Base-stock Level Research Articles

A TWO-ECHELON SPARE PARTS NETWORK WITH LATERAL AND EMERGENCY SHIPMENTS: A PRODUCT-FORM APPROXIMATION

We consider a single-item, two-echelon spare parts inventory model for repairable parts for capital goods with high downtime costs. The inventory system consists of multiple local warehouses, a central warehouse, and a central repair facility. When a part at a customer fails, if possible his request for a ready-for-use part is fulfilled by his local warehouse. Also, the failed part is sent to the central repair facility for repair. If the local warehouse is out of stock, then, via an emergency shipment, a ready-for-use part is sent from the central warehouse if it has a part in stock. Otherwise, it is sent via a lateral transshipment from another local warehouse, or via an emergency shipment from the external supplier. We assume Poisson demand processes, generally distributed leadtimes for replenishments, repairs, and emergency shipments, and a basestock policy for the inventory control.Our inventory system is too complex to solve for a steady-state distribution in closed form. We approximate it by a network of Erlang loss queues with hierarchical jump-over blocking. We show that this network has a product-form steady-state distribution. This enables an efficient heuristic for the optimization of basestock levels, resulting in good approximations of the optimal costs.

Optimizing stock levels for rental systems with a support warehouse and partial backordering

Various rental systems, such as public libraries and tool rental companies, have a support warehouse for storing rental products at low cost and carrying out expedited shipments in response to stock-outs at local warehouses. In case of stock-outs, rental systems commonly employ partial backordering, i.e., a limited number of demands is backordered while additional demand is lost. We include partial backordering in our models and demonstrate its relevance. We fully characterize costs and optimal base stock policies in cases with one support and one local warehouse and provide upper bounds for base stock levels in the general system. By enumerating base stock policies and evaluating exact costs numerically, we determine optimal base stock policies for small systems with up to six local warehouses. For larger systems we develop a greedy algorithm based on approximate cost evaluations. The resulting base stock policies have costs within 0.2% from optimality on average in experiments. Among other things, experiments indicate that existing methods with no backordering may lead to poor solutions with partial backordering and that partial backordering is an effective means to reduce lost demand even with limited partial backorder levels.

Dynamic Supply Risk Management with Signal‐Based Forecast, Multi‐Sourcing, and Discretionary Selling

We examine the critical role of advance supply signals—such as suppliers’ financial health and production viability—in dynamic supply risk management. The firm operates an inventory system with multiple demand classes and multiple suppliers. The sales are discretionary and the suppliers are susceptible to both systematic and operational risks. We develop a hierarchical Markov model that captures the essential features of advance supply signals, and integrate it with procurement and selling decisions. We characterize the optimal procurement and selling policy, and the strategic relationship between signal‐based forecast, multi‐sourcing, and discretionary selling. We show that higher demand heterogeneity may reduce the value of discretionary selling, and that the mean value‐based forecast may outperform the stationary distribution‐based forecast. This work advances our understanding on when and how to use advance supply signals in dynamic risk management. Future supply risk erodes profitability but enhances the marginal value of current inventory. A signal of future supply shortage raises both base stock and demand rationing levels, thereby boosting the current production and tightening the current sales. Signal‐based dynamic forecast effectively guides the firm's procurement and selling decisions. Its value critically depends on supply volatility and scarcity. Ignoring advance supply signals can result in misleading recommendations and severe losses. Signal‐based dynamic supply forecast should be used when: (a) supply uncertainty is substantial, (b) supply‐demand ratio is moderate, (c) forecast precision is high, and (d) supplier heterogeneity is high.

Quantifying sustainable control of inventory systems with non-linear backorder costs

Traditionally, when optimizing base-stock levels in spare parts inventory systems, it is common to base the decisions either on a linear shortage cost or on a certain target fill rate. However, in many practical settings the shortage cost is a non-linear function of the customer waiting time. In particular, there may exist contracts between the spare parts provider and the customer, where the provider is obliged to pay a fixed penalty fee if the spare part is not delivered within a certain time window. We consider a two-echelon inventory system with one central warehouse and multiple local sites. Focusing on spare parts products, we assume continuous review base stock policies. We first consider a fixed backorder cost whenever a customer’s time in backorder exceeds a prescribed time limit, second a general non-linear backorder cost as a function of the customer waiting time, and third a time window service constraint. We show from a sustainability perspective how our model may be used for evaluating the expected hbox {CO}_2 emissions associated with not satisfying the customer demands on time. Finally, we generalize some known inventory models by deriving exact closed form expressions of inventory level distributions.

