Preferable-Interval Method for the Multiple-Sink Fixed-Charge Transportation Problem Runchang Lin (Texas Center Research Fellows Grant Program 2007-2008 Final Report) August 31, 2008 1 Introduction In this technical report, we study the multiple-sink fixed-charge transportation problem (MS- FCTP), which arises frequently in application areas of scheduling and cost control, such as facility planning, capital budgeting, resource allocation, buffer allocation, pollution control, etc. The MSFCTP problem involves the distribution from a set of supply centers (sources) to a set of demand centers (destinations) such that the demand at each destination is satis- fied without exceeding the supply at any source. The objective is to determine a distribution scheme that has the least cost of transformation. The MSFCTP is traditionally formulated as a mixed integer programming problem described as follows [23]: min TC = m X i=1 n X k=1 (c ik x ik + f ik y ik ) s.t. n X k=1 x ik = S i for 1 ≤ i ≤ m, m X i=1 x ik = D k for 1 ≤ k ≤ n, 0 ≤ x ik ≤ m ik y ik for 1 ≤ i ≤ m, 1 ≤ k ≤ n, y ik ∈{0, 1} for 1 ≤ i ≤ m, 1 ≤ k ≤ n, (1.1) where n is the number of destinations, m is the number of sources, c ik is the cost per unit amount transported from source i to destination k, x ik is the amount transported from source i to destination k, f ik ≥ 0 is the fixed-charge incurred if x ik 6= 0, S i > 0 is the supply available at source i, D k > 0 is the demand at destination k, m ik = min{S i ,D k } is the maximum amount that can be transported from source i to destination k, and y ik is 1 if x ik 6= 0 and 0 otherwise. We assume that ∑ i S i = ∑ k D k . 1