An integrated weighted fuzzy multi-objective model for supplier selection and order scheduling in a supply chain

This paper presents a new weighted fuzzy multi-objective model to integrated supplier selection, order quantity allocation and customer order scheduling problem to prepare a responsive and order-oriented supply chain in a make-to-order manufacturing system. Total cost and quality of purchased parts as well as the reliability of on-time delivery of customer orders are regarded as the objectives of the model. On the other hand, flexible suppliers can contribute to the responsiveness and flexibility of entire supply chain in the face of uncertain customer orders. Therefore, a mathematical measure is developed for evaluating the volume flexibility of suppliers and is considered as the other objective of the model. Furthermore, by considering the effect of interdependencies between the selection criteria and to handle inconsistent and uncertain judgments, a fuzzy analytic network process method is used to identify top suppliers and consider as the last objective. In order to optimise these objectives, the decision-maker needs to decide from which supplier to purchase parts needed to assemble the customer orders, how to allocate the demand for parts between the selected suppliers, and how to schedule the customer orders for assembled products over the planning time horizon. Numerical examples are presented and computational analysis is reported.     

On the robust decision-making in a supply chain under disruption risks

This paper considers a robust decision-making problem associated with supplies of parts and deliveries of finished products in a customer driven supply chain under disruption risks. The robustness refers to an equitably efficient performance of a supply chain in average-case as well as in the worst-case, which reflects the decision-makers common requirement to maintain an equally good performance of a supply chain under different conditions. Given a set of customer orders for products, the decision-maker needs to select suppliers of parts required to complete the orders, allocate the demand for parts among the selected suppliers and schedule the orders over the planning horizon, to equitably optimise average and worst-case performance of the supply chain. The supplies are subject to independent random local and regional disruptions. The obtained combinatorial stochastic optimisation problem is formulated as a mixed-integer program with conditional value-at-risk as a risk measure. The ordered weighted averaging aggregation of the expected value and the conditional value-at-risk of the selected optimality criterion is applied to obtain a robust solution. The risk-neutral, risk-averse and robust solutions that optimise, respectively average, worst-case and equitable average and worst-case performance of a supply chain are determined and compared for cost and customer service level objective functions. Numerical examples and computational results, in particular comparison with the mean-risk approach, are presented and some managerial insights are reported.     

Supply chain design to guarantee quoted lead time and inventory replenishment: model and insights

Do lead time constraints only lead to re-think and re-optimise the inventory positioning along the supply chain or can they impact on the design of the supply chain itself? To answer such a question, we integrate the lead time constraints in a multi-echelon supply chain design model and challenge the difficulty of combining in the same model the long-term decisions (facility location, supplier selection) with the midterm decisions (inventory placement and replenishment, delivery lead time). The model guarantees the respect of the quoted lead time associated with each customer order and the replenishment of the different stocks (raw materials, intermediate and final products) in the different stages of the supply chain between any pair of consecutive orders. We use the model to investigate the impact of the quoted lead time and customer’s order frequency on supply chain design decisions and costs. Some of our results indicate that the lead time constraints can lead to bringing the sites of manufacturing and distribution close to the demand zone and to select local suppliers in spite of their higher cost.     

Analysis of parts requirements variance for a JIT supply chain

Metrics used to assess level parts usage for some JIT supply chains are based on the product-unit by product-unit launch of products on the assembly line. However, many automobile assembly plants require parts suppliers to deliver parts to the assembly line by using a constant order cycle, non-constant order quantity framework. The paper proposes metrics that are suited to this parts delivery framework. Through extensive simulation over a wide range of assembly parameter values, it assesses the ability of supplier plants to match assembly requirements at each supply epoch. Among other things, the study finds that the conventional JIT scheduling framework also works well in general under this parts delivery arrangement, but acute parts stockout conditions could sometimes occur. Therefore, managers need to consider this in determining appropriate inventory levels for each part. This will prevent stockouts and reduce supply chain costs.     

