Effective bullwhip metrics for multi-echelon distribution systems under order batching policies with cyclic demand

A large number of problems in a distribution supply chain require that decisions are made in the presence of the bullwhip effect phenomenon. The impact of the order batching policies on the bullwhip effect is analysed in this paper, when cycle demand on a multi-echelon supply chain operating is considered. While investigating which bullwhip effect metrics are more adequate to measure the bullwhip effect in these type of systems, the optimal reordering plan that minimises the operation costs of the overall system is calculated. A Mixed Integer Linear Programming (MILP) model is developed that takes into account an inventory and distribution system formed by multiple warehouses and retailers with lateral transshipments. The bullwhip effect is measured through four metrics: the echelon average inventory; the echelon inventory variance ratio; the echelon average order; and the echelon order rate variance ratio. As conclusion the inventory metrics suggest that (i) using batching policy reduces instability; (ii) batching may reduce in general order variance if using larger batches and (iii) cycle demand length has no major impact in the bullwhip effect. A motivational example and a real word case study are used and tested.     

Design of an integrated supplier selection and multi-echelon distribution inventory model in a built-to-order supply chain environment

The paper deals with the development of an integrated supplier selection and multi-echelon distribution inventory model (MEDIM) for the original equipment manufacturing company in a built-to-order supply chain environment using fuzzy analytical hierarchy process (FAHP) and a genetic algorithm. The main objective is to design the integrated qualitative decision-making of the supplier selection model using FAHP with that of the quantitative mathematical model for the distribution inventory supply chain using a genetic algorithm to the built-to-order environment. The proposed model is validated by considering the case study in a tyre industry in Southern India. The software used for programming is C++ language.     

Integrated inventory valuation in multi-echelon production/distribution systems

The pressure to reduce inventory has increased as competition expands, product variety grows, and capital costs increase. This investigation addresses the problem of inventory quantification and distribution within multi-echelon supply chains under market uncertainty and management flexibility. This approach is based on an optimisation model emphasising demand uncertainty and the relevant dimensions of network design as number of echelons, lead time, service level, and cost of processing activities. Overstock quantification enables the understanding of inventory level sensitivity to market uncertainty. A comparison among production sites and storage facilities revealed that higher downstream overstock levels decrease upstream echelons of uncertainty exposition. The contribution of this study relies on management's ability to establish inventory targets for each stocking point according to risk exposure and to promote the optimisation of working capital. Overall, this investigation increases knowledge related to the treatment of demand uncertainty in flexible and integrated supply chains     

Cooperative inventory planning in a distribution network

This study addresses the problem of optimal ordering and collaborative inventory management in a distribution network as a two-stage decision problem. In the first stage, when demand is uncertain, the retailers (sellers) order the products from a warehouse. Then, when demand becomes known with certainty, retailers may exchange their products to better match local demands. Sellers should determine their optimal order quantities for the first stage, and quantities and prices of products exchanged in the second stage. This paper proposes to build sellers’ coalitions and solve the two-stage decision problem as a cooperative game. Stability of a sellers’ coalition can be achieved only if the benefits resulting from collaboration are maximised and distributed according to an allocation policy that is both efficient and rational. The profit maximisation problem is formulated as a stochastic optimisation problem with recourse. Using the scenario method, this problem is approximated by a deterministic linear problem for which the existence of a solution is guaranteed. The proposed pricing policy guarantees the rational allocation of benefits under the scenario approximation. An industrial example supports the modelling approach and is used to evaluate the profitability of the exchange practice in the case of real data.     

Reverse Logistics: a stochastic EOQ-based inventory control model for mixed manufacturing/remanufacturing systems with return policies

This paper focuses on mixed manufacturing/remanufacturing systems, where manufacturing or purchase of new items integrates product reuse or remanufacturing, with the purpose to achieve a complete and timely demand satisfaction. We formulate a stochastic Economic Order Quantity (EOQ)-based inventory control model for a mixed manufacturing/remanufacturing system. The model is intended to identify the need of placing a manufacturing/purchasing order, to avoid the occurrence of stock-out situations. We then formulate a total cost minimisation problem, to derive the optimal return policy, this latter being a financial incentive paid to customers to increase the flow of returned items. The model developed is investigated through simulations, in order to assess the effect of stochasticity (of demand, return fraction and return delay) on the optimal return policy of the system; then, it is validated through a case study, to derive indications concerning its practical application in real cases. Our study ultimately provides a framework for practitioners to establish EOQ policies in reverse logistics contexts and to evaluate the opportunity of establishing a return policy in those contexts.     

