Changing Bases: Multistage Optimization for Matroids and Matchings

This paper is motivated by the fact that many systems need to be maintained continually while the underlying costs change over time. The challenge is to continually maintain near-optimal solutions to the underlying optimization problems, without creating too much churn in the solution itself. We model this as a multistage combinatorial optimization problem where the input is a sequence of cost functions (one for each time step); while we can change the solution from step to step, we incur an additional cost for every such change. We study the multistage matroid maintenance problem, where we need to maintain a base of a matroid in each time step under the changing cost functions and acquisition costs for adding new elements. The online version of this problem generalizes online paging. E.g., given a graph, we need to maintain a spanning tree $T_t$ at each step: we pay $c_t(T_t)$ for the cost of the tree at time $t$, and also $| T_t\setminus T_{t-1} |$ for the number of edges changed at this step. Our main result is an $O(\log m \log r)$-approximation, where $m$ is the number of elements/edges and $r$ is the rank of the matroid. We also give an $O(\log m)$ approximation for the offline version of the problem. These bounds hold when the acquisition costs are non-uniform, in which caseboth these results are the best possible unless P=NP. We also study the perfect matching version of the problem, where we must maintain a perfect matching at each step under changing cost functions and costs for adding new elements. Surprisingly, the hardness drastically increases: for any constant $\epsilon>0$, there is no $O(n^{1-\epsilon})$-approximation to the multistage matching maintenance problem, even in the offline case

Design of Closed Loop Supply Chains

Increased concern for the environment has lead to new techniques to design products and supply chains that are both economically and ecologically feasible. This paper deals with the product - and corresponding supply chain design for a refrigerator. Literature study shows that there are many models to support product design and logistics separately, but not in an integrated way. In our research we develop quantitative modelling to support an optimal design structure of a product, i.e. modularity, repairability, recyclability, as well as the optimal locations and goods flows allocation in the logistics system. Environmental impacts are measured by energy and waste. Economic costs are modelled as linear functions of volumes with a fixed set-up component for facilities. We apply this model using real life R&D data of a Japanese consumer electronics company. The model is run for different scenarios using different parameter settings such as centralised versus decentralised logistics, alternative product designs, varying return quality and quantity, and potential environmental legislation based on producer responsibility.supply chain management;reverse logistics;facility location;network design;product design

