A New Dantzig-Wolfe Reformulation And Branch-And-Price Algorithm For The Capacitated Lot Sizing Problem With Set Up Times

The textbook Dantzig-Wolfe decomposition for the Capacitated LotSizing Problem (CLSP),as already proposed by Manne in 1958, has animportant structural deficiency. Imposingintegrality constraints onthe variables in the full blown master will not necessarily givetheoptimal IP solution as only production plans which satisfy theWagner-Whitin condition canbe selected. It is well known that theoptimal solution to a capacitated lot sizing problem willnotnecessarily have this Wagner-Whitin property. The columns of thetraditionaldecomposition model include both the integer set up andcontinuous production quantitydecisions. Choosing a specific set upschedule implies also taking the associated Wagner-Whitin productionquantities. We propose the correct Dantzig-Wolfedecompositionreformulation separating the set up and productiondecisions. This formulation gives the samelower bound as Manne'sreformulation and allows for branch-and-price. We use theCapacitatedLot Sizing Problem with Set Up Times to illustrate our approach.Computationalexperiments are presented on data sets available from theliterature. Column generation isspeeded up by a combination of simplexand subgradient optimization for finding the dualprices. The resultsshow that branch-and-price is computationally tractable andcompetitivewith other approaches. Finally, we briefly discuss how thisnew Dantzig-Wolfe reformulationcan be generalized to other mixedinteger programming problems, whereas in theliterature,branch-and-price algorithms are almost exclusivelydeveloped for pure integer programmingproblems.branch-and-price;Lagrange relaxation;Dantzig-Wolfe decomposition;lot sizing;mixed-integer programming

The two-echelon capacitated vehicle routing problem: models and math-based heuristics

Multiechelon distribution systems are quite common in supply-chain and logistics. They are used by public administrations in their transportation and traffic planning strategies, as well as by companies, to model own distribution systems. In the literature, most of the studies address issues relating to the movement of flows throughout the system from their origins to their final destinations. Another recent trend is to focus on the management of the vehicle fleets required to provide transportation among different echelons. The aim of this paper is twofold. First, it introduces the family of two-echelon vehicle routing problems (VRPs), a term that broadly covers such settings, where the delivery from one or more depots to customers is managed by routing and consolidating freight through intermediate depots. Second, it considers in detail the basic version of two-echelon VRPs, the two-echelon capacitated VRP, which is an extension of the classical VRP in which the delivery is compulsorily delivered through intermediate depots, named satellites. A mathematical model for two-echelon capacitated VRP, some valid inequalities, and two math-heuristics based on the model are presented. Computational results of up to 50 customers and four satellites show the effectiveness of the methods developed

Tedarik zinciri optimizasyon çalışmaları: Literatür araştırması ve sınıflama

Supply chain planning is an integrated process in which a group of several organizations, such as suppliers, producers, distributors and retailers, work together. It comprises procurement, production, distribution and demand planning topics. These topics require taking strategical, tactical and operational decisions. This research aims to reveal which supply chain topics, which decision levels, and which optimization methods are mostly studied in supply chain planning. This paper presents a total of 77 reviewed works published between 1993 and 2016 about supply chain planning. The reviewed works are categorized according to following elements: decision levels, supply chain optimization topics, objectives, optimization models.Tedarik Zinciri, tedarikçiler, üreticiler, dağıtıcılar ve toptancılar gibi bir grup organizasyonu birleştiren entegre bir süreçtir. Tedarik, üretim, dağıtım ve talep planlama konularını içerir. Bu konular stratejik, taktik ve operasyonel kararlar almayı gerektirir. Bu araştırma tedarik zinciri planlamasında hangi tedarik zinciri konularının, hangi karar/planlama seviyelerinin ve hangi optimizasyon metotlarının literatürde en çok çalışıldığını göstermektedir. Çalışma 1993 ve 2016 yılları arasındaki tedarik zinciri planlama konusundaki 77 adet çalışmanın incelenmesine ait sonuçları sunmaktadır. İncelenen çalışmalar şu kriterlere gore kategorize edilmiştir: karar seviyesi, tedarik zinciri optimizasyon konuları, amaçlar, optimizasyon modelleri