Two-echelon, multi-commodity supply chain network design with mode selection, lead-times and inventory costs

Designing distribution networks - as one of the most important strategic issues in supply chain management - has become the focus of research attention in recent years. This paper deals with a two-echelon supply chain network design problem in deterministic, single-period, multi-commodity contexts. The problem involves both strategic and tactical levels of supply chain planning including locating and sizing manufacturing plants and distribution warehouses, assigning the retailers' demands to the warehouses, and the warehouses to the plants, as well as selecting transportation modes.We have formulated the problem as a mixed integer programming model, which integrates the above mentioned decisions and intends to minimize total costs of the network including transportation, lead-times, and inventory holding costs for products, as well as opening and operating costs for facilities. Moreover, we have developed an efficient Lagrangian based heuristic solution algorithm for solving the real-sized problems in reasonable computational time.     

A vendor managed inventory model under contractual storage agreement

Vendor managed inventory (VMI) is a supply chain partnership strategy that allows a supplier to place orders on behalf of its customers. This paper considers a supply chain composed of a single vendor and multiple retailers operating under a VMI contract that specifies limits on retailers' stock levels. We address the problem of synchronizing the vendor's cycle time with the buyers' unequal ordering cycles by developing a mixed integer non-linear program that minimizes the joint relevant inventory costs under storage restrictions. We also propose a cost efficient heuristic to solve the developed optimization problem. We conducted computational experiments to assess the reduction in the total supply chain costs resulting from relaxing the restriction of equal ordering cycles. It is found that the heuristic generates greater cost savings in cases of increased variability in retailers' demand and cost parameters.     

Rationing mechanisms and inventory control-policy parameters for a divergent supply chain operating with lost sales and costs of review

We consider a static divergent two-stage supply chain with one distributor and many retailers. The unsatisfied demands at the retailers’ end are treated as lost sales, whereas the unsatisfied demand is assumed to be backlogged at the distributor. The distributor uses an inventory rationing mechanism to distribute the available on-hand inventory among the retailers, when the sum of demands from the retailers is greater than the on-hand inventory at the distributor. The present study aims at determining the best installation inventory control-policy or order-policy parameters such as the base-stock levels and review periods, and inventory rationing quantities, with the objective of minimizing the total supply chain costs (TSCC) consisting of holding costs, shortage costs and review costs in the supply chain over a finite planning horizon. An exact solution procedure involving a mathematical programming model is developed to determine the optimum TSCC, base-stock levels, review periods and inventory rationing quantities (in the class of periodic review, order-up-to S policy) for the supply chain model under study. On account of the computational complexity involved in optimally solving problems over a large finite time horizon, a genetic algorithm (GA) based heuristic methodology is presented.     

B2B e-commerce supply chain integration and performance: A contingency fit perspective on the role of environment

Drawing upon contingency theory “fit” research in the IT and supply chain management literature, we applied the “fit” concept to the relationship between B2B e-commerce supply chain integration and performance. The results demonstrated that the effect of B2B supply chain integration on financial, market, and operational performance decreased as product turbulence and demand unpredictability jointly increased. Managerial implications include the conditions under which IT investments yield performance improvement and the need for firms to actively manage demand uncertainty.     

An efficient algorithm for stochastic capacity portfolio planning problems

This study investigates capacity portfolio planning problems under demand, price, and yield uncertainties. We model this capacity portfolio planning problem as a Markov decision process. In this research, we consider two types of capacity: dedicated and flexible capacity. Among these capacity types, flexible capacity costs higher but provides flexibility for producing different products. To maximize expected profit, decision makers have to choose the optimal capacity level and expansion timing for both capacity types. Since large stochastic optimization problems are intractable, a new heuristic search algorithm (HSA) is developed to reduce computational complexity. Compare to other algorithms in literature, HSA reduces computational time by at least 30% in large capacity optimization problems. In addition, HSA yields optimal solution in all numerical examples that we have examined.     

Location and transportation planning in supply chains under uncertainty and congestion by using an improved electromagnetism-like algorithm

Supply chain decision makers are constantly trying to improve the customer demand fulfillment process and reduce the associated costs via decision making models and techniques. As two of the most important parameters in a supply chain, supply and demand quantities are subject to uncertainty in many real-world situations. In addition, in recent decades, there is a trend to think of the impacts of supply chain design and strategies on society and environment. Especially, transportation of goods not only imposes costs to businesses but also has socioeconomic influences. In this paper, a fuzzy nonlinear programming model for supply chain design and planning under supply/demand uncertainty and traffic congestion is proposed and a hybrid meta-heuristic algorithm, based on electromagnetism-like algorithm and simulated annealing concepts, is designed to solve the model. The merit of this paper is presenting a realistic model of current issues in supply chain design and an efficient solution method to the problem. These are significant findings of this research which can be interesting to both researchers and practitioners. Several numerical examples are provided to justify the model and the proposed solution approach.     

