Single-Source Multi-Period Problem Model with Active Constraints-Based Approach Algorithm

In this paper, we introduce the multi-period single sourcing problem as an assignment problem. The multi- period single-sourcing problem in this research is seen as a problem of finding assignments, from time to time to obtain the minimum possible total transportation and inventory costs for distributing goods to customers. The case considered in this problem is the case of placing inventory items that are distributed to customers online, so this case is seen as a non-polynomial or NP hard problem that requires a solution algorithm, and the algorithm we offer is a direct search algorithm to solve the problem. multi period single sourcing. The direct search algorithm offered is the Branch and Price algorithm which was developed for Generalized Assignment Problems (GAP) to a much more complete class of problems, called CAP (Convex Assignment Problems). We offer this algorithm because the results it will obtain are more optimal, the computing time is superior, and it shows greater stability, that is, fewer outliers are observed. Specifically, we generalize the strategy of separating nonbasic variables from their constraints, combined with using active constraint methods to solve the Generalized Assignment Problem (GAP) into a Convex Assignment problem. Then, identification of important subclasses of the problem is carried out, which contains many variations of multi- period single sourcing problems, as well as GAP variants. The final result we found is an active depth-based single source multi-period model that can minimize the damage to the optimal integer solution for solving the MPSSP convex problem

Global supply chains of high value low volume products

Imperial Users onl

Multiperiod Dispatching and Routing for On-Time Delivery in a Dynamic and Stochastic Environment

On-demand delivery has become increasingly popular around the world. Brick-and-mortar grocery stores, restaurants, and pharmacies are providing fast delivery services to satisfy the growing home delivery demand. Motivated by a large meal and grocery delivery company, we model and solve a multiperiod driver dispatching and routing problem for last-mile delivery systems where on-time performance is the main target. The operator of this system needs to dispatch a set of drivers and specify their delivery routes in a stochastic environment, in which random demand arrives over a fixed number of periods. The resulting dynamic program is challenging to solve due to the curse of dimensionality. We propose a novel approximation framework to approximate the value function via a simplified dispatching program. We then develop efficient exact algorithms for this problem based on Benders decomposition and column generation. We validate the superior performance of our framework and algorithms via extensive numerical experiments. Tested on a real-world data set, we quantify the value of adaptive dispatching and routing in on-time delivery and highlight the need of coordinating these two decisions in a dynamic setting. We show that dispatching multiple vehicles with short trips is preferable for on-time delivery, as opposed to sending a few vehicles with long travel times

Production distribution planning in a multiechelon supply chain using carbon policies: A review and reflections

Sustainability of a supply chain has gained more attention from economists, environmentalists, consumers, manufacturers, government and the academia. In this paper, the literature survey has been performed on production allocation problem in a multi-echelon supply chain with carbon policies. With web-based search engines such as Scopus and Web of Science several resources such as journals, conference proceedings and books are selected and reviewed. It is observed from the literature that the mentioned problem traces the progression of carbon policies in a supply chain over the past 22 years to provide substantiation for Green Supply Chain. The research papers are then analyzed and categorized to construct the useful foundation of previous studies. Moreover, the importance of this problem in recent years needs has been highlighted by mentioning the gaps in the literature. Further, at the end of the paper, several future work directions in this area also suggested.(undefined)info:eu-repo/semantics/publishedVersio

The vehicle routing problem with partial outsourcing

This paper introduces the vehicle routing problem with partial outsourcing (VRPPO) in which a customer can be served by a single private vehicle, by a common carrier, or by both a single private vehicle and a common carrier. As such, it is a variant of the vehicle routing problem with private fleet and common carrier (VRPPC). The objective of the VRPPO is to minimize fixed and variable costs of the private fleet plus the outsourcing cost. We propose two different path-based formulations for the VRPPO and solve these with a branch-and-price-and-cut solution method. For each path-based formulation, two different pricing procedures are designed and used when solving the linear relaxations by column generation. To assess the quality of the solution methods and gain insight in potential cost improvements compared with the VRPPC, we perform tests on two instance sets with up to 100 customers from the literature

Analysis of the supply chain design and planning issues: Models and algorithms

Ph.DDOCTOR OF PHILOSOPH

Integrated production-distribution systems : Trends and perspectives

During the last two decades, integrated production-distribution problems have attracted a great deal of attention in the operations research literature. Within a short period, a large number of papers have been published and the field has expanded dramatically. The purpose of this paper is to provide a comprehensive review of the existing literature by classifying the existing models into several different categories based on multiple characteristics. The paper also discusses some trends and list promising avenues for future research

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

Models and algorithms for decomposition problems

This thesis deals with the decomposition both as a solution method and as a problem itself. A decomposition approach can be very effective for mathematical problems presenting a specific structure in which the associated matrix of coefficients is sparse and it is diagonalizable in blocks. But, this kind of structure may not be evident from the most natural formulation of the problem. Thus, its coefficient matrix may be preprocessed by solving a structure detection problem in order to understand if a decomposition method can successfully be applied. So, this thesis deals with the k-Vertex Cut problem, that is the problem of finding the minimum subset of nodes whose removal disconnects a graph into at least k components, and it models relevant applications in matrix decomposition for solving systems of equations by parallel computing. The capacitated k-Vertex Separator problem, instead, asks to find a subset of vertices of minimum cardinality the deletion of which disconnects a given graph in at most k shores and the size of each shore must not be larger than a given capacity value. Also this problem is of great importance for matrix decomposition algorithms. This thesis also addresses the Chance-Constrained Mathematical Program that represents a significant example in which decomposition techniques can be successfully applied. This is a class of stochastic optimization problems in which the feasible region depends on the realization of a random variable and the solution must optimize a given objective function while belonging to the feasible region with a probability that must be above a given value. In this thesis, a decomposition approach for this problem is introduced. The thesis also addresses the Fractional Knapsack Problem with Penalties, a variant of the knapsack problem in which items can be split at the expense of a penalty depending on the fractional quantity