Case Study $1$ Container Transportation Company

a$)$ Develop a Solver model to investigate CTC$$s existing pricing. Your objective is to determine the maximum revenue that can be obtained per vessel $($i$.$e$.$ ship$)$ with the existing prices. You are expected to solve your model only for the high$-$season $($low$-$season model would be the same with different data$).$ Note that in the optimal solution the vessel may not pick any cargo from some of the Asian ports $($this is allowed$).$

b$)$ Create a copy of the worksheet you developed in part a$.$ Change the objective to maximizing total TEU shipped $($this would be a reasonable objective if CTC wants to maximize customer service, by meeting as much of the demand as possible$).$

c$)$ If you carefully look into the solution you have found, you will see that all the demand in some ports is met, while in others it is not. Since the vessel has a fixed capacity $($just like an airplane$)$ CTC cannot increase its revenue by increasing capacity. In such industries $($we call them industries with perishable inventory, since any container space on the vessel or seat on an airplane, that is not sold, is $$lost$$ forever$),$ maximizing revenue is achieved by segmenting the market and adjusting the price in each market to match demand to inventory $($here $$inventory$$ is the capacity of the vessel$).$ This requires that the relationship between price and demand $($demand curve$)$ for each segment is known. In this case study each port is a natural segment. You can use the $\%$ change in demand for a given $\%$ change in price to determine the linear demand function for each port $($i$.$e$.$ the slope and intercept of the function, demand $=$ intercept $+$ slope$*$price$).$

d$)$ Use the demand functions you have developed in part c to create a new optimization model in which you determine the prices at each port, as well as the number of containers loaded on the vessel at each port so that revenue is maximized.