공컨테이너관리 기법을 활용한 효율적인 컨테이너 공급망

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2021. 2. 문일경.Due to a remarkable surge in global trade volumes led by maritime transportation, shipping companies should make a great effort in managing their container flows especially in case of carrier-owned containers. To do so, they comprehensively implement empty container management strategies and accelerate the flows in a cost- and time-efficient manner to minimize total relevant costs while serving the maximal level of customers demands. However, many critical issues in container flows universally exist due to high uncertainty in reality and hinder the establishment of an efficient container supply chain. In this dissertation, we fully discuss such issues and provide mathematical models along with specific solution procedures. Three types of container supply chain are presented in the following: (i) a two-way four-echelon container supply chain; (ii) a laden and empty container supply chain under decentralized and centralized policies; (iii) a reliable container supply chain under disruption. These models explicitly deal with high risks embedded in a container supply chain and their computational experiments offer underlying managerial insights for the management in shipping companies. For (i), we study empty container management strategy in a two-way four-echelon container supply chain for bilateral trade between two countries. The strategy reduces high maritime transportation costs and long delivery times due to transshipment. The impact of direct shipping is investigated to determine the number of empty containers to be repositioned among selected ports, number of leased containers, and route selection to satisfy the demands for empty and laden containers for exporters and importers in two regions. A hybrid solution procedure based on accelerated particle swarm optimization and heuristic is presented, and corresponding results are compared. For (ii), we introduce the laden and empty container supply chain model based on three scenarios that differ with regard to tardiness in the return of empty containers and the decision process for the imposition of fees with the goal of determining optimal devanning times. The effectiveness of each type of policy - centralized versus decentralized - is determined through computational experiments that produce key performance measures including the on-time return ratio. Useful managerial insights on the implementation of these polices are derived from the results of sensitivity analyses and comparative studies. For (iii), we develop a reliability model based on container network flow while also taking into account expected transportation costs, including street-turn and empty container repositioning costs, in case of arc- and node-failures. Sensitivity analyses were conducted to analyze the impact of disruption on container supply chain networks, and a benchmark model was used to determine disruption costs. More importantly, some managerial insights on how to establish and maintain a reliable container network flow are also provided.해상 수송이 주도함으로써 전 세계 무역량이 급증하기 때문에 회사 소유 컨테이너는 컨테이너 흐름을 관리하는 데 많은 노력을 기울여야 한다. 이를 위해 공 컨테이너 관리 전략을 포괄적으로 구현하고 효율적인 수송 비용 및 시간 절감 방식으로 컨테이너 흐름을 원활히 하여 관련 총비용을 최소화하는 동시에 고객의 수요를 최대한 충족하게 된다. 그러나 현실에서는 높은 불확실성 때문에 컨테이너 흐름에 대한 많은 주요한 이슈가 보편적으로 존재하고 효율적인 컨테이너 공급망 구축을 방해한다. 본 논문에서는 이러한 이슈에 대해 전반적으로 논의하고 적절한 해법과 함께 수리 모형을 제공한다. 이를 위해 세 가지 유형의 컨테이너 공급망을 다룬다. 먼저 (i) 양방향 네 단계 컨테이너 공급망, (ii) 분권화 및 중앙 집중화 정책에 따른 적∙공 컨테이너 공급망; 그리고 (iii) disruption 상황 속에서 신뢰성을 고려하는 컨테이너 공급망이다. 본 논문에서 제시한 세 가지 모형은 컨테이너 공급망에 내재 된 높은 위험을 직접 다루며 계산 실험은 해운 회사의 경영진이나 관계자를 위해 주요한 관리 인사이트를 제공한다. (i)의 경우, 두 지역 간 양자 무역을 위한 양방향 네 단계 컨테이너 공급망에서 공 컨테이너 관리 전략을 연구한다. 이 전략은 환적으로 인한 높은 해상 운송 비용과 긴 배송 시간을 줄일 수 있다. 또한, 직항 수송의 영향을 조사하여 선택된 항구 중 재배치 할 공 컨테이너 수, 임대 컨테이너 수, 두 지역의 수출업자와 수입업자의 적∙공 컨테이너 대한 수요를 만족하기 위한 경로 선택을 결정하게 된다. APSO 및 휴리스틱을 기반으로 하는 하이브리드 해법을 제시하며 비교 실험을 하였다. (ii)의 경우 최적 devanning time 결정을 목표로 공 컨테이너의 반환 지연과 해당 수수료 부과 결정 프로세스와 관련하여 서로 다른 세 가지 시나리오를 기반으로 적∙공 컨테이너 공급망 모형을 제시한다. 각 유형의 정책적(분권화 및 중앙 집중화) 효과는 정시 반환율을 포함한 주요 성능 측정을 고려하는 계산 실험을 통해 결정된다. 이러한 정책 실행에 대한 유용한 관리 인사이트는 민감도 분석 및 비교 연구의 결과에서 도출한다. (iii)의 경우, 본 논문은 컨테이너 네트워크 흐름을 기반으로 하는 신뢰성 모형을 개발하는 동시에 아크 및 노드 failure가 있을 때 street-turn 및 공 컨테이너 재배치 비용을 포함한 기대 총 비용을 구한다. 중단이 컨테이너 공급망 네트워크에 미치는 영향을 분석하기 위해 민감도 분석을 수행했으며 disruption 비용을 결정하기 위해 벤치마크 모형을 활용한다. 더불어 신뢰성을 고려한 컨테이너 네트워크 흐름을 구축하고 신뢰성을 유지하는 방법에 대한 관리적 인사이트도 제공한다.Abstract i Contents ii List of Tables vi List of Figures viii 1. Introduction 1 1.1 Empty Container Repositioning Problem 1 1.2 Reliability Problem 3 1.3 Research Motivation and Contributions 4 1.4 Outline of the Dissertation 7 2. Two-Way Four-Echelon Container Supply Chain 8 2.1 Problem Description and Literature Review 8 2.2 Mathematical Model for the TFESC 15 2.2.1 Overview and Assumptions 15 2.2.2 Notation and Formulation 19 2.3 Solution Procedure for the TFESC 25 2.3.1 Pseudo-Function-based Optimization Problem 25 2.3.2 Objective Function Evaluation 28 2.3.3 Heuristics for Reducing the Number of Leased Containers 32 2.3.4 Accelerated Particle Swarm Optimization 34 2.4 Computational Experiments 37 2.4.1 Heuristic Performances 39 2.4.2 Senstivity Analysis of Varying Periods 42 2.4.3 Senstivity Analysis of Varying Number of Echelons 45 2.5 Summary 48 3. Laden and Empty Container Supply Chain under Decentralized and Centralized Policies 50 3.1 Problem Description and Literature Review 50 3.2 Scenario-based Model for the LESC-DC 57 3.3 Model Development for the LESC-DC 61 3.3.1 Centralized Policy 65 3.3.2 Decentralized Policies (Policies I and II) 67 3.4 Computational Experiments 70 3.4.1 Numerical Exmpale 70 3.4.2 Sensitivity Analysis of Varying Degree of Risk in Container Return 72 3.4.3 Sensitivity Analysis of Increasing L_0 74 3.4.4 Sensitivity Analysis of Increasing t_r 76 3.4.5 Sensitivity Analysis of Decreasing es and Increasing e_f 77 3.4.6 Sensitivity Analysis of Discounting 〖pn〗_{f1} and 〖pn〗_{f2} 78 3.4.7 Sensitivity Analysis of Different Container Fleet Sizes 79 3.5 Managerial Insights 81 3.6 Summary 83 4. Reliable Container Supply Chain under Disruption 84 4.1 Problem Description and Literature Review 84 4.2 Mathematical Model for the RCNF 90 4.3 Reliability Model under Disruption 95 4.3.1 Designing the Patterns of q and s 95 4.3.2 Objective Function for the RCNF Model 98 4.4 Computational Experiments 103 4.4.1 Sensitivity Analysis of Expected Failure Costs 106 4.4.2 Sensitivity Analysis of Different Network Structures 109 4.4.3 Sensitivity Analysis of Demand-Supply Variation 112 4.4.4 Managerial Insights 115 4.5 Summary 116 5. Conclusions and Future Research 117 Appendices 120 A Proof of Proposition 3.1 121 B Proof of Proposition 3.2 124 C Proof of Proposition 3.3 126 D Sensitivity Analyses for Results 129 E Data for Sensitivity Analyses 142 Bibliography 146 국문초록 157 감사의 글 160Docto

