Outstanding Orders Research Articles

Integrated inventory models with controllable lead time and backorder discount considerations

Many companies use time as a means of differentiating themselves in the marketplace. In many literatures, the controllable lead time is regarded as a decision variable and decomposed into several components, each having a crashing cost function for the respective reduced lead time. When an item is out of stock, the loyal, patient and captive customers will wait until the outstanding orders arrive and are served from them. To compensate for the inconvenience of backordering and to secure orders, the supplier may offer a price discount on the stockout item. In this paper, an integrated inventory system in which shortage is allowed and both lead time and backordering are negotiable is investigated. The lead time crashing cost is represented as a function of reduced lead time and the quantities in the orders. There are two inventory models proposed in the paper, one with normally distributed demand, and another with generally distributed demand.

Multi-period dynamic supply contracts with cancellation

This paper considers a class of multi-period dynamic supply contracts in which a buyer orders a product from a supplier in each period and the supplier allows the buyer to cancel a portion of an outstanding order with penalty during a planning horizon. We assume that both the buyer and the supplier have common knowledge. We first characterize the buyer's ordering and canceling policy that minimizes his expected cost during the planning horizon. We also characterize the supplier's optimal production policy under a very mild assumption on the costs of production and storage. Based on this structure, we then use simulation to show how the supplier chooses cancellation costs that minimize her expected cost during the planning horizon. Our simulation shows that both the buyer and the supplier would benefit from the contract.

Limit Order Imbalances and Return Predictability

An event study methodology is employed to examine the size and predictability of stock price movements subsequent to the occurrence of a limit order imbalance. Whilst existing studies have examined the association between price pressure and stock prices, there has been no research that has directly examined whether information regarding outstanding limit order imbalances at the end of the trading day can be used to predict subsequent stock price movements. The results indicate that a statistically significant mean positive (negative) abnormal return of 0.63 percent (0.64 percent) is experienced on the day subsequent to a buyside (sell-side) order imbalance. Also statistically significant is the finding that 60.00 percent of abnormal returns for firms experiencing buy-side imbalances are positive and 62.15 percent of abnormal returns for firms experiencing sell-side imbalances are negative, suggesting some degree of predictability. It should be noted however, that whilst the size of the abnormal returns and the ratio of positive-to-negative abnormal returns are statistically significant, they are possibly not economically significant in terms of implementing a profitable trading strategy.

Measured effects of user and clinical engineer training using a queuing model.

This article puts forward a new proposal to calculate count, turnaround, response, and service time of work orders in a clinical engineering (CE) department. These are calculated by means of a queuing model as a measurement tool. This proposal was tested in a 600-bed hospital with an inventory of 1094 medical devices and with 6 full-time clinical engineers. In April 1999, a simulation (with ARENA 3.01 developed by System Modeling Corporation) of the working of this proposal was performed with desired values being applied to the queuing model. At the end of 2002, real work order data from the database was recorded. As predicted, the results showed that all the indicators of nonscheduled work orders decreased. Response and turnaround time were reduced from 27 to 0.56 hours and 27.48 to 1.13 hours, respectively. From a backlog of 22 outstanding repair orders per month between April 1999 and January 2000, the number was reduced to 4 in December 2002. The queuing model also helped to measure the positive effects on arrival and service rates when users and CE were trained. The difference between simulated and real values was under 5%.

Functional Limit Theorems for a Simple Auction

We consider a continuous transparent auction with one asset. Buyers and sellers arrive at the auction according to independent renewal processes, willing to transact a random number of units (shares) of the asset for one of N possible prices. Upon arrival, they buy/sell as many units of the asset as they can for the best price available at that time. However, if the prices offered for sale/purchase are worse than their initial preferences, they do not transact, but instead they stay at the auction, posting buying/selling orders and waiting for a suitable counterparty. We model the numbers of outstanding orders of each type, together with the numbers of assets exchanged up to date by customers of different types, by stochastic processes and find the limiting distributions of these (suitably scaled) processes.