On component commonality for periodic review assemble-to-order systems

Akcay and Xu (Manag Sci 50(1):99–116, 2004) studied a periodic review assemble-to-order (ATO) system with an independent base stock policy and a first-come-first-served allocation rule, where the base stock levels and the component allocation are optimized jointly. The formulation is non-convex and, thus theoretically and computationally challenging. In their computational experiments, Akcay and Xu (Manag Sci 50(1):99–116, 2004) modified the right hand side of the inventory availability constraints by substituting linear functions for piece-wise linear ones. This modification may have a significant impact for low budget levels. The optimal solutions obtained via the original formulation; that is, without the modification, include zero base stock levels for some components and indicate consequently a bias against component commonality. We study the impact of component commonality on ATO systems. We show that lowering component commonality may yield a higher type-II service level. The lower degree of component commonality is achieved via separating inventories of the same component for different products. We substantiate this property via computational and theoretical approaches. We show that for low budget levels the use of separate inventories of the same component for different products could achieve a higher reward than with shared inventories. Finally, considering a simple ATO system consisting of one component shared by two products, we characterize the budget ranges such that the use of separate inventories is beneficial, as well as the budget ranges such that component commonality is beneficial.

Exact analysis of the [formula omitted] inventory policy in a two-echelon production–inventory system

We consider a two-echelon production–inventory system with a single manufacturer operating from a warehouse and a distribution center (DC) using the continuous review (R,Q) inventory policy where transportation times between the two echelons are generally distributed. We first derive the optimal reorder point at the DC, and then, propose a heuristic to approximate the optimal base-stock level in the warehouse as well as the batch order size at the DC.

An inventory system with quasi-hyperbolic discounting rate

ABSTRACTIn this article, we consider a periodic-review inventory system with stochastic demands for an infinite horizon, where the manager has a time-inconsistent preference with a quasi-hyperbolic discounting rate. We model the inventory system as an intra-personal sequential decision problem. It is shown that the ordering decision follows a base-stock policy but has a systematic bias in that the base-stock level is lower than the standard optimal level. We extend our analysis to a supply chain that is composed of a perfectly rational supplier and a quasi-hyperbolic retailer. The results show that the time-inconsistent preference of the retailer can cause considerable loss in system performance. We propose a contract with a delay-in-payment and income-sharing for such a supply chain. The results show that the contract can effectively un-bias the ordering decision of the retailer and can reach the goal of coordinating the supply chain to improve the performance.

Managing capacity and inventory jointly for multi-server make-to-stock queues

We consider joint capacity---inventory management for multi-server make-to-stock queues operating under a base stock policy. The number of servers corresponds to the capacity decision, and the base stock level is the inventory decision. Our goal is to minimize a combination of capacity, inventory, and backordering costs. We develop a square-root rule for the joint decision and justify the rule analytically in a many-server queue asymptotic framework. We demonstrate the accuracy of the square-root rule, first via our derivation and numerical assessment of a novel corrected diffusion approximation and then more directly by conducting extensive numerical experiments. Finally, we provide operational insights into the trade-offs involved in such joint management problems, through various analysis based on the square-root rule as well as a comparison with analogous results for single-server make-to-stock queues.

Inventory management of reusable surgical supplies.

We investigate the inventory management practices for reusable surgical instruments that must be sterilized between uses. We study a hospital that outsources their sterilization services and model the inventory process as a discrete-time Markov chain. We present two base-stock inventory models, one that considers stockout-based substitution and one that does not. We derive the optimal base-stock level for the number of reusable instruments to hold in inventory, the expected service level, and investigate the implied cost of a stockout. We apply our theoretical results to a dataset collected from a surgical unit at a large tertiary care hospital specializing in colorectal operations. We demonstrate how to implement our model when determining base-stock levels for future capacity expansion and when considering alternative stockout protocols. Our analysis suggests that the hospital can reduce the number of reusable instrument sets held in inventory if on-site sterilization techniques (e.g., flash sterilization) are employed. Our results will guide future procurement decisions for surgical units based on costs and desired service levels.

Redistributing stock in library systems with a depot

Public library organizations often utilize depots for carrying out shipments to libraries in case of stock-outs and for storing low demand rental items at low cost. Similar systems may be employed by rental companies for other rental products such as tools, DVDs, and jewelry. Since shipments deplete the depot’s inventory, stock must be taken back from the libraries in order to deal with future shipment requests. These shipment and take-back operations are carried out periodically, e.g. daily or weekly. This work focuses on optimizing the decisions for shipments and take-backs. We model the system by means of a Markov decision process and investigate its optimal policy for various problem instances. For the take-back decision, we distinguish between so-called threshold, reactive, and preventive take-backs. We use the insights from the MDP to develop a three-phase take-back heuristic. In experiments, our heuristic performs within 1% on average from the optimal solution. For settings with a large number of libraries, it is shown that an acceptable performance can be achieved by setting a base-stock level at the depot and taking back sufficient stock from the libraries to achieve this level.

