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.     

Multistage stochastic programming for the closed-loop supply chain planning with mobile modules under uncertainty

Traditional supply chains usually follow fixed facility designs which coincide with the strategic nature of supply chain management (SCM). However, as the global market turns more volatile, the concept of mobile modularization has been adopted by increasingly more industrial practitioners. In mobile modular networks, modular units can be installed or removed at a particular site to expand or reduce the capacity of a facility, or relocated to other sites to tackle market volatility. In this work, we formulate a mixed-integer linear programming (MILP) model for the closed-loop supply chain network planning with modular distribution and collection facilities. To further deal with uncertain customer demands and recovery rates, we extend our model to a multistage stochastic programming model and efficiently solve it using a tailored stochastic dynamic dual integer programming (SDDiP) with Magnanti-Wong enhanced cuts. Computational experiments show that the added Magnanti-Wong cuts in the proposed algorithm can effectively close the gap between upper and lower bounds, and the benefit of mobile modules is evident when the temporal and spatial variability of customer demand is high.     

Supply chain design and multilevel planning—An industrial case

In this paper we address a case study, inspired by a real agrochemicals supply chain, with two main objectives, structured in two stages. In the first stage we redesign the global supply chain network and optimise the production and distribution plan considering a time horizon of 1 year, providing a decision support tool for long term investments and strategies. The output decisions from the first stage, mainly the supply chain configuration and allocation decisions, are the input parameters for the second stage where a short term operational model is used to test the accuracy of the derived design and plan. The outputs of this stage are detailed production and distribution plans and an assessment of the customer service level.At the operational level, failure to meet on time the demand fulfilment targets established at the planning stage is usually caused by allocation of too many products/customers to the same resource in the first stage, especially to those surrounding the system bottlenecks. This introduces idle periods in the planning of the bottleneck resources, preventing the whole system from operating at its maximum capacity. An analytical methodology was developed to use the information gathered in the second step to improve the supply chain design and plan by enforcing a more distributed allocation of products/customers to the available resources in each time period.     

Distributionally robust chance constrained programming with generative adversarial networks (GANs)

This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to fully extract distributional information from historical data in a nonparametric and unsupervised way without a priori approximation or assumption. Since GAN utilizes deep neural networks, complicated data distributions and modes can be learned, and it can model uncertainty efficiently and accurately. Distributionally robust chance constrained programming takes into consideration ambiguous probability distributions of uncertain parameters. To tackle the computational challenges, sample average approximation method is adopted, and the required data samples are generated by GAN in an end-to-end way through the differentiable networks. The proposed framework is then applied to supply chain optimization under demand uncertainty. The applicability of the proposed approach is illustrated through a county-level case study of a spatially explicit biofuel supply chain in Illinois.     

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     

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.     

Strategic network design of downstream petroleum supply chains: Single versus multi-entity participation

The petroleum supply chain (PSC) is a highly competitive system that motivates complex studies for decisions involving different problems such as the redesign aimed at optimizing existing distribution networks. This paper considers a multi-entity, multi-echelon, multi-product and multi-transportation downstream PSC network with shared installations, resource capacities, supply sources and demand requirements. A deterministic mixed integer linear program (MILP) is developed for strategic design and planning of the downstream PSC network that determines optimal depot locations, capacities, transportation modes, routes and network affectations for long term planning. The MILP maximizes the multi-echelon total profits for the petroleum companies along the supply, refining, distribution and retail stages. A multi-entity PSC network is considered, involving companies’ financial participation in refineries, transportation and storage depots. The MILP is tested with the real-case Portuguese PSC network involving production at local refineries and supply from a regional hub. Uni-entity networks as well as multi-entity networks with competitive or individualistic operation are modeled, presenting the current, grassroots and retrofit designs.     

