Three Rivers Shipping Company Example
As an illustration, let’s look at the case of the Three Rivers Shipping Company. Three Rivers
runs a huge docking facility located on the Ohio River near Pittsburgh. Approximately five ships
arrive to unload their cargoes of steel and ore during every 12-hour work shift. Each hour that a
ship sits idle in line waiting to be unloaded costs the firm a great deal of money, about $1,000
per hour. From experience, management estimates that if one team of stevedores is on duty to
handle the unloading work, each ship will wait an average of 7 hours to be unloaded. If two
teams are working, the average waiting time drops to 4 hours; for three teams, it’s 3 hours; and
for four teams of stevedores, only 2 hours. But each additional team of stevedores is also an
expensive proposition, due to union contracts.
Three Rivers’s superintendent would like to determine the optimal number of teams of
stevedores to have on duty each shift. The objective is to minimize total expected costs. This
analysis is summarized in Table 13.1. To minimize the sum of service costs and waiting costs,
the firm makes the decision to employ two teams of stevedores each shift.