A portfolio approach to supply chain disruption management

A new, computationally efficient portfolio approach to supplier selection in the presence of supply chain disruption risks is proposed, where the selection of supply portfolios for parts is combined with production scheduling of finished products. Unlike most of reported research on the supply chain risk management which focuses on the risk mitigation decisions taken prior to a disruption, the proposed portfolio approach combines decisions made before, during and after the disruption. The two decision-making approaches are considered: an integrated approach with the perfect information about the future disruption scenarios, and a hierarchical approach with no such information available. In the integrated approach, which accounts for all potential disruption scenarios, the primary supply portfolio that will hedge against all scenarios is determined along with the recovery supply portfolio and production schedule for each scenario. In the hierarchical approach, first the primary supply portfolio is determined, and then, when a primary supplier is hit by a disruption, the recovery supply portfolio is selected. For the integrated and the hierarchical decision-making, mixed integer programming models are developed with the two risk-neutral conflicting objectives that account for both time and cost of recovery: minimising expected cost or maximising expected service level. The findings indicate that for both objectives, the integrated decision-making selects a more diversified primary supply portfolio than the hierarchical approach and when all primary suppliers are shutdown by disruption, a single sourcing recovery portfolio is usually selected.     

The economic lot and delivery scheduling problem: common cycle, rework, and variable production rate

The economic lot and delivery scheduling problem is to simultaneously determine the production sequence of several assembly components at a supplier and the delivery interval of those components to the customer. The customer, an assembly facility, is assumed to use the components at a constant rate. The objective is to find the production sequence and delivery interval that minimize the holding, setup, and transportation cost for the supply chain. Previous solutions to the problem assume a constant production rate for each component and that all components are of acceptable quality. These assumptions ignore volume flexibility and quality cost. Volume flexibility permits a system to adjust the production rate upwards or downwards within wide limits. Also, component quality may deteriorate with larger lot sizes and decreased unit production times. In this paper, we develop an algorithm for solving the economic lot and delivery scheduling problem for a supplier using a volume flexible production system where component quality depends on both lot sizes and unit production times. We test the performance of the algorithm and illustrate the models with numerical examples.     

Applied column generation-based approach to solve supply chain scheduling problems

More and more enterprises have chosen to adopt a made-to-order business model in order to satisfy diverse and rapidly changing customer demand. In such a business model, enterprises are devoted to reducing inventory levels in order to upgrade the competitiveness of the products. However, reductions in inventory levels and short lead times force the operation between production and distribution to cooperate closely, thus increasing the practicability of integrating the production and distribution stages. The complexity of supply chain scheduling problems (integrated production and distribution scheduling) is known to be NP-hard. To address the issues above, an efficient algorithm to solve the supply chain scheduling problem is needed. This paper studies a supply chain scheduling problem in which the production stage is modelled by an identical parallel machine scheduling problem and the distribution stage is modelled by a capacitated vehicle routing problem. Given a set of customer orders (jobs), the problem is to find a supply chain schedule such that the weighted summation of total job weighted completion time and total job delivering cost are minimised. The studied problem was first formulated as an integer programme and then solved by using column generation techniques in conjunction with a branch-and-bound approach to optimality. The results of the computational experiments indicate that the proposed approach can solve the test problems to optimality. Moreover, the average gap between the optimal solutions and the lower bounds is no more than 1.32% for these test problems.     

A hybrid VNS-HS algorithm for a supply chain scheduling problem with deteriorating jobs

This paper investigates a coordinated scheduling problem in a two stage supply chain where parallel-batching machine, deteriorating jobs and transportation coordination are considered simultaneously. During the production stage, jobs are processed by suppliers and there exists one parallel-batching machine in each supplier. The actual processing time of a job depends on its starting time and normal processing time. The normal processing time of a batch is equal to the largest normal processing time among all jobs in its batch. During the transportation stage, the jobs are then delivered to the manufacturer. Since suppliers are distributed in different locations, the transportation time between each supplier and the manufacturer is different. Based on some structural properties of the studied problem, an optimal algorithm for minimising makespan on a single supplier is presented. This supply chain scheduling problem is proved to be NP-hard, and a hybrid VNS-HS algorithm combining variable neighbourhood search (VNS) with harmony search (HS) is proposed to find a good solution in reasonable time. Finally, some computational experiments are conducted and the results demonstrate the effectiveness and efficiency of the proposed VNS-HS.     

