Supply chain management using an optimization driven simulation approach

In this work, we propose a hybrid simulation‐based optimization framework to solve the supply chain management problem. The hybrid approach combines a mathematical programming model with an agent‐based simulation model and uses them in an iterative framework. The optimization model is used to guide the decisions toward an optimal allocation of resources given the realistic supply chain representation given by the simulation. Thus, the proposed approach provides a more realistic solution compared to a stand‐alone optimization model, often a simplified representation of the actual system, by making use of the simulation model, which captures the detailed dynamic behavior of the system. A multiobjective problem has been formulated by taking into consideration the environmental impact of supply chain operations. The proposed framework has been applied to small‐scale case studies to study the effectiveness of the approach for such problems. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4612–4626, 2013     

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.     

A computationally efficient simulation-based optimization method with region-wise surrogate modeling for stochastic inventory management of supply chains with general network structures

Simulation-based optimization is widely used to improve the performance of an inventory system under uncertainty. However, the black-box function between the input and output, along with the expensive simulation to reproduce a real inventory system, introduces a huge challenge in optimizing these performances. We propose an efficient framework for reducing the total operation cost while satisfying the service level constraints. The performances of each inventory in the system are estimated by kriging models in a region-wise manner which greatly reduces the computational time during both sampling and optimization. The aggregated surrogate models are optimized by a trust-region framework where a model recalibration process is used to ensure the solution's validity. The proposed framework is able to solve general supply chain problems with the multi-sourcing capability, asynchronous ordering, uncertain demand and stochastic lead time. This framework is demonstrated by two case studies with up to 18 nodes with inventory holding capability in the network.     

Integrated multi‐echelon supply chain design with inventories under uncertainty: MINLP models,computational strategies

We address in this article a problem that is of significance to the chemical industry, namely, the optimal design of a multi‐echelon supply chain and the associated inventory systems in the presence of uncertain customer demands. By using the guaranteed service approach to model the multi‐echelon stochastic inventory system, we develop an optimization model to simultaneously determine the transportation, inventory, and network structure of a multi‐echelon supply chain. The model is an MINLP with a nonconvex objective function including bilinear, trilinear, and square root terms. By exploiting the properties of the basic model, we reformulate this problem as a separable concave minimization program. A spatial decomposition algorithm based on the integration of Lagrangean relaxation and piecewise linear approximation is proposed to obtain near global optimal solutions with reasonable computational expense. Examples for specialty chemicals and industrial gas supply chains with up to 15 plants, 100 potential distribution centers, and 200 markets are presented. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

A hybrid CPU-Graphics Processing Unit (GPU) approach for computationally efficient simulation-optimization

Simulation-optimization (Sim-Opt) is a widely used optimization technique that enables the use of simulation model so as naturally describe system complexity and stochastics. A key barrier to its broader adoption is the high computational cost associated with simulation that often limits its practicability. In this paper, we propose the use of GPU parallel computing, to enhance the computational efficiency of Sim-Opt. The main objective of this work is to develop a systematic framework that can be used to construct an efficient hybrid CPU-GPU program. The optimization of a process monitoring model using a Genetic Algorithm is used as a case study to illustrate the proposed approach. Our results show an over 100× acceleration of computation time by the developed hybrid program in comparison to a traditional CPU-based approach.     

Mid-term supply chain planning under demand uncertainty: customer demand satisfaction and inventory management

This paper utilizes the framework of mid-term, multisite supply chain planning under demand uncertainty to safeguard against inventory depletion at the production sites and excessive shortage at the customer. A chance constraint programming approach in conjunction with a two-stage stochastic programming methodology is utilized for capturing the trade-off between customer demand satisfaction (CDS) and production costs. In the proposed model, the production decisions are made before demand realization while the supply chain decisions are delayed. The challenge associated with obtaining the second stage recourse function is resolved by first obtaining a closed-form solution of the inner optimization problem using linear programming duality followed by expectation evaluation by analytical integration. In addition, analytical expressions for the mean and standard deviation of the inventory are derived and used for setting the appropriate CDS levels in the supply chain. A three-site example supply chain is studied within the proposed framework for providing quantitative guidelines for setting customer satisfaction levels and uncovering effective inventory management options. Results indicate that significant improvement in guaranteed service levels can be obtained for a small increase in the total cost.     

