A newsvendor model with service and loss constraints

Actual performance measurement systems do not only consider financial measures like costs and profits but also non-financial indicators with respect customer service, quality and flexibility. Using the newsvendor model we explore the influence of possibly conflicting performance measures on important operations decisions like the order quantity and the selling price of a product. For price-independent as well as price-dependent demand distribution like in the classical newsvendor model the objective is to maximise the expected profit. But the optimal decisions are computed with respect to a service constraint - a lower bound for the level of product availability - and to a loss constraint - an upper bound for the probability of resulting in loss. For the price-independent model a condition for the existence of an optimal order quantity and its structure is presented. For the price-setting newsvendor the admissible region of the order quantity and the selling price is characterised for the additive and the multiplicative model. Furthermore, it is shown that higher variability of demand leads to a smaller admissible region of the decision variables thereby easing the computation of the optimal decisions.Constrained Newsvendor Model, Price-Setting Newsvendor

Supply chain collaboration

In the past, research in operations management focused on single-firm analysis. Its goal was to provide managers in practice with suitable tools to improve the performance of their firm by calculating optimal inventory quantities, among others. Nowadays, business decisions are dominated by the globalization of markets and increased competition among firms. Further, more and more products reach the customer through supply chains that are composed of independent firms. Following these trends, research in operations management has shifted its focus from single-firm analysis to multi-firm analysis, in particular to improving the efficiency and performance of supply chains under decentralized control. The main characteristics of such chains are that the firms in the chain are independent actors who try to optimize their individual objectives, and that the decisions taken by a firm do also affect the performance of the other parties in the supply chain. These interactions among firms’ decisions ask for alignment and coordination of actions. Therefore, game theory, the study of situations of cooperation or conflict among heterogenous actors, is very well suited to deal with these interactions. This has been recognized by researchers in the field, since there are an ever increasing number of papers that applies tools, methods and models from game theory to supply chain problems

Dynamic Inventory Control with Satisfaction-Dependent Demand

In this paper, we consider the discrete multiperiod newsvendor dynamic inventory control problem where customers follow a simple satisfaction-based demand process, where their probability of demand depends on whether their demand was satised the last time they demanded a product, and observe the differences between optimal policies and myopic policies which do not directly consider how inventory policies can affect future demand. We conrm the intuitive result that inventory managers should tend to order more than the myopic policy when satised customers are more likely to demand product, and less than the myopic policy when satised customers are less likely to demand. Moreover, we and that, when choosing a fixed order policy, even an empirically myopic solution with perfect demand distribution information will move away from the optimum towards a suboptimal solution.

Stochastic Stackelberg equilibria with applications to time dependent newsvendor models

In this paper we prove a sufficient maximum principle for general stochastic differential Stackelberg games, and apply the theory to continuous time newsvendor problems. In the newsvendor problem a manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits under a random demand rate. Our demand rate is an Ito-Levy process, and to increase realism information is delayed, e.g., due to production time. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time variable coefficients. Moreover, these results are operational because we are able to offer explicit solution formulas. An interesting finding is that more precise information may be a considerable disadvantage for the retailer.Stochastic differential games; newsvendor model; delayed information; Ito-Levy processes

The Expectation-Based Loss-Averse Newsvendor

We modify the classic single-period inventory management problem by assuming that the newsvendor is expectation-based loss averse according to Koszegi and Rabin (2006, 2007). Expectation-based loss aversion leads to an endogenous psychological cost of leftovers as well as stockouts. If there are no monetary stockout costs, then the loss-averse newsvendor orders a quantity lower than the quantity ordered by a profit-maximizing newsvendor. If there are positive monetary costs associated with stockouts, then the loss-averse newsvendor places suboptimal orders, which can be either too high or too low

