The heterogeneous vehicle routing and truck scheduling problem in a multi-door cross-dock system

Cross-docking is a logistics technique applied by many industrial firms to get substantial savings in two warehousing costly functions like storage and order picking. Incoming shipments are unloaded from inbound trucks on a cross-dock terminal with minimal storage space and directly transferred to outbound vehicles that carry them to their destinations. The major decisions at the operational level are the vehicle routing and scheduling, the dock door assignment and the truck scheduling at the cross-dock. Because such decisions are interdependent, all of them are simultaneously considered in the so-called vehicle routing problem with cross-docking (VRPCD). Previous contributions on VRPCD assume that pickup and delivery tasks are accomplished by a homogeneous vehicle fleet, and they mostly ignore the internal transportation of goods through the cross-dock. This work introduces a new rigorous mixed-integer linear programming (MILP) formulation for the VRPCD problem to determine the routing and scheduling of a mixed vehicle fleet, the dock door assignment, the truck docking sequence and the travel time required to move the goods to the assigned stack door all at once. To improve the computational efficiency of the branch-and-cut search, an approximate sweep-based model is developed by also considering a set of constraints mimicking the sweep algorithm for allocating nodes to vehicles. Numerous heterogeneous VRPCD examples involving up to 50 transportation requests and a heterogeneous fleet of 10 vehicles with three different capacities were successfully solved using the proposed approaches in acceptable CPU times.     

A monolithic approach to vehicle routing and operations scheduling of a cross-dock system with multiple dock doors

Cross-docking is a logistic strategy for moving goods from suppliers to customers via a cross-dock terminal with no permanent storage. The operational planning of a cross-dock facility involves different issues such as vehicle routing, dock door assignment and truck scheduling. The vehicle routing problem seeks the optimal routes for a homogeneous fleet of vehicles that sequentially collects goods at pickup points and delivers them to their destinations. The truck scheduling problem deals with the timing of unloading and reloading operations at the cross-dock. This work introduces a mixed-integer linear programming formulation for the scheduling of single cross-dock systems that, in addition to selecting the pickup/delivery routes, simultaneously decides on the dock door assignment and the truck scheduling at the cross-dock. The proposed monolithic formulation is able to provide near-optimal solutions to medium-size problems involving up to 70 transportation orders, 16 vehicles and 7 strip/stack dock doors at acceptable CPU times.     

Optimal design of closed-loop supply chain networks with multifunctional nodes

This paper introduces a general mathematical programming framework that employs an innovative generalized supply chain network (SCN) composition coupled with forward and reverse logistics activities. Generalized echelon will have the ability to produce/distribute all forward materials/products and recover/redistribute simultaneously all the returned which are categorized with respect to their quality zone. The work addresses a multi-product, multi-echelon and multi-period Mixed-Integer Linear Programming (MILP) problem in a closed-loop supply chain network design solved to global optimality using standard branch-and-bound techniques. Further, the model aims to find the optimal structure of the network in order to satisfy market demand with the minimum overall capital and operational cost. Applicability and robustness of the proposed model are illustrated by using a medium real case study from a European consumer goods company whereas its benefits are valued through a comparison with a counterpart model that utilizes the mainstream fixed echelon network structure.     

Financial and financial engineering considerations in supply chain and product development pipeline management

Enterprise-wide decision problems are receiving increasing attention in the process systems engineering literature. In particular, the supply chain and product development pipeline management components of this general class of problems have been subjects of intensive research in both their deterministic and their stochastic forms. The supply chain management (SCM) problem has seen work largely focused on the process operations and logistics components while for the product development pipeline management (PDPM) problem much of the attention has been on MILP formulations addressing the consequences of product failure during its development. In their full realization, both are recognized as challenging stochastic multi-stage decision problems. In this paper we discuss three important aspects of these problems that require further research: the realistic representation of the financial components and appropriate criteria for this class of problems, strategic management of supplier and customer relationships through inventory management and option contracts, and innovative approaches to suitably value and integrate a broader range of decisions available to management. We highlight and extend relevant contributions and case examples drawn from the recent literature that are emerging on these topics and use this work to point out further challenges.     