A heuristic algorithm for master planning that satisfies multiple objectives

This study proposes a heuristic algorithm, called the multi-objective master planning algorithm (MOMPA), to solve master planning (MP) problems for a supply chain network with multiple finished products. MOMPA has three objectives: to minimize delay penalties, to minimize use of outsourcing capacity, and to minimize the costs of materials, production, processing, transportation, and inventory holding—all while respecting the capacity limitations and the demand deadlines of all those involved in a given supply chain network. MOMPA plans each demand, one by one, without backtracking, and sorts those demands using a sorting mechanism that is part of the algorithm. For each demand, the minimum production cost tree is determined within the limits of the time bucket for the demand deadline. The maximum available capacity of this tree is then computed for the “no delay” case. Following this calculation, the delay-or-not criterion is evaluated to determine whether or not further delay is necessary. MOMPA compares the results of these two procedures and allocates the appropriate capacities to the demand for all the nodes on the selected tree. If the minimum cost production tree has no available capacity, MOMPA adjusts the network and looks for a new tree. With complexity and computational analysis, MOMPA is shown to be very efficient in solving MP problems, sometimes generating the same optimal solution as the LP model.     

An evaluation of new heuristics for the location of cross-docks distribution centers in supply chain network design

This paper addresses an evaluation of new heuristics solution procedures for the location of cross-docks and distribution centers in supply chain network design. The model is characterized by multiple product families, a central manufacturing plant site, multiple cross-docking and distribution center sites, and retail outlets which demand multiple units of several commodities. This paper describes two heuristics that generate globally feasible, near optimal distribution system design and utilization strategies utilizing the simulated annealing (SA) methodology. This study makes two important contributions. First, we continue the study of location planning for the cross-dock and distribution center supply chain network design problem. Second, we systematically evaluate the computational performance of this network design location model under more sophisticated heuristic control parameter settings to better understand interaction effects among the various factors comprising our experimental design, and present convergence results. The central idea of the paper is to evaluate the impact of geometric control mechanism vis-a-vis more sophisticated ones on solution time, quality, and convergence for two new heuristics. Our results suggest that integrating traditional simulated annealing with TABU search is recommended for this supply chain network design and location problem.     

Scheduling concurrent production over a finite planning horizon: polynomially solvable cases

The paper analyzes a manufacturing system made up of one workstation which is able to produce concurrently a number of product types with controllable production rates in response to time-dependent product demands. Given a finite planning horizon, the objective is to minimize production cost, which is incurred when the workstation is not idle and inventory and backlog costs, which are incurred when the meeting of demand results in inventory surpluses and shortages. With the aid of the maximum principle, optimal production regimes are derived and continuous-time scheduling is reduced to a combinatorial problem of sequencing and timing the regimes. The problem is proved to be polynomially solvable if demand does not exceed the capacity of the workstation or it is steadily pressing and the costs are “agreeable”.

Scope and purpose

Efficient utilization of modern flexible manufacturing systems is heavily dependent on proper scheduling of products throughout the available facilities. Scheduling of a workstation which produces concurrently a number of product types with controllable production rates in response to continuous, time-dependent demand is under consideration. Similar to the systems considered by many authors in recent years, a buffer with unlimited capacity is placed after the workstation for each product type. The objective is to minimize inventory storage, backlog and production costs over a finite planning horizon. Numerical approaches are commonly used to approximate the optimal solution for similar problems. The key contribution of this work is that the continuous-time scheduling problem is reduced to a combinatorial problem, exactly solvable in polynomial time if demand does not exceed the capacity of the workstation or the manufacturing system is organized such that the early production and storage of a product to reduce later backlogs are justified.     

