Qi Fu

Procurement management using option contracts: random spot price and the portfolio effect

This article considers the value of portfolio procurement in a supply chain, where a buyer can either procure parts for future demand from sellers using fixed price contracts or, option contracts or tap into the market for spot purchases. A single-period portfolio procurement problem when both the product demand and the spot price are random (and possibly correlated) is examined and the optimal portfolio procurement strategy for the buyer is constructed. A shortest-monotone path algorithm is provided for the general problem to obtain the optimal procurement solution and the resulting expected minimum procurement cost. In the event that demand and spot price are independent, the solution algorithm simplifies considerably. More interestingly, the optimal procurement cost function in this case has an intuitive geometrical interpretation that facilitates managerial insights. The portfolio effect, i.e., the benefit of portfolio contract procurement over a single contract procurement is also studied. Finally, an extension to a two-period problem to examine the impact of inventory on the portfolio procurement strategy is discussed.

Endogenous information acquisition in supply chain management

In this paper, we analyze an endogenous determination of efforts put into information acquisition and its impact on supply chain management. More specifically, we consider a supplier who sells a product to a buyer during a single selling season. Prior to placing an order with the supplier, the buyer has an option to acquire additional information about the demand by hiring experts (who are capable of providing forecasts). Because a commission fee must be paid to each hired expert, there exists a tradeoff between the cost and the value of the information, and the buyer needs to determine how much information to acquire. We derive the optimal information-acquisition level in an integrated setting and compare it with that determined in a decentralized setting. We also analyze several types of supply contracts to examine if they can coordinate the supply chain and allow an arbitrary division of system profit between the supplier and the buyer.

Beacon placement strategies in an ultrasonic positioning system

Ultrasonic Positioning Systems (UPSs) are widely used to detect, locate, or track targets. One of the key factors that determines the performance of a UPS is beacon placement. In this article, beacon placement strategies for a two-dimensional array in the xy-plane above the target with an adaptive height are studied and optimized as a function of the beacon’s characteristics and application requirements in terms of positioning precision and particularly reliability. The effect of positioning requirements on placement is also investigated. It is shown that for triangle or square placements or a hexagon placement with a low precision requirement, the optimal side length of each placement pattern is restricted by the upper bounds of the geometry and reliability, and the placement pattern is valid only when there is a gap between those upper bounds and the lower bound specified by the precision requirement. However, for a hexagon placement with a high precision requirement, the optimal side length is restricted by the upper bound imposed by the precision requirement. The use of a high beacon height with respect to the target allows positioning requirements to significantly reduce the optimal side length. In addition to the beacon height, another important factor is the beacon placement pattern, such as triangle, square, or hexagon. A comparison of the obtained results shows that under a loose precision requirement, triangle placement is the best; when it is moderate, either square or hexagon placement is preferred; and if the precision requirement is stringent, only hexagon placement is feasible. From the comparison of beacon placement strategies, an 18% reduction in the numbers of beacons is readily achievable for commonly available beacons.

Profit sharing agreements in decentralized supply chains: a distributionally robust approach

How should decentralized supply chains set the profit sharing terms using minimal information on demand and selling price? We develop a distributionally robust Stackelberg game model to address this question. Our framework uses only the first and second moments of the price and demand attributes, and thus can be implemented using only a parsimonious set of parameters. More specifically, we derive the relationships among the optimal wholesale price set by the supplier, the order decision of the retailer, and the corresponding profit shares of each supply chain partner, based on the information available. Interestingly, in the distributionally robust setting, the correlation between demand and selling price has no bearing on the order decision of the retailer. This allows us to simplify the solution structure of the profit sharing agreement problem dramatically. Moreover, the result can be used to recover the optimal selling price when the mean demand is a linear function of the selling price (cf. Raza 2014...

Costly information acquisition under horizontal competition

Abstract We analyze endogenous acquisition of costly information for two firms that sell homogeneous products. Prior to determining its production quantity, either firm has an opportunity to acquire a costly forecast. There exists a correlation between errors in the acquired forecasts. We model the problem as a two-stage game in which the firms first decide whether to acquire their respective forecasts and then decide their production quantities. We derive the equilibrium outcome on information acquisition and production quantity.

Effect of beacon orientation on beacon placement strategies in the ultrasonic positioning system

Ultrasonic positioning system (UPS) is useful in warehouse and underwater applications to track automated objects. One of the key factors determining the performance of the UPS is the beacon placement. Existing literatures are restricted to placing beacons perpendicularly downward to the target moving plane. In this study, considering three common placement patterns: triangle, square and hexagon, by relaxing beacon orientation, our analysis shows that hexagon placement is the best option, and the improvement in terms of qualified coverage per beacon has a negative relationship with the beacon height. Even conditioning on a height of 20% of the sensing range, a factor of 8 and 7 can be achieved in the non-regular placement and regular placement, respectively. Furthermore, critical heights which differentiate the non-perpendicular placement (NPP) and perpendicular placement (PP) for all patterns are identified. In general, regular NPP with the hexagon pattern is advised. In addition, our analysis investigates the advantage of increasing the cone angle by clustering which groups transducers by relaxing transducer orientation, and result shows that continuous clustering of seven transducers has the largest marginal contribution of 24% and 41% to improve the qualified coverage in the non-regular NPP with hexagon placement and regular PP, respectively. Finally, considering the beacon clustering cost and the beacon station cost, the economic beacon placement strategies are identified for applications with different clustering cost and beacon height.