  Generally, in transportation problem, full vehicles (e.g., light commercial
vehicles, medium duty and heavy duty trucks, etc.) are to be booked, and
transportation cost of a vehicle has to be paid irrespective of the fulfilment
of the capacity of the vehicle. Besides the transportation cost, total time
that includes travel time of a vehicle, loading and unloading times of products
is also an important issue. Also, instead of a single item, different types of
items may need to be transported from some sources to destinations through
different types of conveyances. The optimal transportation policy may be
affected by many other issues like volume and weight of per unit of product,
unavailability of sufficient number of certain types of vehicles, etc. In this
paper, we formulate a multi-objective multi-item solid transportation problem
by addressing all these issues. The problem is formulated with the
transportation cost and time parameters as fuzzy variables. Using credibility
theory of fuzzy variables, a chance-constraint programming model is formulated,
and is then transformed into the corresponding deterministic form. Finally
numerical example is provided to illustrate the problem.