软计算求解分布式多工厂多顾客的供应链准时化生产计划问题

描述了分布式多工厂、多顾客的供应链准时化生产计划问题,以实现最小化提前／拖期惩罚费用、生产成本、产品运输费用之和为目标建立了数学模型,将遗传算法与模糊逻辑相结合,设计了软计算方法求解模型,采用基于规则方法的模糊规则量化方法求解模糊决策,并将模糊决策嵌入遗传算法,使得算法具有比分枝定界法更快的寻优能力和更广的适应范围。实例计算结果表明了该模型和算法的有效性和应用潜力。     

Planning tools for managing the supply chain

In this paper, we introduce a new way to manage the supply chain. The proposed solution reduces the problem's complexity using a two-stage hierarchical production planning method and is applicable to realistic transportation optimization problems. The approach is based on planning and operations scheduling models, and is designed to minimize travel and production costs within a flexible organizational network. In the aggregate planning phase, a mathematical model involving an aggregation of products, demand and time periods is solved. It is at this initial stage that the size of the problem is reduced and its output is used as input to the detailed phase in order to improve resolution time. The second stage produces a detailed schedule. It is shown that the proposed approach generates good and feasible solutions to practical problems within a reasonable computational time.     

基于Prim-DMGA算法的闭环供应链网络鲁棒优化研究

针对不确定环境下的闭环供应链网络优化问题,在需求不确定及设施中断风险的条件下,基于鲁棒对等优化方法建立了一种以闭环供应链网络总成本最小为目标的鲁棒优化模型,以解决供应链网络中的不确定性问题,并提出了Prim-DMGA。首先基于Prim算法得到高质量的初始种群,其次让路径规划方案和设施选址方案在两层自适应GA的不断反馈中达到最优。实验结果表明,Prim-DMGA得到的目标函数值优于单层Prim-MGA与传统GA,且在求解大规模算例时,求解结果优于CPLEX软件。研究结论表明,Prim-DMGA能以较少的计算时间获得质量更优的解,鲁棒优化模型可以有效减少不确定因素带来的不利影响,提高闭环供应链网络的鲁棒性能。     

Open vehicle routing problem with demand uncertainty and its robust strategies

We investigate the open vehicle routing problem with uncertain demands, where the vehicles do not necessarily return to their original locations after delivering goods to customers. We firstly describe the customer’s demand as specific bounded uncertainty sets with expected demand value and nominal value, and propose the robust optimization model that aim at minimizing transportation costs and unsatisfied demands in the specific bounded uncertainty sets. We propose four robust strategies to cope with the uncertain demand and an improved differential evolution algorithm (IDE) to solve the robust optimization model. Then we analyze the performance of four different robust strategies by considering the extra costs and unmet demand. Finally, the computational experiments indicate that the robust optimization greatly avoid unmet demand while incurring a small extra cost and the optimal return strategy is the best strategy by balancing the trade-off the cost and unmet demand among different robust strategies.     

An SDP approach for multiperiod mixed 0–1 linear programming models with stochastic dominance constraints for risk management

In this paper we consider multiperiod mixed 0–1 linear programming models under uncertainty. We propose a risk averse strategy using stochastic dominance constraints (SDC) induced by mixed-integer linear recourse as the risk measure. The SDC strategy extends the existing literature to the multistage case and includes both the first-order and second-order constraints. We propose a stochastic dynamic programming (SDP) solution approach, where one has to overcome the negative impact of the cross-scenario constraints on the decomposability of the model. In our computational experience we compare our SDP approach against a commercial optimization package, in terms of solution accuracy and elapsed time. We use supply chain planning instances, where procurement, production, inventory, and distribution decisions need to be made under demand uncertainty. We confirm the hardness of the testbed, where the benchmark cannot find a feasible solution for half of the test instances while we always find one, and show the appealing tradeoff of SDP, in terms of solution accuracy and elapsed time, when solving medium-to-large instances.     

需求随机的变质性产品生产计划模型

研究了能力约束的有限计划展望期生产计划问题,各周期的需求随机,库存产品存在变质且变质率为常数。建立了问题的期望值模型,目标函数为极小化生产准备成本、生产成本、库存成本的期望值。提出了随机模拟、遗传算法和启发式算法相结合的求解算法。用数值实例对模型和算法进行了验证,优化结果表明模型和算法是有效的。     

Production and Maintenance Planning for Electricity Generators: Modeling and Application to Indian Power Systems

This paper describes the development of an optimization model to perform the fuel supply, electricity generation, generator maintenance, and inter-regional transmission planning for the Northern Regional Electricity Board (NREB) of India. A review of the existing planning process of NREB revealed several areas of potential improvement. In the past, NREB did not use optimization and/or probabilistic methods in their planning. Their decision-making on maintenance, generation and fuel allocation was being performed in a sequential and 'fragmented' fashion, ignoring the possibility of interaction between the generation, transmission, and fuel supply subsystems. The deterministic treatment of outages of generators, and the planning criterion of spreading demand shortfall uniformly across the regions, were other areas of potential improvement. An integrated model, using linear programming together with a heuristic, has been developed to perform joint decision-making on fuel supply, maintenance, generation, and transmission. Monte Carlo simulation is used to incorporate the random outages of generators. The model has been prototyped using GAMS language together with a spreadsheet interface, and implemented for the NREB system. Substantial reduction in system costs is envisaged based on the results of a case study. The model is expected to aid the complex decision-making process of NREB planning engineers in several important ways.     

