Real-time procurement policy with yield and price uncertainty

This study formulates and analyses a procurement model in which a procurer faces both yield and price uncertainty. We propose a simple and effective real-time procurement policy where the decisions are made only based on the current arriving price and inventory level. The only information we need is the first two moments for the random yield rate, and the lower and upper bounds for price. Thus, our policy delivers robust performance to changing yield and price over time. In addition, simple decision rules are summarised for determining the optimal procurement quantity for different cases. Analytical results and numerical experiments are presented to show that the proposed policy achieves a superior performance guarantee.     

Supply chain flexibility and operations optimisation under demand uncertainty: a case in disaster relief

After a disaster happens, emergency response operations are critical to save humans’ lives and properties. The limited resources and time requirements call for coordinated supply chain operations. This paper studies supply chain operations for rescue kits in disaster reliefs, motivated by a real-world application. The objective is to minimise the total tardiness and peak tardiness of product delivery over the multi-period planning horizon. One major challenge is the lack of reliable prediction of customer demand in disasters. In order to cope with demand uncertainty while maintaining the tractability of the optimisation model, we decompose the demand into two components: a relatively stable base demand predicted by historical data and unpredictable demand surges. For the base demand, an optimisation model is developed to optimise the production and distribution operations, as well as the inventory replenishment policy for manufacturers and distribution centres, so as to minimise the total tardiness. For the demand surges, we propose to deploy supply chain flexibility to cope with the uncertainty. An empirical study shows the effectiveness of increasing supply chain flexibility and suggests some managerial insights on configuring such flexibility in emergency operations.     

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.     

Return policy and supply chain coordination with network-externality effect

The benefits of a consumer return policy have been extensively studied in extent literature. This paper explores the potentially damaging impact of a return policy on the retailer. We develop an analytical framework and examine the economic impact of consumer return among consumers, retailer and supply chain. We distinguish three network-externality (NE) cases: no network externality, fixed network-externality and variable network-externality contingent on return amount to discuss the retailer’s selling price, refund and inventory policies. Our analysis derives the optimal policies and shows that they take the form of contingence model in which the policies depend on consumer initial return and NE return. We also examine the influence of the consumer return NE effect on buy-back contracts of the supply chain and show that while the traditional buy-back contract fails to coordinate the supply chain, the NE effect does not render the differentiated buy-back contract less effective. Finally, we extend our study to a heterogeneous consumer case.     

一类短生命周期产品的回购合同

在考虑短生命周期产品具有价格弹性的随机需求情况下,研究了基于供应链环境下的短生命周期产品回购合同策略,分别分析了零售商和供应商在没有协调情况下各自的最优决策以及在回购合同协调下双方的最优决策,推导出了在回购合同下零售商的最佳订货量和最优零售价,以及供应商的最优回购价格的取值范围,并通过数值分析,验证了在回购合同下双方的最优决策能使供应链的整体利润达到集中控制下的最优状态.     

Newsvendor decisions under supply uncertainty

We analyse the impact of supply uncertainty on newsvendor decisions. First, we derive a solution for a newsvendor facing stochastic supply yield, in addition to stochastic demand. While earlier research has considered independent uncertainties, we derive the optimal order quantity for interdependent demand and supply and provide a closed-form solution for a specific copula-based dependence structure. This allows us to give insights into how dependence impacts the newsvendor’s decision, profit and risk level. In addition to the theory, we present experimental results that show how difficult newsvendor decisions under supply uncertainty are for human subjects. In our experiment, the control group replicated a well-known newsvendor experiment, whereas the test group faced additional supply yield uncertainty. Comparison of these results shows that under low-profit condition, subjects are able to incorporate supply uncertainty quite well in their decisions. Under high-profit condition, the deviation from the optimum is much more significant. We discuss this asymmetry and also propose some ways to improve newsvendor decision-making.     

Optimal manufacturing policy in a reverse logistic system with dependent stochastic returns and limited capacities

The stochastic models of systems with reverse logistics usually assume that the quantity of products returned is independent of sales. This hypothesis is obviously not true and can lead to suboptimal production policies. In this paper a new sales-dependent returns model is described. In this model, the returns depend on the useful life of the products sold and on the probability of an end-of-life product being returned. A Markov decision problem is formulated in order to obtain the optimal manufacturing policy. A numerical example is provided to illustrate the use of the defined model. An approximated Markov decision model is defined where the optimal policy is easily obtained. The optimal policies of the original and the approximated models are compared.     