An optimal ordering strategy for a third-party managed supply chain

The rapid pace of new product introduction and global sourcing of raw materials and manufacturing facilities have created a complex and fragmented supply chain. Retailers in many consumer product industries are relying on third-party supply-chain managers (SCMs) to manage the global supply chain cost-effectively with short production lead times. To meet delivery requirements, the SCM must start the production process before receiving a firm order from retailers. We assume a two-stage production process where, in stage 1, a base product is produced. In stage 2, the base product is customised. The SCM absorbs the penalties associated with over- or underestimating retailers’ demand. Hence, the SCM has to decide on (a) the optimal production quantity of the base products and (b) the number of base products to be customised without delay. We develop a profit maximisation model for this strategy using a nonlinear objective function with two decision variables and one constraint. Applying Kuhn–Tucker conditions, closed-form solutions are obtained for the two decision variables. Also, formulations are given for two additional strategies: postpone customisation of all products and produce customised products only. An example illustrates the use of our model. We also examine the impact of demand variability on the effectiveness of the three strategies. Results show that postponement may not always be the best strategy for an SCM.     

Incorporating risk aversion and fairness considerations into procurement and distribution decisions in a supply chain

This paper considers a three-tier supply chain in which a manufacturer uses raw materials sourced from multiple suppliers to produce an item and sells it through multiple distributors. We develop an integrated optimisation model to study supply chain procurement and distribution decisions incorporating the manufacturer’s aversion to risk and the distributors’ concern for fairness in a climate of uncertain supply and demand. Resilient strategies, such as alternative sourcing and transshipment, are also considered when optimising the supply chain cost and service level. To solve the problem, a Monte Carlo simulation-based multi-objective stochastic programming model is built. It uses the CVaR (Conditional Value-at-Risk) and unfairness aversion utility function to reflect the decision maker’s risk aversion and the customer’s concern for fairness, respectively. A Normalised Normal Constraint based algorithm is adopted to obtain the Pareto Frontier. In addition, the numerical analysis provides some valuable insights for supply chain managers.     

单周期随机需求下供应链库存协调机制设计

研究了单周期随机需求条件下两级供应链的库存协调机制设计问题.建立了基于弹性订货策略的供应链库存风险共担机制,并通过算例验证了弹性订货策略在供应链库存协调中的有效性.研究结果表明,在供应链上下游无合作时,需方承担全部库存风险,其个体理性的决策无法实现供应链的整体优化,而如果双方实施弹性订货策略,分担库存风险,则可以实现供应链的Pareto优化.     

Optimising installation (R,Q) policies in distribution networks with stochastic lead times: a comparative analysis of guaranteed- and stochastic service models

This paper studies two modelling approaches to the multi-echelon inventory optimisation problem in a distribution network with stochastic demands and lead times. It compares the performance of a novel guaranteed-service model (GSM), using an installation (R, Q) inventory control policy, with a stochastic service model (SSM) considering ordering, holding and flexibility costs. From both cycle service level and fill rate perspectives, our numerical analysis of the 1-warehouse 2-retailer network shows that cost difference between both models is driven by the internal service level at the warehouse. The GSM outperforms the SSM for over 80% of the simulated instances and realises an average total cost improvement of approximately 10%. This analysis goes against earlier results that showed a relatively low-cost difference between the two approaches, and demonstrates that it is worthwhile to evaluate competing models for multi-echelon inventory optimisation in real-world supply chains with batch ordering and variable lead times.     

An evolutionary algorithm for a new multi-objective location-inventory model in a distribution network with transportation modes and third-party logistics providers

This paper proposes a multi-objective optimisation algorithm for solving the new multi-objective location-inventory problem (MOLIP) in a distribution centre (DC) network with the presence of different transportation modes and third-party logistics (3PL) providers. 3PL is an external company that performs all or part of a company’s logistics functions. In order to increase the efficiency and responsiveness in a supply chain, it is assumed that 3PL is responsible to manage inventory in DCs and deliver products to customers according to the provided plan. DCs are determined so as to simultaneously minimise three conflicting objectives; namely, total costs, earliness and tardiness, and deterioration rate. In this paper, a non-dominated sorting genetic algorithm (NSGA-II) is proposed to perform high-quality search using two-parallel neighbourhood search procedures for creating initial solutions. The potential of this algorithm is evaluated by its application to the numerical example. Then, the obtained results are analysed and compared with multi-objective simulated annealing (MOSA). It is concluded that this algorithm is capable of generating a set of alternative DCs considering the optimisation of multiple objectives, significantly improving the decision-making process involved in the distribution network design.     