The Logistics Impact of a Mixture of Order-Streams in a Manufacturer-Retailer System

We model a supply chain with two retail warehouses that place replenishment orders with a common manufacturing capacity. The two retailers differ in the variability of their order-streams. The order-stream from one retail warehouse is modeled as a Poisson process and from the other as a hyperexponential renewal process. Each retail warehouse uses a base-stock policy to place replenishment orders with the manufacturer. The manufacturer is modeled as a first-come-first-serve, single exponential server queue. We analyze the supply-side impact of this mixture of order-streams received by the manufacturer on both retailers. An exact analysis of this base-model generates closed-form expressions for distributions of the lead-time, outstanding orders, and expected inventory costs for each retailer, and leads to comparative results about the two retailers- performance measures. The base-model is extended to accommodate finished goods at the manufacturer, more than two retailers, and bulk-arrivals. We use the model to suggest managerial insights about the impact of the presence of a high-variability retailer on other retailers who share capacity, the distorting impact of manufacturer finished goods inventory on retailer incentives, and the incentives for retailers to participate in variability-reduction programs in the grocery industry.

An Internet Appendix to: The Impact of Duplicate Orders on Demand Estimation and Capacity Investment

Motivated by a $2.2 billion inventory write-off by Cisco Systems, we investigate how duplicate orders can lead a manufacturer to err in estimating the demand rate and customers' sensitivity to delay, and to make faulty decisions about capacity investment. We consider a manufacturer that sells through two distributors. If a customer finds that his distributor is out-of-stock, then he will sometimes seek to make a purchase from the other distributor; if the latter is also out-of-stock, the customer will order from both distributors. When his order is filled by one of the distributors, the customer cancels any duplicate orders. Furthermore, the customer cancels all of his outstanding orders after a random period of time. Assuming that the manufacturer is unaware of duplicate orders, we prove that she will overestimate both the demand rate and the cancellation rate. Surprisingly, failure to account for duplicate orders can cause short-term underinvestment in capacity. However, in long term equilibrium under stable demand conditions the manufacturer overinvests in capacity. Our results suggest that Cisco's write-off was caused by estimation errors and cannot be blamed entirely on the economic downturn. Finally, we provide some guidance on estimation in the presence of double orders. The majority of the results in our paper apply to the base case where the manufacturer dedicates a fixed fraction of her capacity to each distributor. This Appendix shows that the results remain true when the manufacturer fills distributors' orders FIFO from pooled capacity.

The Impact of Duplicate Orders on Demand Estimation and Capacity Investment

Motivated by a $2.2 billion inventory write-off by Cisco Systems, we investigate how duplicate orders can lead a manufacturer to err in estimating the demand rate and customers' sensitivity to delay, and to make faulty decisions about capacity investment. We consider a manufacturer that sells through two distributors. If a customer finds that his distributor is out-of-stock, then he will sometimes seek to make a purchase from the other distributor; if the latter is also out-of-stock, the customer will order from both distributors. When his order is filled by one of the distributors, the customer cancels any duplicate orders. Furthermore, the customer cancels all of his outstanding orders after a random period of time. Assuming that the manufacturer is unaware of duplicate orders, we prove that she will overestimate both the demand rate and the cancellation rate. Suprisingly, failure to account for duplicate orders can cause short-term underinvestment in capacity. However, in long term equilibrium under stable demand conditions the manufacturer overinvests in capacity. Our results suggest that Cisco's write-off was caused by estimation errors and cannot be blamed entirely on the economic downturn. Finally, we provide some guidance on estimation in the presence of double orders.

A two-echelon inventory system with supply lead time flexibility

The impact of manufacturing flexibility on inventory investments in a distribution network consisting of a central depot and a number of local stockpoints is investigated. The lead time of outstanding orders in the pipeline of the central depot can be shortened by the use of flexibility. Stock levels are controlled by a periodic review echelon-order-up-to-policy under service level constraints.

