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).     

Flexibility analysis of process supply chain networks

One of the key fundamentals for organizations to remain competitive in the present economic climate is to effectively manage their supply chains under uncertainty. The notion of supply chain flexibility attempts to characterize the ability of a supply chain to perform satisfactorily in the face of uncertainty. However, limited quantitative analysis is available. In this work, we utilize a flexibility analysis framework developed within the context of process operations and design to characterize supply chain flexibility. This framework also provides a quantitative mapping to various types of flexibility discussed in the operations research and management science literature. Two case studies are included to illustrate the application of this framework for analyzing the flexibility of existing supply chain processes, as well as utilizing it in supply chain design.     

Theoretical framework for formulating MIP scheduling models with multiple and non-uniform discrete-time grids

We present a framework for the formulation of MIP scheduling models based on multiple and nonuniform discrete time grids. In a previous work we showed that it is possible to use different (possibly non-uniform) time grids for each task, unit, and material. Here, we generalize these ideas to account for general resources, and a range of processing characteristics such as limited intermediate storage and changeovers. Each resource has its own grid based on resource consumption and availability allowing resource constraints to be modeled more accurately without increasing the number of binary variables. We develop algorithms to define the unit-, task-, material-, and resource-specific grids directly from problem data. Importantly, we prove that the multi-grid formulation is able to find a schedule with the same optimal objective as the discrete-time single-grid model with an arbitrarily fine grid. The proposed framework leads to the formulation of models with reduced number of binary variables and constraints, which are able to find good solutions faster than existing models.     

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.     

An adjustable robust optimization approach to scheduling of continuous industrial processes providing interruptible load

To ensure the stability of the power grid, backup capacities are called upon when electricity supply does not meet demand due to unexpected changes in the grid. As part of the demand response efforts in recent years, large electricity consumers are encouraged by financial incentives to provide such operating reserve in the form of load reduction capacities (interruptible load). However, a major challenge lies in the uncertainty that one does not know in advance when load reduction will be requested. In this work, we develop a scheduling model for continuous industrial processes providing interruptible load. An adjustable robust optimization approach, which incorporates recourse decisions using linear decision rules, is applied to model the uncertainty. The proposed model is applied to an illustrative example as well as a real-world air separation case. The results show the benefits from selling interruptible load and the value of considering recourse in the decision-making.     

Robust design and operations of hydrocarbon biofuel supply chain integrating with existing petroleum refineries considering unit cost objective

This paper addresses the optimal design and planning of the advanced hydrocarbon biofuel supply chain with the unit cost objective. Benefited from the drop-in properties of advanced hydrocarbon biofuels, the supply chain takes advantage of the existing petroleum infrastructure, which may lead to significant capital and transportation savings. A mixed-integer linear programming model is proposed to simultaneously consider the supply chain design, integration strategy selection, and production planning. A robust optimization approach which tradeoffs the performance and conservatism is adopted to deal with the demand and supply uncertainty. Moreover, the unit cost objective makes the final products more cost-competitive. The resulting mixed-integer linear fractional programming model is solved by tailored optimization algorithm. County level cases in Illinois are analyzed and compared to show the advantage of the proposed optimization framework. The results show that the preconversion to petroleum-upgrading pathway is more economical when applying the unit cost objective.     

Integration of production planning and scheduling: Overview, challenges and opportunities

We review the integration of medium-term production planning and short-term scheduling. We begin with an overview of supply chain management and the associated planning problems. Next, we formally define the production planning problem and explain why integration with scheduling leads to better solutions. We present the major modeling approaches for the integration of scheduling and planning decisions, and discuss the major solution strategies. We close with an account of the challenges and opportunities in this area.     

Optimal scheduling of single stage batch plants with direct heat integration

This paper addresses the multi-objective optimization problem arising in the operation of heat integrated batch plants, where makespan and utility consumption are the two conflicting objectives. A new continuous-time MILP formulation with general precedence variables is proposed to simultaneously handle decisions related to timing, product sequencing, heat exchanger matches (selected from a two-stage superstructure) and their heat loads. It features a complex set of timing constraints to synchronize heating and cooling tasks, derived from Generalized Disjunctive Programming. Through the solution of an industrial case study from a vegetable oil refinery, we show that major savings in utilities can be achieved while generating the set of Pareto optimal solutions through the ɛ-constraint method.     

Biomass-to-bioenergy and biofuel supply chain optimization: Overview,key issues and challenges

This article describes the key challenges and opportunities in modeling and optimization of biomass-to-bioenergy supply chains. It reviews the major energy pathways from terrestrial and aquatic biomass to bioenergy/biofuel products as well as power and heat with an emphasis on “drop-in” liquid hydrocarbon fuels. Key components of the bioenergy supply chains are then presented, along with a comprehensive overview and classification of the existing contributions on biofuel/bioenergy supply chain optimization. This paper identifies fertile avenues for future research that focuses on multi-scale modeling and optimization, which allows the integration across spatial scales from unit operations to biorefinery processes and to biofuel value chains, as well as across temporal scales from operational level to strategic level. Perspectives on future biofuel supply chains that integrate with petroleum refinery supply chains and/or carbon capture and sequestration systems are presented. Issues on modeling of sustainability and the treatment of uncertainties in bioenergy supply chain optimization are also discussed.     