Inventory Management under Product Mis-identification/Shipment Errors

“Wrong-product” delivery - the delivery of a product different from that desired - is a significant, but as yet unexplored problem in supply-chain management research. There are basically two reasons for wrong-product delivery: either the wrong product is mistakenly ordered or the right product is ordered but the wrong product is picked/shipped. This paper defines and analyzes the “wrong-product delivery” problem using a 2-product newsvendor model. Two non-substitutable products may be ordered at the beginning of each time period. However, whenever product i is ordered, then with known probability i, product j is delivered; i, j = 1, 2(i 6= j). First, we analyze the “no-recourse scenario”, where management correctly stores whatever was received, but takes no other action. We establish the form of the optimal policy and conduct sensitivity analysis. Although our modeling framework is simple, our results are unexpected and non-intuitive. For example, it is well known that in the single-product newsvendor model, increasing the uncertainty of demand or supply will yield an increase in the corresponding target basestocks and safety stocks. However, increasing the risk of a wrong-product error yields a decrease in the corresponding basestocks and safety stocks. Further, although target basestocks in the single-product newsvendor model are invariant to increases in on-hand inventory, we show that the target basestock for either product is non-decreasing as its inventory increases. We also demonstrate that the cost impact of wrong-product uncertainty is comparable, if not larger than, the cost impact of demand uncertainty. Next, we analyze the “recourse scenario” where management is able to correct errors but only by incurring a fixed cost of $K. We show that it is optimal to take recourse when the wrong-product uncertainty is sufficiently small, but not take recourse when the wrong-product uncertainty is high. In strategic terms, our analysis provides insight into the cost impact of wrong-product errors, and, hence, the importance of reducing them.Supply chain management, Inventory management, Shipment errors, Ordering errors, Yield management, Unreliable supply

Buyback and return policies for a book publishing firm = Egy könyvkiadó vállalat visszavásárlási stratégiája

A dolgozat célja egy vállalati gyakorlatból származó eset elemzése. Egy könyvkiadót tekintünk. A kiadó kapcsolatban van kis- és nagykereskedőkkel, valamint a fogyasztók egy csoportjával is vannak kapcsolatai. A könyvkiadók projekt rendszerben működnek. A kiadó azzal a problémával szembesül, hogy hogyan ossza el egy frissen kiadott és nyomtatott könyv példányszámait a kis- és nagykereskedők között, valamint mekkora példányszámot tároljon maga a fogyasztók közvetlen kielégítésére. A kiadóról feltételezzük, hogy visszavásárlási szerződése van a kereskedőkkel. A könyv iránti kereslet nem ismert, de becsülhető. A kis- és nagykereskedők maximalizálják a nyereségüket. = The aim of the paper is to analyze a practical real world problem. A publishing house is given. The publishing firm has contacts to a number of wholesaler / retailer enterprises and direct contact to customers to satisfy the market demand. The book publishers work in a project industry. The publisher faces with the problem how to allocate the stocks of a given, newly published book to the wholesaler and retailer, and to hold some copies to satisfy the customers direct from the publisher. The publisher has a buyback option. The distribution of the demand is unknown, but it can be estimated. The wholesaler / retailer maximize the profits. The problem can be modeled as a one-warehouse and N-retailer supply chain with not identical demand distribution. The model can be transformed in a game theory problem. It is assumed that the demand distribution follows a Poisson distribution

Optimal Dynamic Procurement Policies for a Storable Commodity with L\'evy Prices and Convex Holding Costs

In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm's optimal procurement problem as a singular stochastic control problem in which controls are nondecreasing processes and represent the cumulative investment made by the firm in the spot market (a so-called stochastic "monotone follower problem"). We assume a general exponential L\'evy process for the commodity's spot price, rather than the commonly used geometric Brownian motion, and general convex holding costs. We obtain necessary and sufficient first order conditions for optimality and we provide the optimal procurement policy in terms of a "base inventory" process; that is, a minimal time-dependent desirable inventory level that the firm's manager must reach at any time. In particular, in the case of linear holding costs and exponentially distributed demand, we are also able to obtain the explicit analytic form of the optimal policy and a probabilistic representation of the optimal revenue. The paper is completed by some computer drawings of the optimal inventory when spot prices are given by a geometric Brownian motion and by an exponential jump-diffusion process. In the first case we also make a numerical comparison between the value function and the revenue associated to the classical static "newsvendor" strategy.Comment: 28 pages, 3 figures; improved presentation, added new results and section