Meta-heuristic based Construction Supply Chain Modelling and Optimization

Driven by the severe competition within the construction industry, the necessity of improving and optimizing the performance of construction supply chain has been aroused. This thesis proposes three problems with regard to the construction supply chain optimization from three perspectives, namely, deterministic single objective optimization, stochastic optimization and multi-objective optimization respectively. Mathematical models for each problem are constructed accordingly and meta-heuristic algorithms are developed and applied for resolving these three problems

A Two-Echelon Location-inventory Model for a Multi-product Donation-demand Driven Industry

This study involves a joint bi-echelon location inventory model for a donation-demand driven industry in which Distribution Centers (DC) and retailers (R) exist. In this model, we confine the variables of interest to include; coverage radius, service level, and multiple products. Each retailer has two classes of product flowing to and from its assigned DC i.e. surpluses and deliveries. The proposed model determines the number of DCs, DC locations, and assignments of retailers to those DCs so that the total annual cost including: facility location costs, transportation costs, and inventory costs are minimized. Due to the complexity of problem, the proposed model structure allows for the relaxation of complicating terms in the objective function and the use of robust branch-and-bound heuristics to solve the non-linear, integer problem. We solve several numerical example problems and evaluate solution performance

Robust optimisation of dry port network design in the container shipping industry under uncertainty

