Flexibility in service parts supply chain: a study on emergency resupply in aviation MRO

Recent trends in the commercial aviation industry have resulted in rapidly increasing complexity and decentralisation in service parts logistics systems. As a consequence, MRO service providers tend to adopt more flexible strategies, such as service parts sourcing and demand fulfilment for customers with different service-level requirements. The MRO service providers often enter into cooperative agreements with other service providers to pool inventories, enabling them to increase their flexibility in delivering services to multiple airlines with different contractual terms. Although using cooperative strategies, such as emergency resupply, is useful to increase flexibility, the inherent complexity of optimal mechanism is a critical issue that needs to be further investigated. To this aim, we consider a repairable service parts inventory system with multi-customer classes and develop an optimal emergency resupply policy. Following this, to overcome the intractability issue of finding the optimal policy, an efficient approximation method is proposed. Numerical results indicate that the proposed approximation method is highly accurate, and leads to a significant costs reduction. This paper sheds light on the effectiveness of emergency resupply policy that improves MRO service providers’ flexibility and enables them to ensure responsive service parts inventory.     

Dynamic rationing and ordering policies for multiple demand classes

In this paper, we study the dynamic rationing problem for multiple demand classes with Poisson demands. We first consider a multi-period problem with zero lead time and show that the optimal rationing and ordering policies are, respectively, the dynamic rationing policy and the base stock policy. We then extend this model to a non-zero lead time and show that there is no simple optimal structure for this extended problem. A myopic policy and a lower bound are proposed. The numerical results show that the dynamic rationing policy outperforms the static rationing policy and its performance is very close to the optimal policy under a wide range of operating conditions.     

Service differentiation in a single-period inventory model with numerous customer classes

We study critical-level inventory-management policies as means to provide differentiated (\(\alpha \) and \(\beta \)) service levels to more than two classes of customers. First, we derive closed-form expressions for the service levels of a single-period critical-level policy with an arbitrary number of customer classes (with Poisson demand). Based on the service-level expressions, we derive additional structural insights and provide an efficient algorithm with which to compute the essential system parameters, that is, the minimum required starting inventory and the associated critical levels. Based on these results, we conduct numerical experiments and develop structural insights into the system’s behavior.     

Cost allocation in inventory pools of spare parts with service-differentiated demand classes

Holding inventory of spare parts is critical to assure safety and production. In order to save costs, different producers may collaborate through an inventory pool. We consider an inventory pool of spare parts, subject to a service level constraint, where the members of the pool may have different target service levels, so that they represent different demand classes. The pool is implemented either by round-up or rationing policies. The members should agree on how to share the costs. Based on cooperative game theory concepts, we show the important effects that different targets can have in the core stability for this problem. We perform a computational study in a large number of instances, providing insights on the emptiness of the core and the performance of seven allocation methods. We also propose the novel Minimum Deviation from Service Level Referential Cost Method (MIND). This method looks for a stable allocation such that the maximum difference between a cost allocated to a player and its service level referential cost is minimised. The MIND allocation is the solution to a linear programming model and is core guaranteed, in the sense that if the core is not empty, the allocation belongs to the core.     

库存随机折损的季节性商品服务策略和库存控制

研究一类随机需求环境下库存随机折损的季节性产品服务策略和库存控制问题.提出按照客户购买行为特征对需求进行分类,并在不同类型的客户之间进行差别化服务的策略.通过构建动态规划模型,得出动态的最优服务和库存控制策略.同无差别服务的报童模型相比,该策略能显著提升零售商的利润,减少商品损坏的损失.利润提高率与零售商对客户的区分力...     

DEALER INVENTORY MANAGEMENT SYSTEMS

This paper presents a model for analyzing inventory control policies for dealers that support the sales and service of manufactured goods. The environment faced by dealers is characterized by multiple stochastic demand classes (prioritized into emergency and regular), a principal source for boui emergency and regular requirements, multiple secondary sources for expedite requirements, and constraints on the lead time and service performance. We are concerned, in particular, with how dealers manage their inventory stockpiles and select expedite sources for replenishment when they have the option of prioritizing customers. The analysis is based on a periodic review, stochastic demand, (s,S) inventory model of dealer stock control. Exact Markov processes and approximate renewal based models are derived based on Cohen, Kleindorfer and Lee [4] and Cohen and Lee [5]. An approximation is used to develop a heuristic algorithm. Extensive numerical testing indicates that the algorithm generates solutions with acceptable cost and service penalties.     

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.     

Dynamic pricing for multiple class deterministic demand fulfillment

We consider how a firm should allocate inventory to multiple customer classes that differ based on the price they pay and their willingness to incur delay in fulfillment of their demand. The problem is set in a deterministic demand, economic-order-quantity-like environment with holding, backorder, lost demand and setup costs. The firm either fulfills demand or offers a price discount to induce the demand to wait for fulfillment from the next reorder. We determine the optimal policy and discuss how changes in various parameters affect profitability, customer service, and operational measures such as order frequency and base stock levels. We compare the results to a policy that only rations inventory without dynamic discounting and to a policy that only provides discounts. Through the comparison, we observe that dynamic pricing can be seen as a combination of a pricing mechanism which determines demand and an allocation mechanism that differentiates between customer classes, serving each ones needs. We show that if lower-value customers are distinguished by accepting reduced service, it is possible that both high and low-value customer classes see better levels of service under the optimal policy than under a discounting only policy. In addition we demonstrate the applicability of the results to a stochastic version of the problem.     