OPTIMAL DESIGN OF MULTISITE BATCH-STORAGE NETWORK UNDER SCENARIO-BASED DEMAND UNCERTAINTY

An effective methodology is reported for the optimal design of multisite batch production/transportation and storage networks under uncertain demand forecasting. We assume that any given storage unit can store one material type that can be purchased from suppliers, internally produced, internally consumed, transported to or from other plant sites, and/or sold to customers. We further assume that a storage unit is connected to all processing and transportation stages that consume/produce or move the material to which that storage unit is dedicated. Each processing stage transforms a set of feedstock materials or intermediates into a set of products with constant conversion factors. A batch transportation process can transfer one material or multiple materials at once between plant sites. The objective for optimization is to minimize the probability averaged total cost, which consists of the raw material procurement cost, the cost of setting up processes, inventory holding costs of the storage units, and the capital costs of processes and storage units. A novel production and inventory analysis formulation, the PSW (periodic square wave) model, provides useful expressions for the upper/lower bounds and average level of the storage inventory. The expressions for the Kuhn-Tucker conditions of the optimization problem can be reduced to two sub-problems. The first yields analytical solutions for determining lot sizes, and the second is a separable concave minimization network flow sub-problem whose solution yields the average material flow rates through the networks for the given demand forecast scenario. The result of this study will contribute to the optimal design and operation of large-scale supply chain systems.     

Robust decision making for hybrid process supply chain systems via model predictive control

Model predictive control (MPC) is a promising solution for the effective control of process supply chains. This paper presents an optimization-based decision support tool for supply chain management, by means of a robust MPC strategy. The proposed formulation: (i) captures uncertainty in model parameters and demand by stochastic programming, (ii) accommodates hybrid process systems with decisions governed by logical conditions/rulesets, and (iii) addresses multiple supply chain performance metrics including customer service and economics, within an integrated optimization framework. Two mechanisms for uncertainty propagation are presented – an open-loop approach, and an approximate closed-loop strategy. The performance of the robust MPC framework is analyzed through its application to two process supply chain case studies. The proposed approach is shown to provide a substantial reduction in the occurrence of back orders when compared to a nominal MPC implementation.     

A multi-scale framework for CO2 capture,utilization, and sequestration: CCUS and CCU

We present a multi-scale framework for the optimal design of CO₂ capture, utilization, and sequestration (CCUS) supply chain network to minimize the cost while reducing stationary CO₂ emissions in the United States. We also design a novel CO₂ capture and utilization (CCU) network for economic benefit through utilizing CO₂ for enhanced oil recovery. Both the designs of CCUS and CCU supply chain networks are multi-scale problems which require decision making at material, process and supply chain levels. We present a hierarchical and multi-scale framework to design CCUS and CCU supply chain networks with minimum investment, operating and material costs. While doing so, we take into consideration the selection of source plants, capture processes, capture materials, CO₂ pipelines, locations of utilization and sequestration sites, and amounts of CO₂ storage. Each CO₂ capture process is optimized, and the best materials are screened from large pool of candidate materials. Our optimized CCUS supply chain network can reduce 50% of the total stationary CO₂ emission in the U.S. at a cost of $35.63 per ton of CO₂ captured and managed. The optimum CCU supply chain network can capture and utilize CO₂ to make a total profit of more than 555 million dollars per year ($9.23 per ton). We have also shown that more than 3% of the total stationary CO₂ emissions in the United States can be eliminated through CCU networks at zero net cost. These results highlight both the environmental and economic benefits which can be gained through CCUS and CCU networks. We have designed the CCUS and CCU networks through (i) selecting novel materials and optimized process configurations for CO₂ capture, (ii) simultaneous selection of materials and capture technologies, (iii) CO₂ capture from diverse emission sources, and (iv) CO₂ utilization for enhanced oil recovery. While we demonstrate the CCUS and CCU networks to reduce stationary CO₂ emissions and generate profits in the United States, the proposed framework can be applied to other countries and regions as well.     

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.     

Modular supply chain optimization considering demand uncertainty to manage risk

Supply chain under demand uncertainty has been a challenging problem due to increased competition and market volatility in modern markets. Flexibility in planning decisions makes modular manufacturing a promising way to address this problem. In this work, the problem of multiperiod process and supply chain network design is considered under demand uncertainty. A mixed integer two-stage stochastic programming problem is formulated with integer variables indicating the process design and continuous variables to represent the material flow in the supply chain. The problem is solved using a rolling horizon approach. Benders decomposition is used to reduce the computational complexity of the optimization problem. To promote risk-averse decisions, a downside risk measure is incorporated in the model. The results demonstrate the several advantages of modular designs in meeting product demands. A pareto-optimal curve for minimizing the objectives of expected cost and downside risk is obtained.     