A control-relevant approach to demand modeling for supply chain management

The development of control-oriented decision policies for inventory management in supply chains has drawn considerable interest in recent years. Modeling demand to supply forecasts is an important component of an effective solution to this problem. Drawing from the problem of control-relevant parameter estimation, this paper presents an approach for demand modeling in a production-inventory system that relies on a specialized weight to tailor the emphasis of the fit to the intended purpose of the model, which is to provide forecasts to inventory management policies based on internal model control or model predictive control. A systematic approach to generate this weight function (implemented using data prefilters in the time domain) is presented and the benefits demonstrated on a series of representative case studies. The multi-objective formulation developed in this work allows the user to emphasize minimizing inventory variance, minimizing starts variance, or their combination, as dictated by operational and enterprise goals.     

The effect of uncertainty on the optimal closed-loop supply chain planning under different partnerships structure

In a global economy, the key to success is providing products around the world at the right time in the right quantity and quality, at a low cost. Efficient supply chains have an important role in guaranteeing this success. Optimized planning of such structures is required and uncertainties regarding product demands and prices, amongst other supply chain conditions, should also be considered. In this paper, we look into supply chain planning decisions that account for uncertainty on product portfolios demand and prices. A multi-period planning model is developed where the supply chain operational decisions on supply, production, transportation, and distribution at the actual period consider the uncertainty on products’ demand and prices. Different decision scenarios, involving the evaluation of the supply chain economical performance, are analyzed (e.g. global operating costs/profit realized) for different criteria on the importance of the partners within the global chain (i.e. partners’ structure). A Mixed Integer Linear Programming (MILP) formulation is formulated for each planning scenario and the optimal solution is reached using a standard Branch and Bound (B&B) procedure. The final results provide details on the supply chain partners production, transportation and inventory, at each planning period, while accounting for the importance of each partner in the global chain as well as demand/price uncertainties. The applicability of the developed formulation is illustrated through the solution of a real case-study involving an industrial chain in the pharmaceutical sector.     

An optimization framework for the integration of water management and shale gas supply chain design

This study presents the mathematical formulation and implementation of a comprehensive optimization framework for the assessment of shale gas resources. The framework simultaneously integrates water management and the design and planning of the shale gas supply chain, from the shale formation to final product demand centers and from fresh water supply for hydraulic fracturing to water injection and/or disposal. The framework also addresses some issues regarding wastewater quality, i.e., total dissolved solids (TDS) concentration, as well as spatial and temporal variations in gas composition, features that typically arise in exploiting shale formations. In addition, the proposed framework also considers the integration of different modeling, simulation and optimization tools that are commonly used in the energy sector to evaluate the technical and economic viability of new energy sources. Finally, the capabilities of the proposed framework are illustrated through two case studies (A and B) involving 5 well-pads operating with constant and variable gas composition, respectively. The effects of the modeling of variable TDS concentration in the produced wastewater is also addressed in case study B.     

过程工业的集成供应链管理研究

分析了过程工业的特点和供应链管理在过程工业的应用现状,提出过程工业应通过采用集成供应链管理获得效益,即结合过程工业自身的特点,根据过程系统的功能层次模型和流结构模型,建立过程系统在投资决策、市场运营、管理控制3个不同运行层次上的集成供应链模型,并采用适当的优化策略求解,以求得企业在全生命周期内最大的综合效益。最后介绍了面向智能体的过程工业集成供应链建模方法以及求解策略。     

Supply chain planning and scheduling integration using Lagrangian decomposition in a knowledge management environment

The integration of planning and scheduling decisions in rigorous mathematical models usually results in large scale problems. In order to tackle the problem complexity, decomposition techniques based on duality and information flows between a master and a set of subproblems are widely applied. In this sense, ontologies improve information sharing and communication in enterprises and can even represent holistic mathematical models facilitating the use of analytic tools and providing higher flexibility for model building. In this work, we exploit this ontologies’ capability to address the optimal integration of planning and scheduling using a Lagrangian decomposition approach. Scheduling/planning sub-problems are created for each facility/supply chain entity and their dual solution information is shared by means of the ontological framework. Two case studies based on a STN representation of supply chain planning and scheduling models are presented to emphasize the advantages and limitations of the proposed approach.     

