It is well known that general 0-1 programming problems are NP-Complete and their optimal solutions cannot be found with polynomial-time algorithms unless P=NP. In this paper, we identify a specific class of 0-1 programming problems that is polynomially solvable, and propose two polynomial-time algorithms to find its optimal solutions. This class of 0-1 programming problems commits to a wide range of real-world industrial applications. We provide an instance of representative in the field of supply chain management.
Extant studies of cooperative advertising mainly consider a single-manufacturer-single-retailer channel structure. This can provide limited insights, because a manufacturer, in real practices, usually deals with multiple retailers simultaneously. In order to examine the impact of the retailer＇s multiplicity on channel members＇ decisions and on total channel efficiencies, this paper develops a multiple-retailer model. In this model, the manufacturer and the retailers play a Stackelberg game to make the optimal advertising decisions. Based on the quantitative results, it is observed that： 1） When there are multiple symmetric retailers, as the number of retailers scales up, the manufacturer＇s national advertising investment contributes increasingly to add to channel members＇ profits in equilibrium, but the total channel efficiency deteriorates quickly and converges down to a certain value; 2） When there are multiple asymmetric retailers, the distribution channel suffers from the manufacturer＇s uniform participation strategy due to the retailer＇s free-riding, and benefits with the manufacturer＇s retailer-specific participation strategy. This study derives equilibrium solutions in closed form for all games considered and measures explicitly the gains/losses of channel efficiencies under different game settings.