Tracking Not Yet Published Material: Using Bibliographic Record the Smart Way

In July 2001, the Pennsylvania State University Libraries stopped placing purchase orders for materials that were deemed not yet published or available. It was important that our carry-over encumbrances not be too high since that would impact the Libraries' purchasing power for the following year. In addition, it was felt that the collections budget should be spent on titles that are readily available, rather than tied up in materials that may not be published for one to two or even five more years. In should be noted that Penn State's fiscal cycle runs July 1 to June 30, at which time State appropriated funds should be fully expended. Any outstanding orders for library materials are then applied against the new year budget(s). For the first year of implementation of this new policy, manual files that were reviewed at specified intervals, were kept of all titles not yet published. This was a time-consuming and tedious process. In an effort to make this process much more efficient, and to take advantage of our new library management system's capabilities, our Budget Coordinator worked with a group of individuals' in Acquisitions Services to develop a procedure that was not only automated, but would allow selectors to gain up to the minute information on not yet published requests via the Web with a WebCat (public catalog) view of their titles.

Restricted time-remembering policies for the inventory rationing problem

We analyse an ( s, Q) inventory model with unit Poisson demand, several demand classes and lost sales. When dealing with different demand classes the usual approach is to control the inventory by critical levels at which stock is reserved for demand of higher priority. We focus on time-remembering policies where the critical levels are allowed to depend on the time since the actual outstanding order (if any) was issued. In particular, we introduce a new class of policies called restricted time-remembering (RTR) policies. We divide the lead time in m intervals of time and restrict the critical levels of the RTR policy to be constant over each interval of time. This policy is much easier to implement than the optimal rationing policy, where the critical levels can change continuously over time, and in a numerical study we show that the performance of the RTR policy is close to that of the optimal policy, even when the number of intervals is 2 or 3.

Ranking of generalised multi-stage KANBAN policies

We consider KANBAN type batch-ordering policies in a multi-stage production–inventory system. KANBAN policies and various modifications of such policies may be interpreted as installation stock ( Q, r)-policies with constraints on the number of outstanding orders. If the same constraints are applied also to MRP and echelon stock ( Q, r)-policies, the ranking lists established by Axsäter and Rosling (Axsäter, S., Rosling, K., 1993. Management Science 39, 1274–1280; Axsäter, S., Rosling, K., 1994. European Journal of Operational Research 75, 405–412) for such policies remain valid. The result is based on new definitions of the inventory positions, and suggests new classes of generalised KANBAN type batch-ordering policies with potentially improved performance.

An Information Based Multiechelon Inventory System with Emergency Orders

In this paper we study a (S-1, S) type multiechelon inventory system where all the stocking locations have the option to replenish their inventory through either a normal or a more expensive emergency resupply channel. When ordering a unit, each stocking location decides which channel to use based on its inventory level and the remaining leadtimes of the its outstanding orders. We consider the implications of this policy by developing expressions for the operating characteristics of the system and describing a procedure for finding the optimal policy parameters. A numerical study presented in the paper indicates that when alternative resupply modes are available our policy, which incorporates the information on the remaining leadtimes of the outstanding orders in selecting the resupply mode, can result in considerable cost savings when compared to policies which allow a single resupply mode.

Tractable (Q, R) Heuristic Models for Constrained Service Levels

The fill rate (the proportion of demand that is satisfied from stock) is a viable alternative in inventory models to the hard-to-quantify penalty cost. However, a number of difficulties have impeded its implementation, among them that the existing cycle-based approximate solutions do not reflect the possibility of multiple outstanding orders and that the optimal policy cannot be found directly, but must be iteratively calculated. We show that for a large family of leadtime demand distributions, the optimal policy depends on only two parameters: the fill rate and the economic order quantity (EOQ) scaled by the standard deviation of demand over the constant leadtime. If we then assume that the leadtime demand is normally distributed, we can use the asymptotic results as the EOQ goes to zero and to positive infinity to fit atheoretic curves for the order quantity Q and the reorder point R. These fitted curves yield a good (Q, R) policy without iteration. We also find that, among the set of simple heuristics, the limit form as EOQ goes to positive infinity provides a better alternative to simply setting Q equal to the EOQ.

