EXACT AND APPROXIMATE COST FUNCTIONS FOR PRODUCT AGGREGATES.

IT IS SHOWN THAT CERTAIN LARGE, MULTIPRODUCT PROBLEMS CAN BE WELL APPROXIMATED BY SMALLER MODELS OF THE SAME FORM, REPRESENTING ONLY ONE AGGREGATE PRODUCT (OR A FEW SUCH PRODUCTS). THIS REDUCTION FOLLOWS FROM A NEW TECHNIQUE TO APPROXIMATETHE MINIMAL COST OF A SPECIAL ALLOCATION OR ″ DISAGGREGATION ″ PROBLEM, BY A SIMPLE, CLOSED-FORM AGGREGATE COST FUNCTION. THIS FUNCTION, MOREOVER, HAS THE SAME FORM AS THE COST FUNCTIONS FOR THE ORIGINAL, INDIVIDUAL PRODUCTS. FOR SPECIAL CASES THE ″ APPROXIMATION ″ IS EXACT. THE RESULTS ARE APPLIEDTO A ONE-STAGE, MULTIPERIOD, MULTI-ITEM PRODUCTION SMOOTHING MODEL, AND THEN TO A SIMILAR MODEL OF A TWO-STAGE SYSTEM, YIELDING A REDUCTION IN THE NUMBER OF ITEMS TO ONE OR TO RELATIVELY FEW.

Duke Scholars

Author Paul H. Zipkin Fuqua School of Business