MPEC strategies for cost optimization of pipeline operations

This study develops a mathematical program with equilibrium constraints (MPECs) approach for efficient operation of gas pipelines. The resulting model handles time dependent operations in order to determine minimum energy consumption and operating cost over a given time horizon. The MPEC structure also allows flow reversals, flow transitions and other nonsmooth elements to be incorporated within the approach. Applied to industrial gas pipelines, this approach can also deal with customer demand satisfaction in the presence of compressor outages and minimize recovery time for systems that are unable to meet customer demands at all times. A large-scale oxygen pipeline case study is considered to demonstrate this approach and complex energy pricing schemes are also applied to this problem. These schemes include time of day electricity pricing, along with extensions to Real Time Pricing and Day Ahead Pricing. Compared to flat rate and minimum energy optimizations, respectively, we observe operating cost savings up to 5.13% for time of day electricity pricing and up to 12.85% for Real Time Pricing.     

Hybrid simulation based optimization approach for supply chain management

In this work, we propose a hybrid simulation optimization approach that addresses the problem of supply chain management. We formulated the problem as a mathematical model which minimizes the summation of production cost, transportation cost, inventory holding and shortage costs, subject to capacity and inventory balance constraints and propose a hybrid approach combining mathematical programming and simulation model to solve this problem. The main objective of this approach is to overcome the computational complexity associated with solving the underlying large-scale mixed integer linear problem and to provide a better representation of supply chain reality. The simulation-based optimization strategy uses an agent-based system to model the supply chain network. Each entity in the supply chain is represented as an agent whose activity is described by a collection of behavioral rules. The overall system is coupled with an optimization algorithm that is designed to address planning and scheduling level decisions.     

A general modular framework for the integrated optimal management of an industrial gases supply-chain and its production systems

A general modular methodology for the simultaneous optimization of the supply-chain network and the production systems of a general industrial gas producer is developed and implemented in a C++ program. The formulation and solution algorithm are specifically designed to be able to work on-line and to determine the optimal assignments of production site output to customer demand in the supply-chain and the corresponding optimal operating conditions for the production plants in integrated fashion. Here, the production network is not simply modelled as a set of product sources, rather the model is detailed enough to allow effective and feasible optimization of the entire system. Moreover, the proposed approach can be easily combined with the rolling horizon technique to mitigate the uncertainties in demand. The modelling strategies, employed for the supply-chain network and the production sites, along with the solution approach, adopted for the resulting optimization problem, are detailed. BzzMath library classes are used to meet the computational efficiency requirements for on-line applications. The effectiveness of the proposed methodology is demonstrated on a case study involving a portion of the real supply-chain and network of production facilities of Linde Gas Italia S.r.l.     

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.     

Managing demand uncertainty in supply chain planning

In this work, we provide an overview of our previously published works on incorporating demand uncertainty in midterm planning of multisite supply chains. A stochastic programming based approach is described to model the planning process as it reacts to demand realizations unfolding over time. In the proposed bilevel-framework, the manufacturing decisions are modeled as ‘here-and-now’ decisions, which are made before demand realization. Subsequently, the logistics decisions are postponed in a ‘wait-and-see’ mode to optimize in the face of uncertainty. In addition, the trade-off between customer satisfaction level and production costs is also captured in the model. The proposed model provides an effective tool for evaluating and actively managing the exposure of an enterprises assets (such as inventory levels and profit margins) to market uncertainties. The key features of the proposed framework are highlighted through a supply chain planning case study.     

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.     

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.     

Design under uncertainty of hydrocarbon biorefinery supply chains: Multiobjective stochastic programming models,decomposition algorithm,and a Comparison between CVaR and downside risk

A bicriterion, multiperiod, stochastic mixed‐integer linear programming model to address the optimal design of hydrocarbon biorefinery supply chains under supply and demand uncertainties is presented. The model accounts for multiple conversion technologies, feedstock seasonality and fluctuation, geographical diversity, biomass degradation, demand variation, government incentives, and risk management. The objective is simultaneous minimization of the expected annualized cost and the financial risk. The latter criterion is measured by conditional value‐at‐risk and downside risk. The model simultaneously determines the optimal network design, technology selection, capital investment, production planning, and logistics management decisions. Multicut L‐shaped method is implemented to circumvent the computational burden of solving large scale problems. The proposed modeling framework and algorithm are illustrated through four case studies of hydrocarbon biorefinery supply chain for the State of Illinois. Comparisons between the deterministic and stochastic solutions, the different risk metrics, and two decomposition methods are discussed. The computational results show the effectiveness of the proposed strategy for optimal design of hydrocarbon biorefinery supply chain under the presence of uncertainties. © 2012 American Institute of Chemical Engineers AIChE J, 2012