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     

Risk management for a global supply chain planning under uncertainty: Models and algorithms

In this article, we consider the risk management for mid‐term planning of a global multi‐product chemical supply chain under demand and freight rate uncertainty. A two‐stage stochastic linear programming approach is proposed within a multi‐period planning model that takes into account the production and inventory levels, transportation modes, times of shipments, and customer service levels. To investigate the potential improvement by using stochastic programming, we describe a simulation framework that relies on a rolling horizon approach. The studies suggest that at least 5% savings in the total real cost can be achieved compared with the deterministic case. In addition, an algorithm based on the multi‐cut L‐shaped method is proposed to effectively solve the resulting large scale industrial size problems. We also introduce risk management models by incorporating risk measures into the stochastic programming model, and multi‐objective optimization schemes are implemented to establish the tradeoffs between cost and risk. To demonstrate the effectiveness of the proposed stochastic models and decomposition algorithms, a case study of a realistic global chemical supply chain problem is presented. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

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.     

Integration of control theory and scheduling methods for supply chain management

In this paper, we propose to use distributed model predictive control for supply chain optimization. In particular, we focus on inventory management in supply chains. We use cooperative model predictive control, in which each agent makes their local decisions by optimizing the overall supply chain objective. Motivated by recent results in Stewart, Wright, and Rawlings (2011), we develop a new cooperative MPC algorithm that is applicable to any stabilizable system, and in particular to supply chain models. We illustrate cooperative MPC for a two node supply chain example and compare its performance and properties with other classical distributed operating policies.     

Optimal design of batch‐storage network considering ownership

This article develops a model of multi‐national supply chain activities, which incorporates currency storage units to manage currency flows associated with activities such as raw material procurement, processing, inventory control, transportation, and finished product sales. The core contribution of this model is that it facilitates the quantitative investigation of the influence of macroscopic economic factors such as ownership on supply chain operational decisions. The supply chain system is modeled as a batch‐storage network with recycle streams. The supply chain optimization problem is posed with the objective of minimizing the opportunity costs of annualized capital investments and currency/material inventories, while taking into account the benefit to stockholders in the numeraire currency. The major constraints on the optimization are that the material and currency storage units must not be depleted. A production and inventory analysis formulation (the periodic square wave model) provides useful expressions for the upper and lower bounds and for the average levels of the currency and material inventory holdings. The expressions for the Kuhn‐Tucker conditions of the optimization problem are reduced to a subproblem that allows development of analytical lot‐sizing equations. The lot sizes of procurement, production, transportation, and financial transactions can be determined in closed form once the average flow rates are known. The key result we obtain is that optimal value of the economic order quantity changes substantially with variation in ownership, thus showing quantitatively that ownership structure does impact plant operation. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2418–2425, 2018     

Fleet sizing in chemical supply chains using agent-based simulation

Fleet sizing is an essential element of chemical supply chain management. It is expensive to purchase and maintain tank cars. Further, the sizing decision is not an isolated one and is closely linked to fleet routing, inventory management and other aspects of logistics and supply chain management. Traditional methods to determine the size of fleets rely on coarse models of the supply chain. In this paper, we present a detailed agent-based simulation model of a multisite chemical supply chain that brings out the intricacies of the tank car fleet sizing problem. The model explicitly takes into account the independent decision making of the different entities as well as the interactions across operations such as replenishment planning and order assignment. Our simulation studies show that different fleet sizes and routing policies can have significant impact on the overall performance of the supply chain including on customer satisfaction and plant performance.     

炼油企业库存管理

以销售预测为依托,对市场需求不确定的炼油企业供应链的库存管理进行探索性研究.提出了炼油企业库存管理的策略、库存管理参数设计和算法,实际应用结果证明了该策略的合理性.     

Optimal biorefinery product allocation by combining process and economic modeling

The integrated biorefinery has the opportunity to provide a strong, self-dependent, sustainable alternative for the production of bulk and fine chemicals, e.g. polymers, fiber composites and pharmaceuticals as well as energy, liquid fuels and hydrogen. Although most of the fundamental processing steps involved in biorefining are well-known, there is a need for a methodology capable of evaluating the integrated processes in order to identify the optimal set of products and the best route for producing them. The complexity of the product allocation problem for such processing facilities demands a process systems engineering approach utilizing process integration and mathematical optimization techniques to ensure a targeted approach and serve as an interface between simulation work and experimental efforts. The objective of this work is to assist the bioprocessing industries in evaluating the profitability of different possible production routes and product portfolios while maximizing stakeholder value through global optimization of the supply chain. To meet these ends, a mathematical optimization based framework is being developed, which enables the inclusion of profitability measures and other techno-economic metrics along with process insights obtained from experimental as well as modeling and simulation studies.     