Integrated model for supplier selection and negotiation in a make-to-order environment

The paper deals with the development of an integrated supplier selection and negotiation process for multiple parts/materials procurement. The main objective is to integrate decisions in the internal supply chain of a make-to-order manufacturer. Two main decisions during the negotiation process are considered: (1) the manufacturing planning decision responsible for determining the production schedule and fabrication lot size and (2) the supplier selection decision concerning which suppliers are selected for company business and the order volume allocated to each selected supplier. The model is designed to support the negotiation process by generating a set of effective alternatives in each negotiation period. Its structure is multi-objective and non-linear. The combination of the interactive weighted Tchebycheff method and Benders decomposition method is applied to generate a set of effective alternatives to support the decision-maker in each negotiation period.     

Blockchain adoption or contingent sourcing? Advancing food supply chain resilience in the post-pandemic era

In the post-pandemic era, food supply chains and firms therein are facing unprecedented severe challenges, because once infection is detected, numerous products must be recalled or abandoned, and both suppliers and retailers in the supply chain suffer enormous loss. To survive under the pandemic, retailers have adopted different sourcing strategies, such as contingent sourcing, which, in turn, affect the upstream suppliers and hence the resilience of the whole supply chain. With the rapid development of digital technologies, retailers nowadays can utilize blockchain as a reliable and efficient way to reduce product risk and hence advance the resilience of food supply chains by improving product traceability and inspection accuracy, and making sourcing transparent. In this paper, we develop a game-theoretic model to investigate the interrelation between the retailer’s decisions on blockchain adoption and sourcing strategies. We consider that a retailer originally orders from a risky supplier while conducting an imperfect inspection to detect infected products before selling. The retailer may speculatively keep on ordering from the risky supplier or adopt contingent sourcing by ordering from an alternative safe supplier. The retailer also has an option to implement blockchain to improve the inspection accuracy and product traceability. We derive the optimal retail prices under different sourcing strategies with and without blockchain adoption and then analyze the incentives for sourcing strategy and blockchain adoption. Then, we identify the conditions of an all-win situation for food retailer, supplier, supply chain resilience, and consumers with/without government subsidy. Finally, we extend to consider the situation that some consumers have health-safety concerns and preferences for blockchain adoption.     

Evaluating strategic issues in supply chain scheduling using game theory

This paper deals with the problem of scheduling and batch delivery of orders in a supply chain (SC) including a supplier, a manufacturer and a final customer. First, the individual decisions of partners in the SC and their behaviours are analysed through mathematical models. Second, the best policy is obtained assuming that the SC is vertically integrated and the partners fully cooperate (this is called SC scheduling in the relevant literature). Since this strategy is usually against a partner, it might not be implemented in practice as the authors have observed this condition in real world. Hence, a fair sharing mechanism based on game theory concepts is also introduced which can motivate the partners to cooperate and adopt the best policy of the SC. The numerical examples show the superiority of integrated decisions over independent actions and also the importance of the sharing mechanism.     

A clustering algorithm for supplier base management

Supplier base management is an important strategy for managing global, customer driven supply chains. Successful supplier base management can effectively handle supply side exceptions, which may have significant business implications. Currently, there is a trend to reduce the size of the supplier base which makes the coordination and interaction among suppliers more effective, less costly and time consuming. The goal of this research is to present a clustering algorithm, named min-min-roughness (MMR) to cluster suppliers into smaller, more manageable groups with similar characteristics. Due to the fact that supplier data are mainly categorical in nature, MMR, based on rough set theory (RST) is developed for categorical data clustering which is also capable of handling the uncertainty during the clustering process. One potential benefit of applying MMR to supplier base management is that more realistic benchmarking can be obtained and the fulfilment operation can be sped up by reducing the number of variables impacting the operations. In addition, the characteristics of each smaller group of suppliers can be summarised and exploited to handle supply side disruptions.     

