COMPUTATIONAL-COMPLEXITY OF THE CAPACITATED LOT SIZE PROBLEM

A STUDY IS MADE OF THE COMPUTATIONAL COMPLEXITY OF THE CAPACITATED LOT SIZE PROBLEM WITH A PARTICULAR COST STRUCTURE THAT IS LIKELY TO BE USED IN PRACTICAL SETTINGS. FOR THE SINGLE ITEM CASE NEW PROPERTIES ARE INTRODUCED, CLASSES OF PROBLEMS SOLVABLE BY POLYNOMIAL TIME ALGORITHMS ARE IDENTIFIED, AND EFFICIENT SOLUTION PROCEDURES ARE GIVEN. THE AUTHORS SHOW THAT SPECIAL CLASSES ARE NP-HARD, AND THAT THE PROBLEM WITH TWO ITEMS AND INDEPENDENT SETUPS IS NP-HARD UNDER CONDITIONSSIMILAR TO THOSE WHERE THE SINGLE ITEM PROBLEM IS EASY. TOPICS FOR FURTHER RESEARCH ARE DISCUSSED IN THE LAST SECTION.