基础油供应链生产-分销计划模型及其优化

随着市场全球化的飞速发展,供应链思想已渗透到各行各业,是一种新型的企业管理思想。然而在一些 产业结构不合理、急需产业升级的领域,几乎没有相关的供应链研究,譬如石油化工领域的量化研究少之又少。 本文分析了在独立决策下基础油供应链生产、分销系统中,信息不共享,生产商、分销商以及客户只追求各自 利益最大化,忽视甚至是损害了供应链整体利益的现象。针对上述现象,构建了生产-分销集成计划模型,以实 现供应链总成本和总反应时间最小,提出了一种基于粒子群算法寻找多目标供应链网络Pareto 最优解的方法。 仿真实例的结果表明了集成模型的可行性和优越性。     

Multistage distributionally robust optimization for integrated production and maintenance scheduling

In chemical manufacturing processes, equipment degradation can have a significant impact on process performance or cause unit failures that result in considerable downtime. Hence, maintenance planning is an important consideration, and there have been increased efforts in scheduling production and maintenance operations jointly. In this context, one major challenge is the inherent uncertainty in predictive equipment health models. In particular, the probability distribution associated with the stochasticity in such models is often difficult to estimate and hence not known exactly. In this work, we apply a distributionally robust optimization (DRO) approach to address this problem. Specifically, the proposed formulation optimizes the worst-case expected outcome with respect to a Wasserstein ambiguity set, and we apply a decision rule approach that allows multistage mixed-integer recourse. Computational experiments, including a real-world industrial case study, are conducted, where the results demonstrate the significant benefits from binary recourse and DRO in terms of solution quality.     

A rule-based genetic algorithm for the scheduling of single-stage multi-product batch plants with parallel units

This paper presents a heuristic rule-based genetic algorithm (GA) for large-size single-stage multi-product scheduling problems (SMSP) in batch plants with parallel units. SMSP have been widely studied by the researchers. Most of them used mixed-integer linear programming (MILP) formulation to solve the problems. With the problem size increasing, the computational effort of MILP increases greatly. Therefore, it is very difficult for MILP to obtain acceptable solutions to large-size problems within reasonable time. To solve large-size problems, the preferred method in industry is the use of scheduling rules. However, due to the constraints in SMSP, the simple rule-based method may not guarantee the feasibility and quality of the solution. In this study, a random search based on heuristic rules was proposed first. Through exploring a set of random solutions, better feasible solutions can be achieved. To improve the quality of the random solutions, a genetic algorithm-based on heuristic rules has been proposed. The heuristic rules play a very important role in cutting down the solution space and reducing the search time. Through comparative study, the proposed method demonstrates promising performance in solving large-size SMSP.     

考虑切料过程的乙烯裂解炉炉群调度建模与优化

乙烯裂解炉炉群通常由多台裂解炉并行运行,将烃类原料裂解成小分子烃类化合物。由于随着裂解炉连续运行不可避免地在炉管内壁产生结焦,结焦导致裂解炉运行效率下降,所以需要对裂解炉进行周期性的停炉清焦。对于不同价格参数的多种原料不同清焦费用的多台裂解炉来说,整个乙烯裂解炉炉群系统的循环调度应是求得最优解使得收益最大化。本文对此类裂解炉炉群循环调度问题提出了一个新的混合整数非线性（MINLP）模型,相比较以前的研究该模型能够得到更好的求解多原料多裂解炉的问题,同时解决了裂解过程中切料时机选择的问题。最后,以某乙烯厂为研究实例进行切料时机的优化,优化后裂解炉全周期的运行效益显著提高,为操作人员选择最佳切炉时机提供了理论依据,说明了此模型的有效性。     

Inventory policies and safety stock optimization for supply chain planning

In this article, traditional supply chain planning models are extended to simultaneously optimize inventory policies. The inventory policies considered are the (r,Q) and (s,S) policies. In the (r,Q) inventory policy an order for Q units is placed every time the inventory level reaches level r, while in the s,S policy the inventory is reviewed in predefined intervals. If the inventory is found to be below level s, an order is placed to bring the level back to level S. Additionally, to address demand uncertainty four safety stock formulations are presented: (1) proportional to throughput, (2) proportional to throughput with risk-pooling effect, (3) explicit risk-pooling, and (4) guaranteed service time. The models proposed allow simultaneous optimization of safety stock, reserve, and base stock levels in tandem with material flows in supply chain planning. The formulations are evaluated using simulation. © 2018 American Institute of Chemical Engineers AIChE J, 65: 99–112, 2019     

Mathematical modeling for simultaneous design of plants and supply chain in the batch process industry

Most supply chain design models have focused on the integration problem, where links among nodes must be settled in order to allow an efficient operation of the whole system. At this level, all the problem elements are modeled like black boxes, and the optimal solution determines the nodes allocation and their capacity, and links among nodes. In this work, a new approach is proposed where decisions about plant design are simultaneously made with operational and planning decisions on the supply chain. Thus, tradeoffs between the plant structure and the network design are assessed. The model considers unit duplications and the allocation of storage tanks for plant design. Using different sets of discrete sizes for batch units and tanks, a mixed integer linear programming model (MILP) is attained. The proposed formulation is compared with other non-integrated approaches in order to illustrate the advantages of the presented simultaneous approach.     

