Consider a two-stage textile supply chain with one

Consider a two-stage textile supply chain with one manufacturer supplying one retailer. The manufacturer has variable production costs of 60€ per unit and fixed costs of 20,000€. The retailer has a variable distribution cost of 25€ and faces an inverse demand function of p=1,500-4q, where q is the quantity and p is the price. a) Determine the optimal prices and quantities in the case of decentralized planning. What is the retailer’s profit? What is the manufacturer’s profit? (11 points) b) Quantify the resulting inefficiency in decentralized planning in percent and discuss by means of this result the adverse effect of uncoordinated decentralized planning in supply chains. (10 points) c) How can the effect in (b) be minimized and the supply chain profits increased compared to decentralized planning? (4 points)
d) Tourists arrive at the ferry boat to Pulau Ubin according to a Poisson process with a rate of 60 per hour. It has been 15 minutes until the last tourist arrived. What is the expected time until the next tourist arrives? (4 points) e) At the VivoCity monorail station to Sentosa, a deterministic arrival process can be assumed, with 600 customers per hour. The trains also run a strict schedule, with deterministic arrival and journey times. On average, every 5 minutes a train departs from VivoCity. What capacity should the train minimally have to avoid explosion of the queue? With this capacity, describe a deterministic customer arrival process that leads to zero waiting time on average. Also describe a de-terministic customer arrival process that leads to the maximum average waiting time. (6 points)