The Repair Kit Problem with positive replenishment lead times and fixed ordering costs

The Repair Kit Problem (RKP) concerns the determination of a set of items taken by a service engineer to perform on-site product support. Such a set is called a kit. Models developed in the literature have always ignored the lead times associated with delivering items to replenish the kit, thereby limiting the practical relevance of the proposed solutions. Motivated by a real life case, we develop a model with positive lead times to control the replenishment quantities of the items in the kit, and study the performance of (s, S) policies under a service objective. The choice for (s, S) policies is made in order to accommodate fixed ordering costs. We present a method to calculate job fill rates with exact expressions, and discuss a heuristic approach to optimize the reorder level and order-up-to level for each item in the kit. The empirical utility of the model is assessed on real world data from an equipment manufacturer and useful insights are offered to after-sales managers

London and beyond: essays in honour of Derek Keene

This volume contains selected papers from a major conference held in October 2008 to celebrate the 20th anniversary of the setting up of the Centre for Metropolitan History at the IHR, and the contribution of Professor Derek Keene to the Centre, the IHR and the wider world of scholarship. 'One of the pioneer volumes in the handsomely produced new Institute of Historical Research Conference series, this book serves as a fitting tribute to one of the most influential urban historians of our time.' - Ian Archer, Urban History, May 2013

Timing intermittent demand with time-varying order-up-to levels

Current intermittent demand inventory control models assume that the demand interval is memoryless: the probability of observing a positive demand does not depend on the time since the last demand occurred. Contrarily, several forecasting contributions suggest that demand intervals contain more distributional information. We find that the data of the M5 forecasting competition confirms this. Therefore, we propose an inventory control model that explicitly uses the full distributions of the demand sizes and intervals and thereby acknowledges that the probability of a demand occurrence may vary throughout the interval. To exploit this information, we also allow for time-varying order-up-to levels that flexibly adjust inventories according to the dynamic requirements. We derive the long-run average holding costs, non-stockout probability, order fill rate, and volume fill rate. Inspired by an analogy with multi-item inventory control models, we propose a greedy marginal-analysis heuristic to optimize the order-up-to levels, which we benchmark against the optimal solution on theoretical instances. In a simulation study on the M5 competition data we demonstrate this method's improved on-target service performance compared to that of traditional solutions. We furthermore show that target service levels can be achieved at significantly lower costs with time-varying than with fixed order-up-to levels

A general method for addressing forecasting uncertainty in inventory models

In practice, inventory decisions depend heavily on demand forecasts, but the literature typically assumes that demand distributions are known. This means that estimates are substituted directly for the unknown parameters, leading to insufficient safety stocks, stock-outs, low service, and high costs. We propose a framework for addressing this estimation uncertainty that is applicable to any inventory model, demand distribution, and parameter estimator. The estimation errors are modeled and a predictive lead time demand distribution obtained, which is then substituted into the inventory model. We illustrate this framework for several different demand models. When the estimates are based on ten observations, the relative savings are typically between 10% and 30% for mean-stationary demand. However, the savings are larger when the estimates are based on fewer observations, when backorders are costlier, or when the lead time is longer. In the presence of a trend, the savings are between 50% and 80% for several scenarios. (C) 2017 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved

Effects of food quality on larval fish growth in the field

Many inventory control studies consider either continuous review and continuous ordering, or periodic review and periodic ordering. Mixtures of the two are hardly ever studied. However, the model with periodic review and continuous ordering is highly relevant in practice, as information on the actual inventory level is not always up to date while making ordering decisions. This paper will therefore treat this model. Assuming zero fixed ordering costs, and allowing for a non-negative lead time and a general demand process, we first consider a one-period decision problem without salvage cost for inventory remaining at the end of the period. In this setting we derive a base-line optimal order path, described by a simple newsvendor solution with safety stocks increasing towards the end of a review period. We then show that for the general, multi-period problem, the optimal policy in a period is to first arrive at this path by not ordering until the excess buffer stock from the previous review period is depleted, then follow the path by continuous ordering, and stop ordering towards the end to limit excess stocks for the next review period. An important managerial insight is that, typically, no order should be placed at a review moment, although this may seem intuitive and is also the standard assumption in periodic review models. We illustrate that adhering to the optimal ordering path instead can lead to cost reductions of 30-60 percent compared to pure periodic ordering. (C) 2014 Elsevier B.V. All rights reserved