Approximate Order-up-to Policies for Inventory Systems with Binomial Yield

This paper studies an inventory policy for a retailer who orders his products from a supplier whose deliveries only partially satisfy the quality require- ments. We model this situation by an infinite-horizon periodic-review model with binomial random yield and positive lead time. We propose an order- up-to policy based on approximating the inventory model with unreliable supplier by a model with a reliable supplier and suitably modified demand distribution. The performance of the order-up-to policy is verified by com- paring it with both the optimal policy and the safety stock policy proposed in Inderfurth & Vogelgesang (2013). Further, we extend our approximation to a dual-sourcing model with two suppliers: the first slow and unreliable, and the other fast and fully reliable. Compared to the dual-index order- up-to policy for the model with full information on the yield, the proposed approximation gives promising results

Safety Stocks in Centralized and Decentralized Supply Chains under Different Types of Random Yields

Safety stock planning with focus on risk protection to cope with demand uncertainties is a very well researched topic in the field of supply chain management, in central as well as in local decision making systems. In contrast, there is only few knowledge about safety stock management in situations where supply risks have to be covered that are caused by uncertainties with respect to production yields. In this study, a two-stage manufacturer-retailer supply chain is considered in a single-period context that allows for an analytical study of the impact of yield randomness on safety stock determination. In order to concentrate the analysis on the effects of yield uncertainty demand will be assumed to be deterministic. We consider three basic types of yield randomness which represent different reasons for yield losses in production processes each, namely the stochastically proportional, binomial, and interrupted geometric yield type. It will be shown that these different yield risk specifications can bring about completely different properties with regard to the way safety stocks depend on various input parameters in supply chain planning. This holds especially for the impact of the demand size and for the influence of the level of product profitability in a supply chain. In an analytical model-based investigation it is demonstrated that these safety stock properties not only differ between the respective yield types, but also between systems of central and decentralized supply chain decision making. Thus, this study presents general insights into the importance of a correct yield type specification for an effective safety stock management and explains necessary differences in the stock distribution across supply chain stages in both centralized and decentralized settings

Confidence-based Optimization for the Newsvendor Problem

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach can produce an upper and a lower bound for the associated cost. We apply our novel approach to three demand distribution in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist - e.g. based on maximum likelihood estimators - or Bayesian strategies.Comment: Working draf

Parametric Distributionally Robust Optimisation Models for Budgeted Multi-period Newsvendor Problems

In this paper, we consider a static, multi-period newsvendor model under a budget constraint. In the case where the true demand distribution is known, we develop a heuristic algorithm to solve the problem. By comparing this algorithm with off-the-shelf solvers, we show that it generates near-optimal solutions in a short time. We then consider a scenario in which limited information on the demand distribution is available. It is assumed, however, that the true demand distribution lies within some given family of distributions and that samples can be obtained from it. We consider the cases of normal and Poisson demands. For each case, we show that using maximum likelihood estimates in place of the true parameters can lead to poor estimates of the true cost associated with an order quantity. Hence, we make use of likelihood inference to develop confidence sets for the true parameters. These are used as ambiguity sets in a distributionally robust model, where we enforce that the worst-case distribution lies in the same family as the true distribution. We solve these models by discretising the ambiguity set and reformulating them as piecewise linear models. We show that these models quickly become large as the ambiguity set grows, resulting in long computation times. To overcome this, we propose a heuristic cutting surface algorithm that exploits theoretical properties of the objective function to reduce the size of the ambiguity set. We illustrate that our cutting surface algorithm solves orders of magnitude faster than the piecewise linear model, while generating very near-optimal solutions

Dynamic Stochastic Inventory Management in E-Grocery Retailing: The Value of Probabilistic Information

Inventory management optimisation in a multi-period setting with dependent demand periods requires the determination of replenishment order quantities in a dynamic stochastic environment. Retailers are faced with uncertainty in demand and supply for each demand period. In grocery retailing, perishable goods without best-before-dates further amplify the degree of uncertainty due to stochastic spoilage. Assuming a lead time of multiple days, the inventory at the beginning of each demand period is determined jointly by the realisations of these stochastic variables. While existing contributions in the literature focus on the role of single components only, we propose to integrate all of them into a joint framework, explicitly modelling demand, supply shortages, and spoilage using suitable probability distributions learned from historic data. As the resulting optimisation problem is analytically intractable in general, we use a stochastic lookahead policy incorporating Monte Carlo techniques to fully propagate the associated uncertainties in order to derive replenishment order quantities. We develop a general inventory management framework and analyse the benefit of modelling each source of uncertainty with an appropriate probability distribution. Additionally, we conduct a sensitivity analysis with respect to location and dispersion of these distributions. We illustrate the practical feasibility of our framework using a case study on data from a European e-grocery retailer. Our findings illustrate the importance of properly modelling stochastic variables using suitable probability distributions for a cost-effective inventory management process

The Value of Information in Reverse Logistics

We explore the value of information in the context of a remanufacturer that faces uncertainty with respect to demand, product return, and product recovery (yield loss). We assume a single period model in which the operational decision of interest is the quantity of new product to order. Our objective is to evaluate the absolute and relative value of the different types of information that such a firm may choose to invest in order to reduce the uncertainty it experiences in matching supply with demand. The different types of information include demand, return, and yield loss. Our results are extensive and reveal that the value for any specific type of information depends both on the overall level of uncertainty and the level of uncertainty that is attributed to the information for which it explains. We develop and test a theoretical model that is predictive of 1) the value of each type of information, 2) the conditions that give rise to the value for each type of information, and 3) the relative value for each type of information