Observation bias: The impact of demand censoring on newsvendor level and adjustment behavior

In an experimental newsvendor setting we investigate three phenomena: Level behavior ? the decision-maker's average ordering tendency; adjustment behavior ? the tendency to adjust period-to-period order quantities; and observation bias ? the tendency to let the degree of demand feedback influence order quantities. We find that the portion of mismatch cost due to adjustment behavior exceeds the portion of mismatch cost due to level behavior in three out of four conditions. Observation bias is studied through censored demand feedback, a situation which arguably represents the majority of newsvendor settings. When demands are uncensored, subjects tend to order below the normative quantity when facing high margin and above the normative quantity when facing low margin, but in neither case beyond mean demand (a.k.a. the pull-to-center effect). Censoring in general leads to lower quantities, magnifying the below-normative level behavior when facing high margin but partially counterbalancing the above-normative level behavior when facing low margin, violating the pull-to-center effect in both cases.

Making the Newsvendor Smart – Order Quantity Optimization with ANNs for a Bakery Chain

Accurate demand forecasting is particularly crucial for products with short shelf life like bakery products. Over- and underestimation of customer demand affects not only profit margins of bakeries but is also responsible for 600,000 metric tons of food waste every year in Germany. To solve this problem, we develop an IT artifact based on artificial neural networks, which is automating the manual order process and capable of reducing costs as well as food waste. To test and evaluate our artifact, we cooperated with an SME bakery chain from Germany. The bakery chain runs 40 points of sale (POS) in southern Germany. After algorithm based reconstructing and cleaning of the censored sales data, we compare two different data-driven newsvendor approaches for this inventory problem. We show that both models are able to significantly improve the forecast quality (cost savings up to 30%) compared to human planners

Estimating the demand parameters for single period problem, Markov-modulated Poisson demand, large lot size, and unobserved lost sales

We consider a single-period single-item problem when the demand is a Markov-modulated Poisson process with hidden states, unknown intensities and continuous batch size distribution. The number of customers and lot size are assumed to be large enough. The estimators of demand mean and standard deviation for unobservable lost sales in the steady state are considered. The procedures are based on two censored samples: observed selling durations and the demands over the period. Numerical results are given

How Big Should Your Data Really Be? Data-Driven Newsvendor and the Transient of Learning

We study the classical newsvendor problem in which the decision-maker must trade-off underage and overage costs. In contrast to the typical setting, we assume that the decision-maker does not know the underlying distribution driving uncertainty but has only access to historical data. In turn, the key questions are how to map existing data to a decision and what type of performance to expect as a function of the data size. We analyze the classical setting with access to past samples drawn from the distribution (e.g., past demand), focusing not only on asymptotic performance but also on what we call the transient of learning, i.e., performance for arbitrary data sizes. We evaluate the performance of any algorithm through its worst-case relative expected regret, compared to an oracle with knowledge of the distribution. We provide the first finite sample exact analysis of the classical Sample Average Approximation (SAA) algorithm for this class of problems across all data sizes. This allows to uncover novel fundamental insights on the value of data: it reveals that tens of samples are sufficient to perform very efficiently but also that more data can lead to worse out-of-sample performance for SAA. We then focus on the general class of mappings from data to decisions without any restriction on the set of policies and derive an optimal algorithm as well as characterize its associated performance. This leads to significant improvements for limited data sizes, and allows to exactly quantify the value of historical information

Robust newsvendor problem with autoregressive demand

This paper explores the classic single-item newsvendor problem under a novel setting which combines temporal dependence and tractable robust optimization. First, the demand is modeled as a time series which follows an autoregressive process AR(p), p ≥ 1. Second, a robust approach to maximize the worst-case revenue is proposed: a robust distribution-free autoregressive forecasting method, which copes with non-stationary time series, is formulated. A closed-form expression for the optimal solution is found for the problem for p = 1; for the remaining values of p, the problem is expressed as a nonlinear convex optimization program, to be solved numerically. The optimal solution under the robust method is compared with those obtained under two versions of the classic approach, in which either the demand distribution is unknown, and assumed to have no autocorrelation, or it is assumed to follow an AR(p) process with normal error terms. Numerical experiments show that our proposal usually outperforms the previous benchmarks, not only with regard to robustness, but also in terms of the average revenue.Ministerio de Economía y CompetitividadJunta de Andalucí

Demand Estimation at Manufacturer-Retailer Duo: A Macro-Micro Approach

This dissertation is divided into two phases. The main objective of this phase is to use Bayesian MCMC technique, to attain (1) estimates, (2) predictions and (3) posterior probability of sales greater than certain amount for sampled regions and any random region selected from the population or sample. These regions are served by a single product manufacturer who is considered to be similar to newsvendor. The optimal estimates, predictions and posterior probabilities are obtained in presence of advertising expenditure set by the manufacturer, past historical sales data that contains both censored and exact observations and finally stochastic regional effects that cannot be quantified but are believed to strongly influence future demand. Knowledge of these optimal values is useful in eliminating stock-out and excess inventory holding situations while increasing the profitability across the entire supply chain. Subsequently, the second phase, examines the impact of Cournot and Stackelberg games in a supply-chain on shelf space allocation and pricing decisions. In particular, we consider two scenarios: (1) two manufacturers competing for shelf space allocation at a single retailer, and (2) two manufacturers competing for shelf space allocation at two competing retailers, whose pricing decisions influence their demand which in turn influences their shelf-space allocation. We obtain the optimal pricing and shelf-space allocation in these two scenarios by optimizing the profit functions for each of the players in the game. Our numerical results indicate that (1) Cournot games to be the most profitable along the whole supply chain whereas Stackelberg games and mixed games turn out to be least profitable, and (2) higher the shelf space elasticity, lower the wholesale price of the product; conversely, lower the retail price of the product, greater the shelf space allocated for that product