Energy optimization of water supply system scheduling: Novel MINLP model and efficient global optimization algorithm

This article is concerned with global optimization of water supply system scheduling with pump operations to minimize total energy cost. The scheduling problem is first formulated as a non‐convex mixed‐integer nonlinear programming (MINLP) problem, accounting for flow rates in pipes, operation profiles of pumps, water levels of tanks, and customer demand. Binary variables denote on–off switch operations for pumps and flow directions in pipes, and nonlinear terms originate from characteristic functions for pumps and hydraulic functions for pipes. The proposed MINLP model is verified with EPANET, which is a leading software package for water distribution system modeling. We further develop a novel global optimization algorithm for solving the non‐convex MINLP problem. To demonstrate the applicability of the proposed model and the efficiency of the tailored global optimization algorithm, we present results of two case studies with up to 4 tanks, 5 pumps, 5 check valves, and 21 pipes. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4277–4296, 2016     

Multi-objective modeling and optimization for scheduling of cracking furnace systems

Cracking furnace is the core device for ethylene production. In practice, multiple ethylene furnaces are usual y run in parallel. The scheduling of the entire cracking furnace system has great significance when multiple feeds are simultaneously processed in multiple cracking furnaces with the changing of operating cost and yield of product. In this paper, given the requirements of both profit and energy saving in actual production process, a multi-objective optimization model contains two objectives, maximizing the average benefits and minimizing the average coking amount was proposed. The model can be abstracted as a multi-objective mixed integer non-linear programming problem. Considering the mixed integer decision variables of this multi-objective problem, an improved hybrid encoding non-dominated sorting genetic algorithm with mixed discrete variables (MDNSGA-I ) is used to solve the Pareto optimal front of this model, the algorithm adopted crossover and muta-tion strategy with multi-operators, which overcomes the deficiency that normal genetic algorithm cannot handle the optimization problem with mixed variables. Finally, using an ethylene plant with multiple cracking furnaces as an example to illustrate the effectiveness of the scheduling results by comparing the optimization results of multi-objective and single objective model.     

Optimal design and global sensitivity analysis of biomass supply chain networks for biofuels under uncertainty

Bio-fuels represent promising candidates for renewable liquid fuels. One of the challenges for the emerging industry is the high level of uncertainty in supply amounts, market demands, market prices, and processing technologies. These uncertainties complicate the assessment of investment decisions. This paper presents a model for the optimal design of biomass supply chain networks under uncertainty. The uncertainties manifest themselves as a large number of stochastic model parameters that could impact the overall profitability and design. The supply chain network we study covers the Southeastern region of the United States and includes biomass supply locations and amounts, candidate sites and capacities for two kinds of fuel conversion processing, and the logistics of transportation from the locations of forestry resources to the conversion sites and then to the final markets.To reduce the design problem to a manageable size the impact of each uncertain parameter on the objective function is computed for each end of the parameter's range. The parameters that cause the most change in the profit over their range are then combined into scenarios that are used to find a design through a two stage mixed integer stochastic program. The first stage decisions are the capital investment decisions including the size and location of the processing plants. The second stage recourse decisions are the biomass and product flows in each scenario. The objective is the maximization of the expected profit over the different scenarios. The robustness and global sensitivity analysis of the nominal design (for a single nominal scenario) vs. the robust design (for multiple scenarios) are analyzed using Monte Carlo simulation over the hypercube formed from the parameter ranges.     

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。     

Proactive scheduling of batch processes by a combined robust optimization and multiparametric programming approach

We address short‐term batch process scheduling problems contaminated with uncertainty in the data. The mixed integer linear programming (MILP) scheduling model, based on the formulation of Ierapetritou and Floudas, Ind Eng Chem Res. 1998; 37(11):4341–4359, contains parameter dependencies at multiple locations, yielding a general multiparametric (mp) MILP problem. A proactive scheduling policy is obtained by solving the partially robust counterpart formulation. The counterpart model may remain a multiparametric problem, yet it is immunized against uncertainty in the entries of the constraint matrix and against all parameters whose values are not available at the time of decision making. We extend our previous work on the approximate solution of mp‐MILP problems by embedding different uncertainty sets (box, ellipsoidal and budget parameter regulated uncertainty), and by incorporating information about the availability of uncertain data in the construction of the partially robust scheduling model. For any parameter realization, the corresponding schedule is then obtained through function evaluation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4184–4211, 2013