Multiechelon supply chain planning with sequence‐dependent changeovers and price elasticity of demand under uncertainty

An optimization framework is proposed for a multiechelon multiproduct process supply chain planning under demand uncertainty considering inventory deviation and price fluctuation. In this problem, the sequence‐dependent changeovers occur at the production plants, and price elasticity of demand is considered at the markets. Based on the classic formulation of travelling salesman problem (TSP), a mixed‐integer liner programming (MILP) is developed, whose objective function considers the profit, inventory deviations from the desired trajectories and price changes simultaneously. Model predictive control (MPC) approach is adopted to tackle the uncertain issues, as well as the inventory and price maintenance. The applicability of the proposed model and approach was illustrated by solving a supply chain example. Some issues, including length of the control horizon, price elasticity of demand, weights, inventory trajectories, and changeovers, are discussed based on the computational results. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

多期生物燃料供应链网络建模与多目标优化

建立了一个基于多目标优化以及生命周期评价（LCA）的多期生物燃料供应链模型。该模型的3个目标函数分别为总折现利润、平均单位能量生物燃料的温室气体排放和化石能源投入（economic,energy,environmental,3E）。为了将生物质生产的季节性以及库存等问题引入模型中,需要对每年进行多期划分。考虑到需要进一步引入供应链的扩张,模型的时间跨度设定为3年。此外,该模型还考虑了生物质产地、工厂,生物燃料市场的选址以及各节点间的物流流量等问题。通过将非线性的后两个目标函数利用ε-constraint法转化为线性约束条件,该模型最终被转化为混合整数线性规划（MILP）问题并得以求解。对解得的非劣解在三维坐标系上线性插值可得非劣解所在曲面,它揭示了3E目标之间的权衡取舍关系。还使用了一个基于中国国情的数据的案例对该模型进行检验。     

Decision support for integrated refinery supply chains: Part 1. Dynamic simulation

Supply chain studies are increasingly given top priority in enterprise-wide management. Present-day supply chains involve numerous, heterogeneous, geographically distributed entities with varying dynamics, uncertainties, and complexity. The performance of a supply chain relies on the quality of a multitude of design and operational decisions made by the various entities. In this two-part paper, we demonstrate that a dynamic model of an integrated supply chain can serve as a valuable quantitative tool that aids in such decision-making. In this Part 1, we present a dynamic model of an integrated refinery supply chain. The model explicitly considers the various supply chain activities such as crude oil supply and transportation, along with intra-refinery supply chain activities such as procurement planning, scheduling, and operations management. Discrete supply chain activities are integrated along with continuous production through bridging procurement, production, and demand management activities. Stochastic variations in transportation, yields, prices, and operational problems are considered in the proposed model. The economics of the refinery supply chain includes consideration of different crude slates, product prices, operation costs, transportation, etc. The proposed model has been implemented as a dynamic simulator, called Integrated Refinery In-Silico (IRIS). IRIS allows the user the flexibility to modify not only parameters, but also replace different policies and decision-making algorithms in a plug-and-play manner. It thus allows the user to simulate and analyze different policies, configurations, uncertainties, etc., through an easy-to-use graphical interface. The capabilities of IRIS for strategic and tactical decision support are illustrated using several case studies.     

Decision support for integrated refinery supply chains: Part 2. Design and operation

Supply chain management has continually attracted much attention as companies are constantly looking into areas where they can cut costs and improve profit margin while maintaining customer satisfaction. Optimizing design and operation of the supply chain is vital for this purpose. Simulation models that capture the dynamics and uncertainties of the supply chain can be used to effectively conduct design and operation optimization studies. In Part 1 of this two-part paper, we proposed an integrated refinery supply chain dynamic simulator called Integrated Refinery In-Silico (IRIS). Here, we demonstrate the application of IRIS to provide decision support for optimal refinery supply chain design and operation based on a simulation–optimization framework. Three case studies are presented: identifying the optimal strategy to deal with supply disruptions, optimization of design decisions regarding additional capacity investments, and optimization of policies’ parameters. These decisions are optimized for two objectives: profit margin and customer satisfaction. The framework consists of a linkage between IRIS and a non-dominated sorting genetic algorithm, implemented in a parallel computing environment for computational efficiency. Results indicate that the proposed framework works well for supporting policy and investment decisions in the integrated refinery supply chain.     