A three-stage model for closed-loop supply chain configuration under uncertainty

In this paper, a general closed-loop supply chain (CLSC) network is configured which consists of multiple customers, parts, products, suppliers, remanufacturing subcontractors, and refurbishing sites. We propose a three-stage model including evaluation, network configuration, and selection and order allocation. In the first stage, suppliers, remanufacturing subcontractors, and refurbishing sites are evaluated based on a new quality function deployment (QFD) model. The proposed QFD model determines the relationship between customer requirements, part requirements, and process requirements. In addition, the fuzzy sets theory is utilised to overcome the uncertainty in the decision-making process. In the second stage, the closed-loop supply chain network is configured by a stochastic mixed-integer nonlinear programming model. It is supposed that demand is an uncertain parameter. Finally in the third stage, suppliers, remanufacturing subcontractors, and refurbishing sites are selected and order allocation is determined. To this end, a multi-objective mixed-integer linear programming model is presented. An illustrative example is conducted to show the process. The main novel innovation of the proposed model is to consider the CLSC network configuration and selection process simultaneously, under uncertain demand and in an uncertain decision-making environment.     

The value of buyback contract under price competition

We investigate the value of buyback contract by analysing a supply chain with one manufacturer and two competing retailers. Three scenarios, depending on whether buyback contracts are offered to neither, one, or both of the retailers, are considered. We first study the case when the manufacturer can only determine his buyback price. We show how the demand uncertainty, the competition level and the handling cost of buyback contract influence the profits of the manufacturer, the two retailers and the whole supply chain. Interestingly, contrary to the conventional wisdom that the buyback contract may intensify competition between the retailers, we show that offering the buyback contract to two competing retailers can benefit every channel member even if the competition level is high. Next, we study the return contract, a special type of buyback contract, and show the effect of competition level and industry outlook on supply chain parties' choices on return contract. We extend Padmanabhan and Png [1997. “Manufacturer's Returns Policies And Retail Competition.” Marketing Science 16 (1): 81–94] to the case with an asymmetric contract structure, i.e. one return contract and one whole-sale contract. We show that an asymmetric contract structure may better off both the retailers and the whole supply chain.     

Generalized information reuse for optimization under uncertainty with non‐sample average estimators

In optimization under uncertainty for engineering design, the behavior of the system outputs due to uncertain inputs needs to be quantified at each optimization iteration, but this can be computationally expensive. Multifidelity techniques can significantly reduce the computational cost of Monte Carlo sampling methods for quantifying the effect of uncertain inputs, but existing multifidelity techniques in this context apply only to Monte Carlo estimators that can be expressed as a sample average, such as estimators of statistical moments. Information reuse is a particular multifidelity method that treats previous optimization iterations as lower fidelity models. This work generalizes information reuse to be applicable to quantities whose estimators are not sample averages. The extension makes use of bootstrapping to estimate the error of estimators and the covariance between estimators at different fidelities. Specifically, the horsetail matching metric and quantile function are considered as quantities whose estimators are not sample averages. In an optimization under uncertainty for an acoustic horn design problem, generalized information reuse demonstrated computational savings of over 60% compared with regular Monte Carlo sampling.     

Robust material requirement planning with cumulative demand under uncertainty

In this paper, we deal with the problem of tactical capacitated production planning with the demand under uncertainty modelled by closed intervals. We propose a single-item with backordering model under small uncertainty in the cumulative demand for the Master Production Scheduling (MPS) problem with different rules, namely the Lot For Lot rule and the Periodic Order Quantity rule. Then we study a general multilevel, multi-item, multi-resource model with backordering and the external demand on components for the Material Requirement Planning (MRP) problem under uncertainty in the cumulative demand. In order to choose robust production plans for the above problems that hedge against uncertainty, we adopt the well-known minmax criterion. We propose polynomial methods for evaluating the impact of uncertainty on a given production plan in terms of its cost and for computing optimal robust production plans for both problems (MPS/MRP) under the assumed interval uncertainty representation. We show in this way that the robust problems (MPS/MRP) under this uncertainty representation are not much computationally harder than their deterministic counterparts.     