The{Q,r)Inventory System With An Unreliable Supplier

AbstractThis paper examines the impact on operating costs of having an unreliable supplier in a continuous review, fixed order quantity (Q) — reorder point (r) inventory system. We assume Poisson demand and exponentially distributed lengths of the supplier’s on and off periods. On (off) periods represent time lengths during which the supplier is able (unable) to fill new orders. Any unsatisfied demand is assumed to be lost. We analyze two situations. The first has a negligible lead time but allows the number of outstanding orders, each of a fixed size Q, to be arbitrary. The second situation, on the other hand, has a constant lead time but there the number of outstanding orders is restricted to at most one. In each case, exact expressions necessary to find the average cost minimizing (Q, r) pair are developed and several numerical examples are solved. Computational results show the cost function to be well behaved and suggest that ignoring supply uncertainty or approximate modeling can be relatively very ...

Base stock level determination for high cost low demand critical repairable spares

The paper presents an ( S − 1, S) policy with three modes of replenishment: normal repair orders, emergency repair orders, and the expediting of outstanding orders. A procedure based on simulation is described in order to determine the parameters of the replenishment policy: the base stock level S, the expediting level S ̂ , and the expediting threshold T 0. The application of this procedure to a category of repairable spares at a paper mill demonstrates the computational feasibility of the solution procedure.

An (S − 1, S) Inventory System with Emergency Orders

In this paper, we develop an approximate model of an inventory control system in which there exist two options for resupply, with one having a shorter lead-time. We assume that demand and the fixed ordering costs are small relative to the holding cost so that a one-for-one ordering policy is appropriate. We consider a policy for placing emergency orders that uses information about the age of outstanding orders. We derive the steady-state behavior of this policy and present some computational results.

Inventory Decision under Demand Uncertainty: A Contingent Claims Approach

AbstractThis study uses the discrete‐time option pricing model for the evaluation of the firm's inventory decision under demand uncertainty. The paper establishes the following optimal inventory decision implications: the optimal order quantity is positively related to the product selling price, product salvage value, interest rate, and the size of the outstanding orders; and negatively related to the product cost. The effect of demand uncertainty on the optimal order quantity is shown to be ambiguous. This study also shows that the maximum present value of profit from the contingent claims approach can be substantially different from that of the modified standard newsboy problem.

Computer System of Library Management and Information Retrieval at the Shaanxi Astronomical Observatory

For modern management and full resource sharing among libraries and scientific departments both in Chinese and worldwide observatories, we established the computer system of library management and information retrieval during the period 1984-1987.The system is composed of ten component sub-systems: 1.Book ordering system. This system can produce orders for books and periodicals, balance accounts, produce statistics as well as claims for outstanding book orders.2.Book cataloguing system. This system can catalogue books under certain rules while appending new records of books to the databases. It can also produce catalogue cards and produce written reports about the new books.3.Book retrieval system has the ability to search for a specific book in several ways.4.Book lending or circulation system. This system is a complete circulation system; including book lending, renewals, waiting lists, and recall of borrowed books.5.Periodical management system. This system is in charge of processing of periodicals and magazines in the library, including cataloguing, management, and lending.6.Scientific information retrieval system. One can retrieve scientific information by keywords or in many other ways.7.Internal material booking system. It can make orders of internal materials, claims for materials outstanding and make exchanges with other observatories and institutions both in or outside the country.8.Internal material management system. It can do the work that is analogous to that done with books and periodicals.9.Information relationship system. It handles exchanges of information between institutions. Computer system of library management ... at Shaanxl 18310.Scientific information network management system. It manages affairs within a certain information network.

(s, S) Policies for a Dynamic Inventory Model with Stochastic Lead Times

This study analyzes a stochastic lead time inventory model under the assumptions that (a) replenishment orders do not cross in time and (b) the lead time distribution for a given order is independent of the number and sizes of outstanding orders. The study extends the existing literature on the finite-horizon version of the model and yields an intuitively appealing dynamic program that is nearly identical to one that would apply in a transformed model with all lead times fixed at zero. Hence, many results that have been derived for fixed lead time models generalize easily. Conditions for the optimality of myopic base-stock policies, and for the optimality of (s, S) policies are established for both finite and infinite planning horizons. The infinite-horizon model analysis is extended by adapting the fixed lead time results for the efficient computation of optimal and approximately optimal (s, S) policies.