PhD ThesisThe concept of dry port has attracted the attention of many researchers in the field of containerised transport industry over the past few decades. Previous research on dry port container network design has dealt with decision-making at different levels in an isolated manner. The purpose of this research is to develop a decision-making tool based on mathematical programming models to integrate strategic level decisions with operational level decisions. In this context, the strategic level decision making comprises the number and location of dry ports, the allocation of customers demand, and the provision of arcs between dry ports and customers within the network. On the other hand, the operational level decision making consists of containers flow, the selection of transportation modes, empty container repositioning, and empty containers inventory control. The containers flow decision involves the forward and backward flow of both laden and empty containers. Several mathematical models are developed for the optimal design of dry port networks while integrating all these decisions. One of the key aspects that has been incorporated in this study is the inherent uncertainty of container demands from end customers. Besides, a dynamic setting has to be adopted to consider the inevitable periodic fluctuation of demands. In order to incorporate the abovementioned decision-making integration with uncertain demands, several models are developed based on twostage stochastic programming approach. In the developed models, the strategic decisions are made in the first stage while the second-stage deals with operational decisions. The models are then solved through a robust sample average approximation approach, which is improved with the Benders Decomposition method. Moreover, several acceleration algorithms including multi-cut framework, knapsack inequalities, and Pareto-optimal cut scheme are applied to enhance the solution computational time. The proposed models are applied to a hypothetical case of dry port container network design in North Carolina, USA. Extensive numerical experiments are conducted to validate the dry port network design models. A large number of problem instances are employed in the numerical experiments to certify the capability of models. The quality of generated solutions is examined via a statistical validation procedure. The results reveal that the proposed approach can produce a reliable dry port container network under uncertain environment. Moreover, the experimental results underline the sensitivity of the configuration of the network to the inventory holding costs iii and the value of coefficients relating to model robustness and solution robustness. In addition, a number of managerial insights are provided that may be widely used in container shipping industry: that the optimal number of dry ports is inversely proportional to the empty container holding costs; that multiple sourcing is preferable when there are high levels of uncertainty; that rail tends to be better for transporting laden containers directly from seaports to customers with road being used for empty container repositioning; service level and fill rate improve when the design targets more robust solutions; and inventory turnover increases with high levels of holding cost; and inventory turnover decreases with increasing robustness

A hybrid polyhedral uncertainty model for the robust network loading problem

[No abstract available

On distributed virtual network embedding with guarantees

To provide wide-area network services, resources from different infrastructure providers are needed. Leveraging the consensus-based resource allocation literature, we propose a general distributed auction mechanism for the (NP-hard) virtual network (VNET) embedding problem. Under reasonable assumptions on the bidding scheme, the proposed mechanism is proven to converge, and it is shown that the solutions guarantee a worst case efficiency of (?????) relative to the optimal solution, and that this bound is optimal, that is, no better approximation exists. Using extensive simulations, we confirm superior convergence properties and resource utilization when compared with existing distributed VNET embedding solutions, and we show how byappropriate policy design, our mechanism can be instantiated to accommodate the embedding goals of different service and infrastructure providers, resulting in an attractive and flexible resource allocation solution.This work is supported in part by the National Science Foundation under grant CNS-0963974

On distributed virtual network embedding with guarantees

To provide wide-area network services, resources from different infrastructure providers are needed. Leveraging the consensus-based resource allocation literature, we propose a general distributed auction mechanism for the (NP-hard) virtual network (VNET) embedding problem. Under reasonable assumptions on the bidding scheme, the proposed mechanism is proven to converge, and it is shown that the solutions guarantee a worst case efficiency of (?????) relative to the optimal solution, and that this bound is optimal, that is, no better approximation exists. Using extensive simulations, we confirm superior convergence properties and resource utilization when compared with existing distributed VNET embedding solutions, and we show how byappropriate policy design, our mechanism can be instantiated to accommodate the embedding goals of different service and infrastructure providers, resulting in an attractive and flexible resource allocation solution.This work is supported in part by the National Science Foundation under grant CNS-0963974