When you eat the inside of an Oreo cookie or munch on a Ritz cracker, you probably don’t realize that the production of the cookie you ate was planned with mathematical programming. Production in the Biscuit Division of Nabisco involves two key operations, baking and secondary operations. In baking, raw materials are fed into an oven. Secondary operations include sorting, packaging and labeling finished products.
Scheduling and operation of bakeries is a difficult task. Each oven is able to produce many but not all products. The efficiency of the ovens varies. The secondary facilities at one site can be shared by several ovens in operation at the same time. Production must be planned to keep the manufacturing and transportation costs as low as possible. The key questions that are routinely addressed with a mathematical model are:
Where should each product be produced?
How much of each product should be assigned to each oven?
From where should product be shipped to each customer?
As new products are developed where should new plants be built?
What facilities should be placed in these plants?
One interesting problem involved the study of the differences between “slug” pack vs. “dump” packs. In a traditional “dump” pack, the crackers are loose inside the box. With the slug pack, crackers are stacked in three or more columns and each column is wrapped separately. The model was used to plan the equipment changeover for different locations to convert to “slug” packaging.
A realistic problem at Nabisco could involve 150 products, 218 facilities, 10 plants, and 127 customer zones. A problem this size involves over 44,000 decision variables and almost 20,000 constraints. These problems were routinely solved in 1983 on an IBM 3033 computer in under 60 CPU seconds.