一类非线性时滞双曲型分布参数系统的振动条件

研究一类非线性时滞双曲型分布参数系统解的振动性问题,利用积分平均法、广义Riccati变换和H(t,s)k(s)型函数,建立了该类系统在第三类边值条件下所有解振动的若干新的充分判据。所得结论充分显示这种振动性是由时滞引起的,并给出一个实例来阐述主要结果的有效性。     

一类非线性时滞双曲型分布参数系统的振动条件

研究一类非线性时滞双曲型分布参数系统解的振动性问题,利用积分平均法、广义Riccati变换和H(t,s)k(s)型函数,建立了该类系统在第三类边值条件下所有解振动的若干新的充分判据。所得结论充分显示这种振动性是由时滞引起的,并给出一个实例来阐述主要结果的有效性。     

Joint economic production allocation and ordering policies in a supply chain consisting of multiple plants and a single retailer

This article discusses the production and ordering policies in a supply chain consisting of a single manufacturer and a single retailer. The retailer places orders based on the EOQ-like policy, and the manufacturer purchases raw materials and allocates them to the multiple plants in parallel to produce demand requirement from the retailer. The model is mathematically formulated, and the solution procedure is developed to determine the production cycle length, ordering quantity and frequency, and production allocation ratios for multiple plants. The closed forms of the production cycle length, ordering quantity, and frequency in terms of the production allocation ratios are obtained. It is also shown that the production allocation problem is NP-hard. An efficient and effective heuristic algorithm is proposed to determine the near-optimal production allocation ratios. A numerical experiment demonstrates that the proposed algorithm performs quite satisfactorily.     

关于值分布论中一个著名猜测的推广

运用Nevanlinna的亚纯函数理论方法，研究了超越亚纯函数的值分布理论，获得了如下的结论：设f为超越亚纯函数，c为f的不恒等于0的的小函数，则当n≥3时，f^n f’-c有无穷多个零点；若附加条件厂只有有限多个级≤2的零点，则对一切正整数n，f^n f’-c都有无穷多个零点．因而对Chiang Y M的问题作出了部分回答．     

The trans-shipment problem in a two-echelon,multi-location inventory system with lost sales

In this paper, we address a two-echelon, multi-location pooling inventory system that consists of an outside supplier, a warehouse and two retailers. To control their inventories, both warehouse and retailers use (R,?s,?S) policy. The retailers face stochastic customer demands for a single product and the warehouse receives only the replenishment orders of retailers. In case of stock-out at retailers, emergency trans-shipments are used to satisfy the unmet demand at one retailer with the surplus from the other retailer. When the stock is insufficient at the warehouse, we propose two rationing policies to allocate on-hand stock between retailers. The demand that cannot be satisfied neither by stock on-hand nor by trans-shipment from retailers is considered lost. Our work has two objectives. First, we propose an inventory model based on three components: the optimisation inventory model, the trans-shipment policy and the rationing policies for determining the best values of (s,?S) at each location that minimise total system cost. Second, we validate this model via an empirical simulation study that allows us to identify the influential parameters on trans-shipment benefits.     

Inline method of droplet and particle size distribution analysis in dilute disperse systems

In the present article a measurement method of particle size distributions (PSD) in industrial installations which use a dispersed phase of low concentration (like spray dryers or spray scrubbers) is introduced. A new type of inline-measurement system has been developed and designed to work in spray drying conditions. A standard digital camera is used to record shadows of flowing particles inside the spray drying chamber. Collected images were analyzed by a newly developed software which recognizes particles only in the focus area and eliminates several types of artifacts. The constructed prototype of the PSD inline-analyzer was installed and used to monitor large laboratory scale spray dryer. All data collected by the designed system during the spray drying experiments were compared with data measured with an offline reference system to show accuracy of the new measurement technique.     

A fuzzy discrete harmony search algorithm applied to annual cost reduction in radial distribution systems

Similarly to other optimization algorithms, harmony search (HS) is quite sensitive to the tuning parameters. Several variants of the HS algorithm have been developed to decrease the parameter-dependency character of HS. This article proposes a novel version of the discrete harmony search (DHS) algorithm, namely fuzzy discrete harmony search (FDHS), for optimizing capacitor placement in distribution systems. In the FDHS, a fuzzy system is employed to dynamically adjust two parameter values, i.e. harmony memory considering rate and pitch adjusting rate, with respect to normalized mean fitness of the harmony memory. The key aspect of FDHS is that it needs substantially fewer iterations to reach convergence in comparison with classical discrete harmony search (CDHS). To the authors’ knowledge, this is the first application of DHS to specify appropriate capacitor locations and their best amounts in the distribution systems. Simulations are provided for 10-, 34-, 85- and 141-bus distribution systems using CDHS and FDHS. The results show the effectiveness of FDHS over previous related studies.