Measuring the Bullwhip Effect: Discrepancy and Alignment Between Information and Material Flows

The bullwhip effect is a phenomenon commonly observed in supply chains. It describes how demand variance amplifies from a downstream site to an upstream site due to demand information distortion. Two different bullwhip effect measures have been used in the literature. Theorists analyze the bullwhip effect based on the information flow (i.e., order and demand information), whereas most empiricists measure it according to the material flow (i.e., shipment and sales data). It is unclear how much the discrepancy between these two measures is, and, if significant, how to reconcile the discrepancy. In this paper, we illustrate and quantify the discrepancy under three inventory systems. For the system with stationary demand and ample supply, we show that the bullwhip effect measure based on the material-flow data is always greater than that based on the information flow. For the system with correlated demand and for the system with supply shortages, we derive conditions under which the material flow measure is either greater or less than the information flow measure. We find that the discrepancy is driven by four factors: stocking level, lead time, demand correlation, and supply service level. We further propose a method to reduce the discrepancy by using the sample variances of aggregated sales data. Our method works for common demand processes with short-range dependence, and it does not require the knowledge of the underlying base-stock levels.

Optimal production, pricing, and substitution policies in continuous review production-inventory systems

We consider the optimal production, pricing, and substitution policies of a continuous-review production-inventory system with two products: a high-end product and a low-end product. Each product has its associated customer stream; however, the demands for the low-end product may be satisfied by the high-end product. We formulate the problem as a Markov decision process and characterize the structure of the optimal control policy, which specifies when to produce for each product, when to use the high-end product as a substitute, and how to set the optimal prices. We show that a base-stock production policy is optimal; however, the optimal base-stock level for each product depends on the inventory level of the other product and it features a monotonic property. We also demonstrate that the optimal substitution policy is a rationing policy with the rationing level depending on the total inventory amount. We find that the optimal prices can be either decreasing or increasing in the inventory levels, depending on the forms of demand functions. Furthermore, we utilize numerical experiments to investigate the impact of different system characteristics on the benefits of using substitution and dynamic pricing. Finally, we investigate when the dynamic pricing strategy and the substitution strategy are complements or substitutes.

Maintenance cost optimisation by integrating human and material resources: a case study

Increasing the operational efficiency of complex technical systems is a major point of interest in logistics, inventory management and maintenance fields. Apart from being a support for the maintenance systems, the integration of resource allocation (especially human resources, inventories, and logistics) affects the availability of spare parts, and the operational efficiency. In this paper, first, a mixed integer nonlinear programming model based on base-stock inventory model is developed to formulate the problem of maintenance cost optimisation with integrating human and material resources. The model seeks the optimal number of workforces who repair equipment, the long run fill rate and the base-stock level in each stocking facility. Next, reformulate the model which contains spare parts demand uncertainty with the robust counterpart optimisation approach. The presented model is executed in one of the major car manufacturers in Iran.

Optimal Control Policy for Stochastic Inventory Models with Two Substitutable Products

In this paper, we consider a stochastic inventory system of two products where a fi xed proportion of the unsatisfied ed demand for one product purchases the other product as a substitute. We formulate the optimal inventory control problem as a dynamic program; and by developing two key technical results, we derive several important structural properties (including joint concavity and submodularity) of the value functions. Based on these properties, we show that the optimal inventory policy for each product in each period is a base-stock policy where the base-stock level is a decreasing function of the maximum of the initial inventory level of the other product and a critical control number. We further prove that, as the initial inventory level of the other product increases, the base-stock level of each product converges to the optimal base-stock level of an auxiliary single-product lost-sales inventory system. We also provide intuitive interpretations and a numerical example to facilitate the understanding of our analytical results.

Stock or Print? Impact of 3D Printing on Spare Parts Logistics

We present a general framework to analyze and quantify the impact of 3D printing on spare parts logistics. We consider multiple parts facing stochastic demands. To minimize long-run average system cost, our model determines which parts should be printed and which should be stocked and the corresponding base-stock levels. When a demand for a stocked part encounters a stockout, it can either be backlogged or overflowed to the 3D printer. We derive various structural properties and characterize the optimal policy for several special systems, which lead to efficient near-optimal heuristic solutions for the general system. We demonstrate that adopting 3D technology can yield significant cost savings and this impact increases in part variety. Also, “a little flexibility goes a long way” in the sense that allowing both the stock and print options can substantially slash system inventory and cost, while the utilization of the 3D printer is surprisingly low.