Optimal inventory control of lumpy demand items using (s,S) policies with a maximum issue quantity restriction and opportunistic replenishments

This paper presents a modified (s, S) inventory model which describes the characteristics of an inventory system with lumpy demand items. A maximum issue quantity restriction of w units and a critical inventory position of A units are incorporated into the inventory control policy. Customer orders with demand sizes larger than the maximum issue quantity will be filtered out from the inventory system and satisfied by using special replenishment orders in order to avoid disruption to the inventory system. The option of opportunistic replenishments is introduced to further minimize the total replenishment cost. An opportunistic replenishment is initiated if the level of the current inventory position is equal to or below the critical level when a customer demand with a size exceeding the maximum issue quantity arrives, which does not only initiate a direct shipment to the customer, but also raises the inventory position to S. Two effective algorithms are developed to determine the optimal values of w, A, s and S simultaneously. The first algorithm is based on the branch-and-bound tree search technique, and the second one is based on the concept of genetic algorithms. Numerical examples are used to illustrate the effectiveness of the algorithms developed. The effects of changes in the cost and system parameters on the optimal inventory control policy are also studied by using sensitivity analysis.     

Periodic review inventory-control for perishable products under service-level constraints

Food retail inventory management faces major challenges by uncertain demand, perishability, and high customer service level requirements. In this paper, we present a method to determine dynamic order quantities for perishable products with limited shelf-life, positive lead time, FIFO or LIFO issuing policy, and multiple service level constraints. In a numerical study, we illustrate the superiority of the proposed method over commonly suggested order-up-to-policies. We show that a constant-order policy might provide good results under stationary demand, short shelf-life, and LIFO inventory depletion.     

Optimal production and pricing policies in a combined make-to-order/make-to-stock system

In this paper, we consider a production system which is capable to produce two types of products. The first type of products is make-to-order, while the second type is make-to-stock whose demand is satisfied by the on-hand inventory. The demand arrival rates of both types of products are price-sensitive. The excess demand that cannot be satisfied immediately is either backlogged or lost. The system costs include the holding costs of product inventories and shortage costs of unsatisfied demand. The objective is to maximise the total discounted profit over an infinite planning horizon by coordinating the production process and pricing decisions. By analysing the properties of objective functions, we characterise the optimal control policy by two switch curves and the optimal price is also given for different ordering and inventory levels. We also explore the monotonicity of both switch curves which will reduce the computation effort. Numerical experiments are conducted to demonstrate the use of the switch curves in managing the production system and illustrate that compared with the static pricing policy, the optimal integrated price and inventory control policy can result in a significant profit improvement in the make-to-order/make-to-stock system that is much higher than in a single-product system.     

Optimal batch ordering policies for assembly systems with guaranteed service

For a supply chain modelled as a multi-echelon inventory system, effective management of its inventory at each stock is critical to reduce inventory costs while assuring a given service level to customers. In our previous work, we used the guaranteed-service approach (GSA) to design optimal echelon batch ordering policies for continuous-review serial systems with Poisson customer demand and fixed order costs. The approach assumes that the final customer demand is bounded and each stock has a guaranteed service time in the sense that the demand of its downstream stock can always be satisfied in the service time. This paper extends this work by considering more general assembly systems. We first derive an analytical expression for the total cost of the system in the long run. The problem of finding optimal echelon batch ordering policies for the system can then be decomposed into two independent sub-problems: order size decision sub-problem and reorder point decision sub-problem. We develop efficient dynamic programming algorithms for the two sub-problems. Numerical experiments on randomly generated instances show the effectiveness of the proposed approach.     

Optimal positioning of safety stocks in MRP

The positioning of safety stock in multi-echelon production networks operating in an MRP environment is considered. Our aim is to maximize the service level achieved for a given total amount of safety stock. Most previous research considering MRP environments has been empirical or heuristic, but the approach we take is analytic and concentrates on two network types: serial and divergent networks. Using previous results on the MRP ordering logic, we show that in serial networks the optimal policy positions all safety stock at the end stock-point. This result is independent of the stochastic nature of the demand, the type of uncertainty and the measure of service used. The analysis of divergent networks is more complicated because of the need for material rationing. We show that the optimal policy may depend on the total amount of safety stock available, the variability of the demand, the structure of the lead times, the choice of the rationing policy and the measure of service used.     

