Solving Multi-Step Fixed Charge Transportation Problem
Fixed charge transportation problem (FCTP), which can be considered as a
distribution problem, is considered to be an NP-hard problem. One of its versions is the Step Fixed
charge transportation problem (SFCTP) where the cost of shipping through every route that is used in
the solution consists of a variable cost plus a fixed cost. New versions of SFCTP in the form of Multi
Step Fixed Charge Transportation Problem (MSFCTP) and also Flat Multi Step Fixed Charge
Transportation Problem (FMSFCTP) - one of the special versions of MSFCTP are proposed. In
FMSFCTP the problem of minimizing transportation cost is considered in situations where an
opening cost is incurred for every route used in the solution and increases proportionately with
shipped quantity. The special version of FMSFCTP considers the opening cost to remain flat up to a
certain quantity and increases in multiples of this flat cost. This cost structure invokes the ceiling
function and causes the value of the objective function to behave like a step function. The
mathematical models of MSFCTP and FMSFCTP, together with a heuristic algorithm for solving
FMSFCTP are described and presented in this paper. Two problems have been solved to evaluate and
demonstrate the performance of the proposed algorithm.
The importance of scheduling in the industrial world is growing rapidly. Customer-driven production scheduling is the need of the hour in the present business environment.
Fixed charge transportation problem (FCTP), which can be considered as a
distribution problem, is considered to be an NP-hard problem. One of its versions is the Step Fixed
charge…
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