A European manufacturer of industrial furniture has a factory located in

Munich and four warehouses in Western Europe. The warehouses collect

customer orders, which are then shipped from the factory. Upon receipt,

the warehouse distributes customer orders using small trucks. Daily

demand at each of the four warehouses along with distance from Munich is

as shown following:

All shipments are by truck. Three truck sizes are available, with capacities of

$40,000$ kg $($small$),60,000$ kg $($medium$),$ and $80,000$ kg $($large$).$

Transportation costs for the three types of trucks are as follows:

Small: $100+0\mathrm{.}1$x euros

Medium: $125+0\mathrm{.}1$x euros

Large: $150+0\mathrm{.}1$x euros

where x is the distance to be traveled in kilometers. For replenishment

frequency varying between one and four days for each warehouse, identify

the optimal transportation option and the associated cost. What other

factors should be considered before deciding on the replenishment

frequency?