In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.

Flows in Networks

Survey: Covering problems in facility location: A review

Supply chain network design (SCND) models and methods have been the subject of several recent literature review surveys, but none of them explicitly includes sustainable development as a main characteristic of the problem considered. The aim of this review is to bridge this gap. The paper analyzes 87 papers in the field of supply chain network design, covering mathematical models that include economic factors as well as environmental and/or social dimensions. The review is organized along four research questions asking (i) which environmental and social objectives are included, (ii) how are they integrated into the models, (iii) which methods and tool are used and finally (iv) which industrial applications and contexts are covered in these models. The review finds that there are a number of limitations to the current research in sustainable SCND. The narrow scope of environmental and social measures in current models should go beyond limited greenhouse gas indicators to broader life-cycle approaches including new social metrics. The more effective inclusion of uncertainty and risk in models with improved multi-objective approaches is also needed. There are also significant gaps in the sectors used to test models limiting more general applicability. The paper concludes with promising new avenues of research to more effectively include sustainability into SCND models.

/pdf/sustainable-supply-chain-network-design-an-optimization-42wek3gyel.pdf

Sustainable supply chain network design: An optimization-oriented review☆

The inventory-routing problem (IRP) dates back 30 years. It can be described as the combination of vehicle-routing and inventory management problems, in which a supplier has to deliver products to a number of geographically dispersed customers, subject to side constraints. It provides integrated logistics solutions by simultaneously optimizing inventory management, vehicle routing, and delivery scheduling. Some exact algorithms and several powerful metaheuristic and matheuristic approaches have been developed for this class of problems, especially in recent years. The purpose of this article is to provide a comprehensive review of this literature, based on a new classification of the problem. We categorize IRPs with respect to their structural variants and the availability of information on customer demand.

/pdf/thirty-years-of-inventory-routing-4gexxt76br.pdf

Thirty Years of Inventory Routing

The Benders decomposition algorithm: A literature review

In this paper we give an overview of recent developments in the field of modeling deterministic single-level dynamic lot sizing problems. The focus of this paper is on the modeling of various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research.

/pdf/modeling-industrial-lot-sizing-problems-a-review-vruq0a6m3b.pdf

Modeling Industrial Lot Sizing Problems: A Review

https://repub.eur.nl/pub/1336/ERS%202004%20042%20LIS.pdf

Meta-Heuristics for Dynamic Lot Sizing: a review and comparison of solution approaches

https://www.cirrelt.ca/DocumentsTravail/CIRRELT-2013-49.pdf

The production routing problem

The inventory routing problem (IRP) and the production routing problem (PRP) are two difficult problems arising in the planning of integrated supply chains. These problems are solved in an attempt to jointly optimize production, inventory, distribution, and routing decisions. Although several studies have proposed exact algorithms to solve the single-vehicle problems, the multivehicle aspect is often neglected because of its complexity. We introduce multivehicle PRP and IRP formulations, with and without a vehicle index, to solve the problems under both the maximum level (ML) and order-up-to level (OU) inventory replenishment policies. The vehicle index formulations are further improved using symmetry breaking constraints; the nonvehicle index formulations are strengthened by several cuts. A heuristic based on an adaptive large neighborhood search technique is also developed to determine initial solutions, and branch-and-cut algorithms are proposed to solve the different formulations. The results show tha...

Raf Jans

Papers

Modeling Industrial Lot Sizing Problems: A Review

Meta-Heuristics for Dynamic Lot Sizing: a review and comparison of solution approaches

The production routing problem

Formulations and Branch-and-Cut Algorithms for Multivehicle Production and Inventory Routing Problems

Formulations and Branch-and-Cut Algorithms for Multi-Vehicle Production and Inventory Routing Problems