Petroleum allocation at PETROBRAS: Mathematical model and a solution algorithm

Petroleum allocation is an important link for the integration of petroleum supply chain at PETROBRAS as it is responsible for refining the strategic supply planning information to be used at the operation levels. In this work we describe how mathematical programming is being used to solve the petroleum allocation problem and we show the effectiveness of a local search method by optimization to solve real industrial problems. We propose a mixed-integer linear programming formulation of the problem that relies on a time/space discretization network. As the model cannot be solved for the industrial size instances of the problem, and not even a feasible solution can be found after 15 days of computation, we implement an algorithm based on a heuristic to find a feasible solution and on a local search procedure based on optimization to improve it. Using this algorithm, solutions are found for all the case studies within 10% of optimality in less than 5 h.     

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 multi-echelon vehicle routing problem with cross docking in supply chain management

Multi-echelon distribution networks are quite common in supply chain and logistics. Deliveries of multiple items from factories to customers are managed by routing and consolidating shipments in warehouses carrying on long-term inventories. On the other hand, cross-docking is a logistics technique that differs from warehousing because products are no longer stored at intermediate depots. Instead, cross-dock facilities consolidate incoming shipments based on customer demands and immediately deliver them to their destinations. Hybrid strategies combining direct shipping, warehousing and cross-docking are usually applied in real-world distribution systems. This work deals with the operational management of hybrid multi-echelon multi-item distribution networks. The goal of the N-echelon vehicle routing problem with cross-docking in supply chain management (the VRPCD-SCM problem) consists of satisfying customer demands at minimum total transportation cost. A monolithic optimization framework for the VRPCD-SCM based on a mixed-integer linear mathematical formulation is presented. Computational results for several problem instances are reported.     

Robust supply chain performance via Model Predictive Control

This paper presents a novel robust Model Predictive Control (MPC) method for real-time supply chain optimization under uncertainties. This method optimizes the closed-loop economic performance of supply chain systems and addresses different sources of uncertainties located external to and within the feedback loop. The future system behavior is predicted by a closed-loop model, which includes both the open-loop system model and a controller model described by an optimization problem. The robust MPC formulation involves the solution of a constrained, bi-level stochastic optimization problem, which is transformed into a tractable problem involving a limited number of deterministic conic optimization problems solved reliably using an interior point method. The robust controller is applied to a real industrial multi-echelon supply chain optimization problem, and its performance is shown to reduce stock-outs without excessive inventories.     

聚氯乙烯生产过程全流程调度

研究了电石法制聚氯乙烯(PVC)全流程生产调度问题, 包括从电石生产、盐水电解到氯乙烯(VCM)聚合产品出厂各环节, 其中电石生产和VCM聚合是间歇过程, 其他生产环节是连续过程, 是一个混杂系统调度问题。本文针对过程特性对该问题进行了合理假设, 以包括电耗、库存、产品型号切换、交货延迟等的成本最小为目标, 建立了基于离散时间表示的混合整数线性规划(MILP)调度优化模型, 并针对一个案例进行了调度优化求解和分析, 验证了模型的可行性。     

Balancing responsiveness and economics in process supply chain design with multi‐echelon stochastic inventory

This article is concerned with the optimal design of multi‐echelon process supply chains (PSCs) under economic and responsive criteria with considerations of inventory management and demand uncertainty. The multi‐echelon inventory systems are modeled with the guaranteed service approach to handle the uncertain demands at each echelon. The maximum guaranteed service time of the last echelon of the PSC is proposed as a measure of a PSC's responsiveness. The problem is formulated as a bi‐criterion mixed‐integer nonlinear program (MINLP) with the objectives of minimizing the annualized cost (economic objective) and minimizing the maximum guaranteed service times of the markets (responsiveness objective). The model simultaneously predicts the optimal network structure, transportation amounts, and inventory levels under different specifications of the PSC responsiveness. An example on acetic acid supply chain is presented to illustrate the application of the proposed model and to comprehensively compare different measures of PSC responsiveness. © 2010 American Institute of Chemical Engineers AIChE J, 2011