Stability and monotonicity in newsvendor situations

Cataloged from PDF version of article.This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, and a supplier. Groups of retailers might increase their expected joint profit by joint ordering and inventory centralization. However, we assume that the retailers impose some level of stock that should be dedicated to them. In this situation, we show that the associated cooperative game has a non-empty core. Afterwards, we concentrate on a dynamic situation, where several model cost parameters and the retailers’ dedicated stock levels can change. We investigate how the profit division might be affected by these changes. We focus on four monotonicity properties. We identify several classes of games with retailers, where some of the monotonicity properties hold. Moreover, we show that pairs of cooperative games associated with newsvendor situations do not necessarily satisfy these properties in general, when changes in dedicated stock levels are in concern

Profit division in newsvendor situations with delivery restrictions

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, and a supplier. Groups of retailers might increase their expected joint profit by joint ordering and inventory centralization, which means that they give a joint order and allocate this quantity among themselves to maximize the total profit after the demands are realized. Furthermore, we assume that the retailers pose some restrictions on the number of items that should be delivered to them. In this situation, we show that the associated cooperative game has a non-empty core. Afterwards, we concentrate on a dynamic situation, where the retailers change their delivery restrictions. We investigate how the profit division might be affected by these changes. We define four new monotonicity properties, which we think are interesting in general, and we derive necessary and sufficient conditions for pairs of totally balanced TU-games to satisfy these properties. We also show that pairs of cooperative games associated with newsvendor situations do not necessarily satisfy these properties in general. Finally, we define a class of games with retailers having a normally distributed demand where one of the monotonicity properties holds

Offshore & Onshore contracts

We study the buyer-seller relationship in a supply chain from the perspective of quality. In particular, we examine situations where quality levels of the product can be observed, yet, conformance cannot be enforced unless the buyer engages in costly, legally-binding activity, which we call audit. We assume that the cost of audit is borne by the buyer. We examine three types of remedies that can be taken in case an audit confirms the existence of quality problems, namely â Full Rebate", â Compensate" and â Repair" contracts. Under the Full Rebate regime, the seller rebates the buyer the purchase price of defective units. Under the Compensate regime (Expectation Damages), the buyer is compensated for his loss of profit due to defects. Finally, under the Repair regime (Specific Performance), the seller is made to repair all the defective units at his own expense. We examine the effects of these contracts on the performance of the supply-chain, and point out the implications for offshore and onshore supply networks, respectively. Our results indicate conditions where the buyer is not motivated to â squeeze" all the profits out of the supply chain, even in a setting of complete information, and even if the relationship is short-term. We extend the analysis to examine supply-chains which include more than one seller or buyer. Also, as part of the analysis, we study a problem, which we call the â Crime and Punishment" problem that is interesting in its own right.Operations Management Working Papers Serie

Spare parts inventory pooling: how to share the benefits?

We consider a stock point for expensive, low-usage items that is operated by multiple decision makers. Each faces a Poisson demand process, and the joint stock point is controlled by a continuous-review base stock policy with full backordering. We consider penalty costs for backorders and holding costs for stock on hand. For this model, we derive structural properties of the resulting cost function. We use these to prove not only that it is cost e�ective to share one stock point with all parties involved, but also that collaboration (inventory pooling) can be supported by a stable cost allocation, i.e., the core of the associated cooperative game is non-empty. These results hold under optimized and under exogenously given base stock levels. For the former case, we further identify a stable cost allocation that would be easy to implement in practice and that induces players to reveal their private information truthfully

Inventory Competition and Incentives to Back-Order

In this paper we consider the issue of inventory control in a multi-period environment with competition on product availability. Specifically, when a product is out of stock, the customer often must choose between placing a back-order or turning to a competitor selling a similar product. We consider a competition in which customers may switch between two retailers (substitute) in the case of a stock-out at the retailer of their first choice. In a multi-period setting, the following four situations may arise if the product is out of stock: (i) sales may be lost; (ii) customers may back-order the product with their first-choice retailer; (iii) customers may back-order the product with their second-choice retailer; or (iv) customers may attempt to acquire the product according to some other more complex rule. The question we address is: how do the equilibrium stocking quantities and profits of the retailers depend on the customers\u27 back-ordering behaviors? In this work we consider the four alternative back-ordering scenarios and formulate each problem as a stochastic multi-period game. Under appropriate conditions, we show that a stationary base-stock inventory policy is a Nash equilibrium of the game that can be found by considering an appropriate static game. We derive conditions for the existence and uniqueness of such a policy and conduct a comparative statics analysis. Analytical expressions for the optimality conditions facilitate managerial insights into the effects of various back-ordering mechanisms. Furthermore, we recognize that often a retailer is willing to offer a monetary incentive to induce a customer to back-order instead of going to the competitor. Therefore, it is necessary to coordinate incentive decisions with operational decisions about inventory control. We analyze the impact of incentives to back-order the product on the optimal stocking policies under competition and determine the conditions that guarantee monotonicity of the equilibrium inventory in the amount of the incentive offered. Our analysis also suggests that, counterintuitively, companies might benefit from making their inventories “visible” to competitors\u27 customers, since doing so reduces the level of competition, decreases optimal inventories and simultaneously increases profits for both players

Local strong D-Monotonicity of the Kalai-Smorodinsky and Nash bargaining solution

bargaining

Competitive Multi-period Pricing with Fixed Inventories

This paper studies the problem of multi-period pricing for perishable products in a competitive (oligopolistic) market. We study non cooperative Nash equilibrium policies for sellers. At the beginning of the time horizon, the total inventories are given and additional production is not an available option. The analysis for periodic production-review models, where production decisions can be made at the end of each period at some production cost after incurring holding or backorder costs, does not extend to this model. Using results from game theory and variational inequalities we study the existence and uniqueness of equilibrium policies. We also study convergence results for an algorithm that computes the equilibrium policies. The model in this paper can be used in a number of application areas including the airline, service and retail industries. We illustrate our results through some numerical examples.Singapore-MIT Alliance (SMA