Uncertain location–allocation decisions for a bi-objective two-stage supply chain network design problem with environmental impacts

In the cases that the historical data of an uncertain event is not available, belief degree-based uncertainty theory is a useful tool to reflect such uncertainty. This study focuses on uncertain bi-objective supply chain network design problem with cost and environmental impacts under uncertainty. As such network may be designed for the first time in a geographical region, this problem is modelled by the concepts of belief degree-based uncertainty theory. This article is almost the first study on belief degree-based uncertain supply chain network design problem with environmental impacts. Two approaches such as expected value model and chance-constrained model are applied to convert the proposed uncertain problem to its crisp form. The obtained crisp forms are solved by some multi-objective optimization approaches of the literature such as TH, Niroomand, MMNV. A deep computational study with several test problems are performed to study the performance of the crisp models and the solution approaches. According to the results, the obtained crisp formulations are highly sensitive to the changes in the value of the cost parameters. On the other hand, Niroomand and MMNV solution approaches perform better than other solution approaches from the solution quality point of view.     

不确定经济环境下基于EVA的鲁棒供应链网络设计模型

针对由制造商、仓库、分销中心和客户组成的四级供应链网络设计问题,考虑以产品需求、短期利率、长期 利率、无风险利率、预期市场回报、证券承销费用和市场流动性等因素描述的经济环境不确定性,建立以供应链 经济增加值绩效为目标,网络设计、物流和财务运作为约束条件,设施选择、连接路径等为网络要素,生产、运输等物 流量和负债、保理、应收账款等财务项为决策变量的多产品、多周期供应链网络鲁棒设计模型.数值结果表明,基于 经济增加值的鲁棒供应链网络能够有效应对经济不确定性的影响.特别地,与传统随机优化方法相比,鲁棒优化能够确保供应链网络具有更好的鲁棒性和财务状况.     

A branch-and-cluster coordination scheme for selecting prison facility sites under uncertainty

A multi-period stochastic model and an algorithmic approach to location of prison facilities under uncertainty are presented and applied to the Chilean prison system. The problem consists of finding locations and sizes of a preset number of new jails and determining where and when to increase the capacity of both new and existing facilities over a time horizon, while minimizing the expected costs of the prison system. Constraints include maximum inmate transfer distances, upper and lower bounds for facility capacities, and scheduling of facility openings and expansion, among others. The uncertainty lies in the future demand for capacity, because of the long time horizon under study and because of the changes in criminal laws, which could strongly modify the historical tendencies of penal population growth. Uncertainty comes from the effects of penal reform in the capacity demand. It is represented in the model through probabilistic scenarios, and the large-scale model is solved via a heuristic mixture of branch-and-fix coordination and branch-and-bound schemes to satisfy the constraints in all scenarios, the so-called branch-and-cluster coordination scheme. We discuss computational experience and compare the results obtained for the minimum expected cost and average scenario strategies. Our results demonstrate that the minimum expected cost solution leads to better solutions than does the average scenario approach. Additionally, the results show that the stochastic algorithmic approach that we propose outperforms the plain use of a state-of-the-art optimization engine, at least for the three versions of the real-life case that have been tested by us.     

Supply chain network design under uncertainty with new insights from contracts

In this paper, the classical problem of supply chain network design is reconsidered to emphasize the rolc of contracts in uncertain environments. The supply chain addressed consists of four layers： suppliers, manufacturers, warehouses, and customers acting within a single period. The single owner of the manufacturing plants signs a contract with each of the suppliers to satisfy demand from downstream. Available contracts consist of long-term and option contracts, and unmet demand is satisfied by purchasing from the spot market. In this supply chain, customer demand, supplier capacity, plants and warehouses, transportation costs, and spot prices are uncertain. Two models are proposed here： a risk-neutral two-stage stochastic model and a risk-averse model that considers risk measures. A solution strategy based on sample average approximation is then proposed to handle large scale problems. Extensive computational studies prove the important role of contracts in the design process, especially a portfolio of contracts. For instance, we show that long-term contract alone has similar impacts to having no contracts, and that option contract alone gives inferior results to a combination of option and long-term contracts. We also show that the proposed solution methodology is able to obtain good quality solutions for large scale problems.