Dynamic buy-back for product recovery in end-of-life spare parts procurement

The efficient supply of spare parts is of prime concern for original equipment manufacturers (OEM). While manufacturing the parent product, spare parts can be sourced efficiently by using existing manufacturing facilities. This situation completely changes once the original equipment manufacturer ceases production of the parent product. In addition to traditional spare parts sources in the form of final order and remanufacturing, the option to buy back parts or products provides a viable alternative in the end-of-life phase. This can prevent the OEM from fulfilling his spare parts availability obligation or increase his ability to remanufacture. Current practice in industry is, on the one hand, to offer trade-in campaigns to acquire functional products from customers by giving substantial discounts on a new-generation product. On the other hand, trade-in rebates are given when customers return their broken parts in exchange for spare parts. We propose the consideration of a third option, i.e. to buy back broken products in order to improve control of both demand for spare parts and supply of recoverable parts. This contribution seeks to assess the potential benefit of buy-back strategies in contrast to both traditional sourcing and trade-in campaigns for different settings regarding information availability and buy-back flexibility. For each situation, a MILP formulation is presented, and in a numerical study we analyse the circumstances under which the buy-back of broken products is especially beneficial for the OEM.     

Dynamic product acquisition in closed loop supply chains

We consider a closed-loop supply chain where demand can either be satisfied by manufacturing new products or by buying back used products from customers and upgrading their functionality by remanufacturing. A joint buy-back pricing and manufacturing–remanufacturing decision model at the operations–marketing interface is presented that allows for dynamic parameters, e.g. product life cycles and seasonal aspects. The model allows the identification of beneficial opportunities for buying back and storing used products for immediate and future recovery. We present a new deterministic, dynamic, continuous-time optimisation model, derive necessary and sufficient optimality conditions, and develop a solution algorithm to find the cost-minimising manufacturing and remanufacturing policies as well as buy-back strategies for used products based on Pontryagin's Maximum Principle. It is shown that, in general, an optimal policy will include time intervals where returns are acquired so as to synchronise demand and remanufacturing, where returns are acquired and stored for future remanufacturing, and intervals where demand is satisfied by a mix of manufactured and remanufactured products. Furthermore, we discuss several reactive and proactive acquisition and remanufacturing heuristics and show under which conditions they are optimal. The findings are illustrated by numerical examples.     

Propagation of unit location uncertainty in dense storage environments

Dense storage systems provide high-space utilisation; however, because not all units are immediately accessible, selectively offloading units can require shifting of other stored units in order to access the requested unit. Given an initial certainty in unit location, a discrete time Markov Chain is developed to quantify the growth of unit location uncertainty as a function of retrieval requests. As the first to mathematically model uncertainty propagation in dense storage operations, metrics are developed to analyse the model. A theoretical understanding of the relationship among storage density, retrieval times and unit location uncertainty is provided. Finally, a case study using inventory and load plan data from a military application illustrates how the developed models can be used by managers to evaluate selective offloading policies and layouts.     

A bi-objective robust model for emergency resource allocation under uncertainty

Emergency resource allocation constitutes one of the most critical elements of response operations in the field of emergency management. This paper addresses an emergency resource allocation problem which involves multiple competing affected areas and one relief resource centre under supply shortage and uncertainty in the post-disaster phase. In humanitarian situations, both the efficiency and fairness of an allocation policy have a considerable influence on the effectiveness of emergency response operations. Thus, we formulate a bi-objective robust emergency resource allocation (BRERA) model which tries to maximise efficiency as well as fairness under different sources of uncertainties. To obtain decision-makers’ most preferred allocation policy, we propose a novel emergency resource allocation decision method which consists of three steps: (1) develop a bi-objective heuristic particle swarm optimisation algorithm to search the Pareto frontier of the BRERA model; (2) select a coefficient to measure fairness; and (3) establish a decision method based on decision-makers’ preference restricted by the fairness coefficient. Finally, a real case study taken from the 5 December 2008 Wenchuan Earthquake demonstrates the effectiveness of the proposed method through numerical results. The solution and model robustness are also analysed.     

A PSO-based optimum consumer incentive policy for WEEE incorporating reliability of components

The world is going digital, human infatuation with gadgets is increasing and a very short product lifecycle of these products has resulted in a horrendous threat to the environment. Waste electrical and electronic equipment (WEEE) reverse logistic management has been a key area for researchers to innovate and produce insights that could sustain businesses without compromising the environment. In this paper, we aim to understand the consumer return behaviour of end of life goods at different incentive levels and make an attempt to incorporate the latest research practices. A novel attempt is made in this paper, where we have for the first time applied product and component reliability in determining the incentives given to the consumer so that the efforts of WEEE recycling and disposal could be conducted in an economically sustainable manner to promote ecological sustainability, thereby envisaging upon the fact that there is a hidden synergy between the trade and environment, and only innovative managerial approaches that are thoroughly pragmatic, could exploit them. The optimisation model has been solved using particle swarm optimisation (PSO) and the insights produce highlight upon the feasibility of such a model.     