Economic model predictive control for inventory management in supply chains

In this paper, we propose economic model predictive control with guaranteed closed-loop properties for supply chain optimization. We propose a new multiobjective stage cost that captures economics as well as risk at a node, using a weighted sum of an economic cost and a tracking stage cost. We also demonstrate integration of scheduling with control using a supply chain example. We integrate a scheduling model for a multiproduct batch plant with a control model for inventory control in a supply chain. We show recursive feasibility of such integrated control problems by developing simple terminal conditions.     

基于收益共享契约的基础油供应链建模方法

针对以炼油企业为主导的基础油供应链中所涉及到的多对一原料采购与定价问题,利用Stackelberg博弈问题求解方法,建立了分散决策模式下实际现有模型与收益共享契约模型,并引入粒子群优化算法,对模型进行参数估计,分析各参数对于供应链各成员利润的影响,同时得到一个广泛适用的采购定价模型。仿真结果表明,采用收益共享契约机制协调了供应链成员间利润分配,提高了原料供应商、炼油企业及供应链总体利润。     

Bi-objective optimization approach to the design and planning of supply chains: Economic versus environmental performances

Traditionally the design of supply chains has been based on economic objectives. However, as societal environment concerns grows, environmental aspects are also emerging at academic and industry levels as decisive factors within the supply chain management context. The investment towards logistics structures that considers both economic and environmental performances is nowadays an important and current research topic.This paper addresses the planning and design of supply chain structures for annual profit maximization, while considering environmental aspects. The latter are accounted for through the Eco-indicator methodology. Profit and environmental impacts are balanced using an optimization approach adapted from symmetric fuzzy linear programming (SFLP), while the supply chain is modelled as a mixed integer linear programming (MILP) optimization problem using the Resource-Task-Network (RTN) methodology. The obtained model applicability is validated through the solution of a set of supply chain problems.     

Optimization for Intelligent Operation of Supply Chains

The schedule for manufacturing and its delivery should be strategically determined to maintain economic and sustainable management of a supply chain. However, most of existing design models for the supply chain assumes that it is known or pre-specified when products are manufactured and delivered, and therefore, only the amount of products and delivery are of interest to optimize within design frameworks. In order to provide high flexibility and cost-effectiveness in manufacturing and supply chain activities, both timing information (i.e., when to produce and deliver) and capacity (i.e., how much to produce and deliver) need to be considered simultaneously. New MILP (mixed integer linear programming) model for the design and optimization of the supply chain has been proposed, in which these two key decision variables are simultaneously optimized. For dealing with computational difficulties resulted from the large-size problem, a sequentially-updating procedure is also proposed. In this sequentially-updating procedure, the whole distribution network is divided into subsystems and optimized interactively within iterative procedure, where each subsystem is sequentially optimized until no profit improvement is observed. The enhanced flexibility of the supply chain can be obtained from this improved design philosophy. This also ensures reliable and robust responsiveness of the supply chain to customers’ demand without sacrificing efficiency and/or cost-effectiveness of manufacturing and delivery activities. Illustrated case studies show that the proposed method is able to deal with large and complex supply chain problems with significant cost savings.     