On the risk-averse optimization of service level in a supply chain under disruption risks

The worst-case optimization of service level in the presence of supply chain disruption risks is considered for the two different service levels measures: the expected worst-case demand fulfillment rate and the expected worst-case order fulfillment rate. The optimization problem is formulated as a joint selection of suppliers and stochastic scheduling of customer orders under random disruptions of supplies. The suppliers are located in different geographic regions and the supplies are subject to random local and regional disruptions. The obtained combinatorial stochastic optimization problem is formulated as a mixed integer program with conditional service-at-risk as a worst-case service level measure. The risk-averse solutions that optimize the worst-case performance of a supply chain are compared for the two service level measures. In addition, to demonstrate the impact on the cost in the process of optimizing the worst-case service level, a joint optimization of expected cost and conditional service-at-risk using a weighted-sum approach is considered and illustrated with numerical examples. The findings indicate that the worst-case order fulfillment rate shows a higher service performance than the worst-case demand fulfillment rate. Maximization of the expected worst-case fraction of fulfilled customer orders better mitigates the impact of disruption risks. The supply portfolio is more diversified and the expected worst-case fraction of fulfilled orders is greater for most confidence levels. Finally, the results clearly show that worst-case service level is in opposition to cost.     

需求和提前期不确定下的两级供应链系统研究

由一个部件提供商和一个装配商组成的两级组装供应链系统,部件提供商提供两种不同的部件给装配商进行装配;分析在单销售周期内,系统上同时存在部件的生产提前期和装配提前期的不确定,以及需求的不确定时,系统的特性.采用博弈论方法,装配商确定装配计划提前期,以及向部件提供商提交的订购量;而部件提供商确定部件生产计划提前期,以及部件批发价格.得出,首先,不确定提前期导致供应链系统订购量减小;其次,在分散控制的组装供应链系统中,系统的总生产、装配计划提前期,要大于集中控制系统中的,并且装配计划提前期与部件生产计划提前期无关;再者,过大的提前期不确定性对组装供应链系统的影响要比需求不确定对组装供应链的影响大.     

The implication of vendor inventory liability period in a decentralised assembly system

This paper investigates a decentralised assembly system that consists of one manufacturer and multiple suppliers who produce the complementary components. In a single selling season, the manufacturer initially sets a vendor inventory liability period (VILP) to control the suppliers’ delivery times, and the suppliers simultaneously determine when to deliver their components. Given the firms’ equilibrium strategies, we find that it is not wise for the manufacturer to set an overly long VILP, since having no inventory is not always beneficial to the manufacturer. A supplier may choose to postpone his delivery when the length of the VILP increases or the other suppliers’ deliveries are delayed, and either of these conditions is detrimental to the supplier’s profitability. We also examine the impact of VILP under different situations and find that having VILPs customised for different suppliers can reduce the manufacturer’s cost as well as improve the supply chain’s overall efficiency.     

Horizontal cooperation and information sharing between suppliers in the manufacturer–supplier triad

In this paper, we analyse a collusion and information-sharing problem between two suppliers in a manufacturer–supplier triad. The manufacturer treats one supplier as a strategic supplier and the other as a backup. While the strategic supplier offers modules of good quality but longer lead times, the backup supplier offers modules with inferior quality but shorter lead times. If there are urgent orders, the manufacturer must turn to the backup supplier. However, it is difficult for the manufacturer to estimate whether the urgent supplier has put extra effort into their production. We formulate this problem by assuming that the urgent supplier has either low or high production costs. To take advantage of the competition between two suppliers, the manufacturer can design a contract menu that defines total payment and lead times, under which both suppliers may be worse off. Meanwhile, it is possible for the suppliers to tacitly form a coalition, and to even share the private cost information. We study this problem by formulating it as a three-stage game. Furthermore, we investigate the variation of profits for each part of the supply chain. We find that the manufacturer is worse off when suppliers cooperate or share private information. Both suppliers, however, can benefit from cooperation and information sharing.     

