Loss of coordination in competitive supply chains

The loss of coordination in supply chains quantifies the inefficiency (i.e. the loss of total profit) due to the presence of competition in the supply chain. In this thesis, we discuss four models: one model with multiple retailers facing the multinomial logit demand, and three supply chain configurations with one supplier and multiple retailers in a i) quantity competition among retailers with substitute products, ii) price competition among retailers with substitute products, and iii) quantity competition among retailers with complement products, producing differentiated products under an affine demand function. As a special case, we also consider the symmetric setting in the four models where all retailers encounter identical demand, marginal costs, quality dierences, and in the multinomial logit demand case, when there are identical variances in the consumers' utility functions. The main contribution in this thesis lies in the precise quantification of the loss of profit due to lack of coordination, through analytical lower bounds. We provide bounds in terms of the eigenvalues of the demand sensitivity matrix, or the demand sensitivities. For the multinomial logit demand model, the lower bounds are in terms of the number of retailers and the predictability of consumer behaviour. We use simulations to provide further insights on the loss of coordination and tightness of the bounds. We find that a supply chain with retailers operating under Bertrand competition offering substitute products is the most ecient with an average profit loss of less than 15%. We also nd that competitive supply chains can be coordinated when offering substitute products.