A GIS-based green supply chain model for assessing the effects of carbon price uncertainty on plastic recycling

Recycling plastic can abate the environmental pollution as well as CO₂ emissions by saving the carbon-intensive feedstock input. The uncertain carbon price places significant effects on the establishment and operation of the whole supply chain. This study develops a green supply chain model combined with geographic information system (GIS) to account for carbon price uncertainty and evaluate its effects on the closed-loop supply chain (CLSC) of plastic recycling. A two-stage stochastic programming model is constructed, in which the stochastic variable, CO₂ price is modelled as a geometric Brownian motion process. Six scenarios are designed with respect to price expectation and volatility. A case study is performed with the GIS information of the plastic supply chain in Zhejiang province, China. The results illustrate that triggering the establishment of reverse logistics requires a carbon price threshold significantly beyond the current level. Lower price volatility would facilitate the decision-making of investment into the reverse logistics. Mechanisms to alleviate the market variation shall be introduced. A sound market condition is desired to obtain the optimal balance that encourages the CLSC without creating extra pressure on the firms. The proposed modelling framework can be easily applied to other sectors with similar characteristics.     

Two-stage stochastic master production scheduling under demand uncertainty in a rolling planning environment

This paper proposes a scenario-based two-stage stochastic programming model with recourse for master production scheduling under demand uncertainty. We integrate the model into a hierarchical production planning and control system that is common in industrial practice. To reduce the problem of the disaggregation of the master production schedule, we use a relatively low aggregation level (compared to other work on stochastic programming for production planning). Consequently, we must consider many more scenarios to model demand uncertainty. Additionally, we modify standard modelling approaches for stochastic programming because they lead to the occurrence of many infeasible problems due to rolling planning horizons and interdependencies between master production scheduling and successive planning levels. To evaluate the performance of the proposed models, we generate a customer order arrival process, execute production planning in a rolling horizon environment and simulate the realisation of the planning results. In our experiments, the tardiness of customer orders can be nearly eliminated by the use of the proposed stochastic programming model at the cost of increasing inventory levels and using additional capacity.     

Adjustable Robust Optimisation approach to optimise discounts for multi-period supply chain coordination under demand uncertainty

In this research, a problem of supply chain coordination with discounts under demand uncertainty is studied. To solve the problem, an Affinely Adjustable Robust Optimisation model is developed. At the time when decisions about order periods, ordering quantities and discounts to offer are made, only a forecasted value of demand is available to a decision-maker. The proposed model produces a discount schedule, which is robust against the demand uncertainty. The model is also able to utilise the information about the realised demand from the previous periods in order to make decisions for future stages in an adjustable way. We consider both box and budget uncertainty sets. Computational results show the necessity of accounting for uncertainty, as the total costs of the nominal solution increase significantly even when only a small percentage of uncertainty is in place. It is testified that the affinely adjustable model produces solutions, which perform significantly better than the nominal solutions, not only on average, but also in the worst case. The trade-off between reduction of the conservatism of the model and the uncertainty protection is investigated as well.     

Production control of hybrid manufacturing–remanufacturing systems under demand and return variations

Hybrid manufacturing systems that use both raw materials and returned products as a supply for their production process are considered. Specifically, the system under study contains two machines: one uses raw materials for manufacturing, while another utilises end-of-life products returned from the market for remanufacturing. Machines are failure-prone, demand and return rates fluctuate in time reflecting market behaviour due to economical, seasonal and environmental changes. The system performance is characterised by a long-term discounted cost that integrates several partial costs (those of manufacturing, remanufacturing, disposal, holding costs in serviceable and return inventories). Optimisation of the hybrid system behaviour requires to determine the combined manufacturing, remanufactruring and disposal policy, withstanding machine failures under dynamic market conditions. Optimality conditions in the form of Hamilton–Jacoby–Bellman equations are obtained and a novel numerical approach, based on the estimation of value function timederivative, is proposed in order to deal with demand and return variations. Extensive simulations are performed to address the numerous scenarios corresponding to evolving relationship between manufacturing capacities and varying demand and return levels. Simulation results show that the optimal policies have an important property of anticipating the future changes in the demand and return, and making the timely decisions relevant to these changes.