarce attention in the supply chain management literature. Particularly, most previous operations research models have typically considered the use of such inventory buffers in a separate fashion, but not together. Here, we propose a decision support system (DSS) to address the problem of integrating optimal safety stock and safety time decisions at the component level, in multi-supplier multi-item single-stage industrial supply chains under dynamic demands and stochastic lead times. The DSS is based on a hybrid bi-objective optimization approach that simultaneously optimizes upstream inventory holding costs and β-service levels, suggesting multiple non-dominated Pareto-optimal solutions to decision-makers. We further explore a weighted closed-form analytical expression to select a single Pareto-optimal point from a set of non-dominated solutions, thereby enhancing the practical application of the proposed DSS. We describe the implementation of our approach in a major automotive electronics company operating under a myriad of components with dynamic demand, uncertain supply and requirements plans with different degrees of sparsity. We show the potential of our approach to improve β-service levels while minimizing inventory-related costs. The results suggest that, in certain cases, it appears to be more cost-effective to combine safety stock with safety time compared to considering each inventory buffer independently.This work has been supported by the European Structural and Investment Funds in the FEDER component, through the Operational Competitiveness and Internationalization Pro-gram (COMPETE 2020) [Project No. 39479, Funding reference: POCI-01–0247-FEDER-39479]

PRODUCTION SEQUENCING AND STABILITY ANALYSIS OF A JUST-IN-TIME SYSTEM WITH SEQUENCE DEPENDENT SETUPS

Just-In-Time (JIT) production systems is a popular area for researchers but real-world issues such as sequence dependent setups are often overlooked. This research investigates an approach for determining stability and an approach for mixed product sequencing in production systems with sequence dependent setups and buffer thresholds which signal replenishment of a given buffer. Production systems in this research operate under JIT pull production principles by producing only when demand exists and idle when no demand exists. In the first approach, an iterative method is presented to determine stability for a multi-product production system that operates with replenishment signals and may have sequence dependent setups. In this method, a network of nodes representing machine states and arcs representing the buffer inventory levels is used to find a stable trajectory for the production system via an iterative procedure. The method determines suitable buffer levels for the production system that ensure that a trajectory originating from any point within a buffer region will always map to a point contained on another buffer region for all future mappings. This iterative method for determining the stability of a production system was implemented using an algorithm to calculate the buffer inventory regions for all arcs in a given arc-node network. The algorithm showed favorable results for two and three product systems in which sequence dependent setups may exist. In the second approach, a product sequencing algorithm determines a product sequence for a production system based on system parameters – setup times, buffer levels, usage rates, production rates, etc. The algorithm selects a product by evaluating the goodness of each product that has reached the replenishment threshold at the current time. The algorithm also incorporates a lookahead function that calculates the goodness for some time interval into the future. The lookahead function considers all branches of the tree of potential sequences to prevent the sequence from travelling down a dead-end branch in which the system will be unable to avoid a depleted buffer. The sequencing algorithm allows the user to weight the five terms of the goodness equations (current and lookahead) to control the behavior of the sequence