Inventory reservation and real-time order promising in a Make-to-Stock system

In this paper we consider a Make-to-Stock order fulfillment system facing random demand with random due date preferences from two classes of customers. We develop an integrated approach for reserving inventory in anticipation of future order arrivals from high priority customers and for order promising in real-time. Our research exhibits three distinct features: (1) we explicitly model uncertain due date preferences of the customers; (2) we consider multiple receipts in the planning horizon that can be utilized to fulfill customer orders; and (3) we choose to utilize a service level measure for reserving inventory rather than estimating short- and long-term implications of order promising with a penalty cost function. We propose an algorithm that exploits the time structure in order arrivals and time-phased material receipts to determine inventory reservations for high priority orders. Numerical experiments are conducted to investigate the performance and the benefits of the inventory reservation and order promising approach under varying system parameters.     

Shortage decision policies for a fluid production model with MAP arrivals

We consider on a continuous production/inventory process where a single machine produces a certain product into a finite buffer. The demands arrive according to a Markov Additive Process governed by a continuous-time Markov chain, and their sizes are independent and have phase-type distributions depending on the type of arrival. Two shortage policies are considered: the backorder policy, in which any demand that cannot be satisfied immediately is backlogged, and the order policy, in which any demand that cannot be satisfied immediately is supplied (alternatively, the latter policy can be considered as lost sales). We assume that the total cost includes a production loss cost, a penalty cost, a fixed cost for an order and a variable cost for the ordered amount. By applying the regenerative theory, we use tools from the exit-time theorem for fluid processes to obtain the discounted cost functionals under both policies. In addition, the models are extended to include a non-zero safety stock. Numerical examples, sensitivity analysis and comparative study are included.     

供应中断情况下动态混合应急策略研究

动态刻画市场需求中断反应行为:自动留存订单、等待制造商应急采购延迟完成订单、由安全库存完成订单、取消订单。综合考虑应急采购的提前期及成本、安全库存储备量、企业恢复能力,构建以中断负面影响最小化为目标的最优控制模型。应用最大值原理,提出三种最优的制造商动态响应策略,包含一种纯库存与两种混合策略,决策如何基于库存量、中断持续时长等相关因素实时消耗库存,同时进行应急采购。     

Inventory and lead time planning with lead-time-sensitive demand

Supply and order lead times can have substantial effects on operations performance and perceived customer service, particularly under uncertain customer demand. Certain customers place a high premium on shorter order lead times, while others may be willing to trade a longer lead time for a lower price. This paper studies a problem in which a supplier wishes to determine the best positioning of a product with respect to order lead time and price. We consider a continuous review inventory replenishment system, where the difference between the procurement lead time and promised sales order lead time influences both cycle stock and safety stock costs, and procurement costs may increase as a result of investment in procurement lead time reduction. We provide models and methods for determining the best combination of price and sales lead time for systems with high economies of scale when demand depends on both sales lead time and price. Our results indicate that for a broad range of practical settings, such systems employ a pure make-to-stock policy or a policy that sets sales lead time equal to the procurement lead time at optimality.     

Optimal Strategy for Limit Order Book Submissions in High Frequency Trading

An optimal selection problem for bid and ask quotes subject to a stock inventory constraint is investigated, formulated as a constrained utility maximisation problem over a finite time horizon. The arrivals of buy and sell orders are governed by Poisson processes, and a diffusion approximation is employed on assuming the Poisson arrivals intensity is sufficiently large. Using the dynamic programming principle, we adopt an efficient numerical procedure to solve this constrained utility maximisation problem based on a successive approximation algorithm, and conduct numerical experiments to analyse the impacts of the inventory constraint on a dealer’s terminal profit and stock inventory level. It is found that the stock inventory constraint significantly affects the terminal stock inventory level.     

An improved ordering policy for continuous review inventory systems with arbitrary inter-demand time distributions

In this paper, we revisit the optimality of (s,S) policies in continuous review inventory models where demand forms a renewal process. We explain why when orders are placed at demand epochs, (s,S) policies are not optimal in general, and propose a simple but practical ordering policy by introducing a delay in order placement as a policy parameter. Under our proposed policy, the operating characteristics of such systems can be evaluated using the existing results in the literature. In order to demonstrate the effectiveness of our policy, we restrict our analysis to a special class of inventory systems where demand follows a counting process, fixed ordering costs are negligible and leadtimes are constant. We derive expressions for the operating characteristics of such systems under our policy and present insights on the behavior of the policy parameters which minimize the average total cost rate under our policy. Using these results, we develop an efficient heuristic for computing the policy parameters. Finally, we investigate the effectiveness of our policy in comparison to policies which place orders only at demand epochs. The results of our numerical experiment indicate that our policy can result in a significant savings.     

Continuous review (s,S) policies for inventory systems incorporating a cutoff transaction size

In this paper, a mathematical model is developed for the analysis of optimal replenishment policies for items which experience lumpy demands. In order to avoid disrupting the inventory system, a cutoff transaction size of w units is specified such that customer demands with sizes exceeding w units will be filtered out of the inventory system and treated as special orders to be satisfied by special deliveries. Customer demands with sizes > units will be met From stock. The control discipline is the (s, S) inventory policy with continuous review and the nature of the demands is approximated by a stuttering Poisson distribution. Recursive formulae are developed for the determination of the probabilities of the lead time demand and the available inventory position. The optimal values of the control parameters, s and S, are determined. The theoretical results obtained are illustrated with a numerical example.