Optimal planning for the reuse of municipal solid waste considering economic,environmental, and safety objectives

A mathematical programming model is presente for the optimal planning of the reuse of municipal solid waste (MSW) to maximize the economic benefit while simultaneously considering sustainability and safety criteria. The proposed methodology considers several phases of the supply chain including waste separation, distribution to processing facilities, processing to obtain useful products, and distribution of products to consumers. Additionally, the safety criteria are based on the potential fatalities associated with waste management. The proposed optimization model is formulated as a multiobjective optimization problem, which considers three different objectives including the maximization of the net annual profit, the maximization of the amount of reused MSW, and the minimization of the social risk associated with the supply chain. The proposed model is applied to a case study in the central‐west region of Mexico. The results show the tradeoff between the social risk and the economic and environmental criteria. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1881–1899, 2015     

A LCA Based Biofuel Supply Chain Analysis Framework

This paper presents a life cycle assessment （LCA） based biofuel supply chain （SC） analysis framework which enables the study of economic, energy and environmental （3E） performances by using multi-objective opti-mization. The economic objective is measured by the total annual profit, the energy objective is measured by the average fossil energy （FE） inputs per MJ biofuel and the environmental objective is measured by greenhouse gas （GHG） emissions per MJ biofuel. A multi-objective linear fractional programming （MOLFP） model with multi-conversion pathways is formulated based on the framework and is solved by using theε-constraint method. The MOLFP prob-lem is turned into a mixed integer linear programming （MILP） problem by setting up the total annual profit as the optimization objective and the average FE inputs per MJ biofuel and GHG emissions per MJ biofuel as constraints. In the case study, this model is used to design an experimental biofuel supply chain in China. A set of the weekly Pareto optimal solutions is obtained. Each non-inferior solution indicates the optimal locations and the amount of biomass produced, locations and capacities of conversion factories, locations and amount of biofuel being supplied in final markets and the flow of mass through the supply chain network （SCN）. As the model reveals trade-offs among 3E criteria, we think the framework can be a good support tool of decision for the design of biofuel SC.     

A novel adaptive surrogate modeling‐based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations

A novel adaptive surrogate modeling‐based algorithm is proposed to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The integrated optimization problem is formulated as a large scale mixed‐integer nonlinear programming (MINLP) problem. To overcome the computational challenge of solving the integrated MINLP problem, an efficient solution algorithm based on the bilevel structure of the integrated problem is proposed. Because processing times and costs of each batch are the only linking variables between the scheduling and dynamic optimization problems, surrogate models based on piece‐wise linear functions are built for the dynamic optimization problems of each batch. These surrogate models are then updated adaptively, either by adding a new sampling point based on the solution of the previous iteration, or by doubling the upper bound of total processing time for the current surrogate model. The performance of the proposed method is demonstrated through the optimization of a multiproduct sequential batch process with seven units and up to five tasks. The results show that the proposed algorithm leads to a 31% higher profit than the sequential method. The proposed method also outperforms the full space simultaneous method by reducing the computational time by more than four orders of magnitude and returning a 9.59% higher profit. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4191–4209, 2015     

Integrated safety stock management for multi-stage supply chains under production capacity constraints

In the petrochemical, chemical and pharmaceutical industries, supply chains typically consist of multiple stages of production facilities, warehouse/distribution centers, logistical subnetworks and end customers. Supply chain performance in the face of various market and technical uncertainties is usually measured by service level, that is, the expected fraction of demand that the supply chain can satisfy within a predefined allowable delivery time window. Safety stock is introduced into supply chains as an important hedge against uncertainty in order to provide customers with the promised service level. Although a higher safety stock level guarantees a higher service level, it does increase the supply chain operating cost and thus these levels must be suitably optimized.The complexities in safety stock management for multi-stage supply chain with multiple products and production capacity constraints arise from: (1) the nonlinear performance functions that relate the service level, expected inventory with safety stock control variables at each site; (2) the interdependence of the performances of different sites; and (3) finally the margin by which production capacity exceeds the uncertain demand. Given the complexities, the integrated management of safety stocks across the supply chain imposes significant computational challenges. In this research, we propose an approach in which the evaluation of the performance functions and the decision on safety stock related variables are decomposed into two separate computational frameworks. For evaluating the performance functions, off-line computation using a discrete event simulation model is proposed. A linear programming based safety stock management model is developed, in which the safety stock control variables (the target inventory levels used in production planning and scheduling models, base-stock levels for the base-stock policy at the warehouses) and service levels at both plant stage and warehouse stages are used as important decision variables. In the linear programming model, the nonlinear performance functions, interdependence of the performances, and the safety production capacity limits in safety stock management are properly represented.To demonstrate the effectiveness of the proposed safety stock management model, a case study of a realistically scaled polymer supply chain problem is presented. In the case problem, the supply chain is composed of two geographically separated production sites and 3–8 warehouses supplying 10 final products to 30 sales regions.     