Coordinating decentralised assembly systems with random yield and random demand

We study coordination of assembly systems with random supplier yields and random customer demand. We propose four contracts which are combinations of well-known contracts in the literature and show that the contracts can coordinate the chain under forced compliance. Our contracts have less payment schemes than the existing contracts given for coordination of assembly systems in the literature. We show that arbitrary profit allocation between the levels of the supply chain (the manufacturer or the suppliers) is possible. We also provide sufficient conditions which enable arbitrary profit allocation among the suppliers and illustrate the profit allocation with numerical examples.     

Fuzzy scheduling of a build-to-order supply chain

The overwhelming majority of the literature in the area of supply chain planning and scheduling considers the traditional make-to-stock (MTS) environment. However, manufacturers of assembled products such as cars, computers, furniture, etc. adopt the build-to-order supply chain (BOSC) to become agile in a mass customization process in order to meet diversified customer requirements. In this paper we propose an integrated production–distribution planning model for a multi-echelon, multi-plant and multi-product supply chain operating in a build-to-order (BTO) environment. The uncertainties associated with estimation of the various operational cost parameters are represented by fuzzy numbers. The BOSC scheduling model is thus constructed as a mixed-integer fuzzy programming (MIFP) problem with the goal of reducing the overall operating costs related to component fabrication, procurement, assembling, inspection, logistics and inventory, while improving customer satisfaction by allowing product customization and meeting delivery promise dates at each market outlet. An efficient compromise solution approach by transforming the problem into an auxiliary multi-objective linear programming model is also suggested.     

装配供应链上合作新产品开发管理研究

以装配供应链为研究对象,构建包含两个供应商和一个制造商的合作新产品开发成本分摊模型。讨论了供应商之间在定价和创新方面的相互影响,制造商的研发成本分摊策略以及整合成本对合作开发的影响。结果表明:任一供应商的研发投资行为,将导致另一供应商借机提高价格;任一供应商的创新能力增强,将激励另一供应商加大研发投入;制造商通过分摊研发成本能够有效激励供应商创新,最优成本分摊比例随整合成本系数递减,最大不超过二分之一。     

Incentives for quality improvement efforts coordination in supply chains with partial cost allocation contract

In this paper, we consider quality improvement efforts coordination in a two-stage decentralised supply chain with a partial cost allocation contract. The supply chain consists of one supplier and one manufacturer, both of which produce defective products. Two kinds of failure cost occur within the supply chain: internal and external. The supplier and the manufacturer determine their individual quality levels to maximise their own profits. We propose a partial cost allocation contract, under which the external failure cost is allocated between the manufacturer and the supplier at different rates based on information derived from failure root cause analysis. If the quality levels of the supplier and the manufacturer are observable, we show that the partial cost allocation contract coordinates the supply chain, provided that the failure root cause analysis does not erroneously identify the manufacturer’s fault as the supplier’s, and the supplier does not take responsibility for the manufacture’s fault. In the single moral hazard model, where only the quality level of the supplier is unobservable, the optimal share rates require the supplier to take some responsibility for the manufacture’s fault. However, in the double moral hazard model, where quality levels of the supplier and the manufacturer are unobservable to each other, the optimal share rates require the supplier not to take responsibility for the manufacturer’s fault. It is noted that the root cause analysis conducted by the manufacturer may have its disadvantage in attributing the fault to the supplier when both sides are at fault. We also propose a contract based on the dual root cause analysis to reduce the supplier’s penalty cost. Numerical results illustrate that the partial cost allocation contract satisfies the fairness criterion compared with the traditional cost allocation contract.