Optimal Inventory Control with Advance Supply Information

It has been shown in numerous situations that sharing information between the companies leads to improved performance of the supply chain. We study a positive lead time periodic-review inventory system of a retailer facing stochastic demand from his customer and stochastic limited supply capacity of the manufacturer supplying the products to him. The consequence of stochastic supply capacity is that the orders might not be delivered in full, and the exact size of the replenishment might not be known to the retailer. The manufacturer is willing to share the so-called advance supply information (ASI) about the actual replenishment of the retailer's pipeline order with the retailer. ASI is provided at a certain time after the orders have been placed and the retailer can now use this information to decrease the uncertainty of the supply, and thus improve its inventory policy. For this model, we develop a dynamic programming formulation, and characterize the optimal ordering policy as a state-dependent base-stock policy. In addition, we show some properties of the base-stock level. While the optimal policy is highly complex, we obtain some additional insights by comparing it to the state-dependent myopic inventory policy. We conduct the numerical analysis to estimate the in uence of the system parameters on the value of ASI. While we show that the interaction between the parameters is relatively complex, the general insight is that due to increasing marginal returns, the majority of the benets are gained only in the case of full, or close to full, ASI visibility. DOI: 10.15458/85451.28

Dynamic Stochastic Inventory Management with Reference Price Effects

We analyze the joint inventory and pricing decisions of a firm when demand depends on not only the current selling price but also a memory-based reference price and customers are loss averse. The presence of reference price effect leads to a nonconcave one-period expected revenue in price and reference price. We introduce a transformation technique that allows us to prove under some mild assumptions the optimality of a reference-price-dependent base-stock list-price policy, which is characterized by a base-stock level and a target reference price. In addition, we show that the target reference price is increasing in the reference price, but except in the loss-neutral case, the base-stock level is not monotone in the reference price. We also show that in the steady state of the model with the reference price effect, the optimal price is lower while the optimal base-stock level is higher than their counterparts in the model without the reference price effect.

Joint Pricing and Production Control for a Manufacturer With Volume Flexibility

We consider a make-to-stock manufacturer that produces a single product and sells it through two different channels, one local and the other contractual. We determine how to manage production and pricing in the local channel in order to maximize the total expected discounted profit earned over an infinite time horizon. We characterize the optimal policy as comprising a base stock level for production control and a collection of thresholds for product pricing in the local channel.

Knowledge You Can Act on: Optimal Policies for Assembly Systems with Expediting and Advance Demand Information

We consider a nonstationary, stochastic, multistage supply system with a general assembly structure, in which customers can place orders in advance of their future demand requirements. This advance demand information is now recognized in both theory and practice as an important strategy for managing the mismatch between supply and demand. In conjunction, we allow expediting of components and partially completed subassemblies in the system to provide the supply chain with the means to manage the stockout risk and significantly enhance cost savings realized through advance demand information. To solve the resulting assembly system, we develop a new method based on identifying local properties of optimal decisions. This new method allows us to solve assembly systems with multiple product flows. We derive the structure of the optimal policy, which represents a double-tiered echelon basestock policy whose basestock levels depend on the state of advance demand information. This form of the optimal policy allows us to: (i) provide actionable policies for firms to manage large-scale assembly systems with expediting and advance demand information; (ii) prove that advance demand information and expediting of stock both reduce the amount of inventory optimally held in the system; and (iii) numerically solve such assembly systems, and quantify the savings realized. In contrast to the conventional wisdom, we discover that advance demand information and expediting of stock are complementary under short demand information horizons. They are substitutes only under longer information horizons.

Competitiveversuscooperative performances of a Stackelberg game between two suppliers

We investigate the competitive and cooperative performances of a supply chain with two capacitated suppliers solicited by a customer who offers a new product procurement suggestion. Suppliers have the option to accept or reject the new product offer according to its profitability. In addition, suppliers have to decide on their base stock levels. We classify suppliers as principal and secondary. The customer usually addresses demand to the principal supplier at first. We consider two schemes: in the first scheme, the principal supplier informs the customer about the demand ratio he wants to be allocated. The customer allocates the remaining quantity to the secondary supplier. In the second scheme, the principal supplier decides to respond to the entire demand and to subcontract a part of it to the secondary supplier. In the competitive situation, we give conditions that allow principal supplier to select the best scheme. We show that the new product offer can be refused while it is accepted when suppliers cooperate. We present a profit allocation policy under which collaboration is beneficial for the two suppliers.