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.     

Design of responsive supply chains under demand uncertainty

This paper addresses the optimization of supply chain design and planning under responsive criterion and economic criterion with the presence of demand uncertainty. The supply chain consists of multi-site processing facilities and corresponds to a multi-echelon production network with both dedicated and multiproduct plants. The economic criterion is measured in terms of net present value, while the criterion for responsiveness accounts for transportation times, residence times, cyclic schedules in multiproduct plants and inventory management. By using a probabilistic model for stock-out, the expected lead time is proposed as the quantitative measure of supply chain responsiveness. The probabilistic model can also predict the safety stock levels by integrating stock-out probability with demand uncertainty. These are all incorporated into a multi-period mixed-integer nonlinear programming (MINLP) model, which takes into account the selection of manufacturing sites and distribution centers, process technology, production levels, scheduling and inventory levels. The problem is formulated as a bi-criterion optimization model that maximizes the net present value and minimizes the expected lead time. The model is solved with the -constraint method and produces a Pareto-optimal curve that reveals how the optimal net present value, supply chain network structure and safety stock levels change with different values of the expected lead time. A hierarchical algorithm is also proposed based on the decoupling of different decision-making levels (strategic and operational) in the problem. The application of this model and the proposed algorithm are illustrated with two examples of polystyrene supply chains.     

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.     

考虑环境影响的多产品间歇化工过程优化排序

提出一种用于多产品厂排序的多目标优化模型 ,其目标函数同时考虑了总生产时间和废物对环境的影响 ,定义了关于废物的环境影响因子及决策因子 ,用以对总生产时间和废物及其对环境的影响进行权衡 .采用改进的模拟退火算法对具有不同决策因子和环境影响因子情况下的算例进行了求解 ,结果表明 ,该模型能够较好地反映环境因素在多产品厂排序问题中的影响 ,使排序结果达到生产时间和环境影响的综合最优     

Chemical supply chain network optimization

Chemical supply chain networks provide large opportunities for cost reductions through the redesign of the flow of material from producer to customer. In this paper we present a mixed-integer linear program (MILP) capable of optimizing a multi-product supply chain network made up of production sites, an arbitrary number of echelons of distribution centers, and customer sites. The emphasis of our approach is on the redesign of existing supply chain networks. The model does not lump customer demand into zones, but rather deals with individual customer demand to directly address customer preferred mode of transport at each location. Historical records can be used to fix decision variables in the model so that a base case can be computed to validate the model and contrast it against the optimized network. The details inherent in this approach allow the optimization results to be partitioned and prioritized for implementation. The model results are processed to assign cost components to individual customer records. A simple case study is presented to illustrate the method and actual industrial results are reviewed.     

多产品间歇化工过程最优设计的研究——启发法

修正了modi等人提出的多产品间歇化工过程最优设计的混合整数非线性规划(MINLP)模型,使之不仅允许中间贮罐的存在,还可调整以同步或异步方式操作的平行单元数.还提出了对以上模型求解的启发算法,其特点是对决策变量的初值要求低,计算速度快,所需内存小,与严格的数学规划法相比较,其相对误差小于1%.以实例说明了方法的有效性.     

Taguchi's parametric design approach for the selection of optimization variables in a refrigerated gas plant

This paper presents a systematic procedure for selecting optimization variables in a refrigerated gas plant (RGP) using the Taguchi method. A dynamic RGP model developed under HYSYS environment is utilized as a test bed. Nine variables with three levels each are employed for optimizing RGP profit. These optimization variables are selected due to their roles as manipulated variables in controlling the process. Results are validated by comparing optimum values of RGP profit obtained through a set of HYSYS experiments and those from analyses of means.