A Lagrangian relaxation approach for a multi-mode inventory routing problem with transshipment in crude oil transportation

An inventory routing problem in crude oil transportation is studied, in which crude oil is transported from a supply center to multiple customer harbors to satisfy their demands over multiple periods. In the problem, a heterogeneous fleet of tankers consisting of tankers owned by a distributor and tankers rented from a third party, a pipeline, and multiple types of routes are considered; both inventory level and shortage level at each customer harbor are limited. The objective is to determine for each period over a given time horizon the number of tankers of each type to be rented/returned at the supply center, the number of tankers of each type to be dispatched on each route, and the quantity of crude oil flowing through the pipeline that minimizes the total logistics cost.After formulating the problem as a mixed integer programming problem, a Lagrangian relaxation approach is developed for finding a near optimal solution of the problem. The approach is also applied to a variant of the problem in which both fully and partially loaded tankers are allowed in the transportation of crude oil. Numerical experiments show that this approach outperforms an existing meta-heuristic algorithm, especially for the instances of large sizes.     

Multi-criteria fuzzy optimization for locating warehouses and distribution centers in a supply chain network

This study considers the planning of a multi-product, multi-period, and multi-echelon supply chain network that consists of several existing plants at fixed places, some warehouses and distribution centers at undetermined locations, and a number of given customer zones. Unsure market demands are taken into account and modeled as a number of discrete scenarios with known probabilities. The supply chain planning model is constructed as a multi-objective mixed-integer linear program (MILP) to satisfy several conflict objectives, such as minimizing the total cost, raising the decision robustness in various product demand scenarios, lifting the local incentives, and reducing the total transport time. For the purpose of creating a compensatory solution among all participants of the supply chain, a two-phase fuzzy decision-making method is presented and, by means of application of it to a numerical example, is proven effective in providing a compromised solution in an uncertain multi-echelon supply chain network.     

石油供应链计划层优化与不确定性风险管理模型

提出了一种基于有限场景的两阶段随机混合整数线性规划（MILP）模型,来优化不确定条件下多周期、多层级的石油工业供应链的计划层管理。模型以碳排放税的形式将减少CO₂排放的环境目标融入到经济目标之中。供应链的各级节点均以黑箱的形式存在,使模型得以简化,在时间尺度相对较长的计划层获得优化结果,为供应链的计划与管理提供指导方案。并且分析了算例最优期望收益的风险性,在此基础上引入风险管理约束,得到了带有风险管理约束的供应链计划层优化模型。该模型的结果与原模型相比,期望收益附近的收益风险性降低。     

Multi-bucket optimization for integrated planning and scheduling in the perishable dairy supply chain

This paper considers a dairy industry problem on integrated planning and scheduling of set yoghurt production. A mixed integer linear programming formulation is introduced to integrate tactical and operational decisions and a heuristic approach is proposed to decompose time buckets of the decisions. The decomposition heuristic improves computational efficiency by solving big bucket planning and small bucket scheduling problems. Further, mixed integer linear programming and constraint programming methodologies are combined with the algorithm to show their complementary strengths. Numerical studies using illustrative data with high demand granularity (i.e., a large number of small-sized customer orders) demonstrate that the proposed decomposition heuristic has consistent results minimizing the total cost (i.e., on average 8.75% gap with the best lower bound value found by MILP) and, the developed hybrid approach is capable of solving real sized instances within a reasonable amount of time (i.e., on average 92% faster than MILP in CPU time).     

Optimal design and operations of supply chain networks for water management in shale gas production: MILFP model and algorithms for the water‐energy nexus

The optimal design and operations of water supply chain networks for shale gas production is addressed. A mixed‐integer linear fractional programming (MILFP) model is developed with the objective to maximize profit per unit freshwater consumption, such that both economic performance and water‐use efficiency are optimized. The model simultaneously accounts for the design and operational decisions for freshwater source selection, multiple transportation modes, and water management options. Water management options include disposal, commercial centralized wastewater treatment, and onsite treatment (filtration, lime softening, thermal distillation). To globally optimize the resulting MILFP problem efficiently, three tailored solution algorithms are presented: a parametric approach, a reformulation‐linearization method, and a novel Branch‐and‐Bound and Charnes–Cooper transformation method. The proposed models and algorithms are illustrated through two case studies based on Marcellus shale play, in which onsite treatment shows its superiority in improving freshwater conservancy, maintaining a stable water flow, and reducing transportation burden. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1184–1208, 2015