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A MAXIMIZATION PROBLEM 35

MANAGEMENT SCIENCE IN ACTION

The Kellogg Company
he Kellogg Company is the world’s largest pro- 1980s in-house planning systems which are struc-
T ducer of cereals and has an international brand tured around a large scale, multi-period linear
awareness. Like many companies Kellogg is faced programming model (KPS). The model is used to
with a variety of routine, inter-connected decisions help with decision making at both the operational
about its cereal production. It produces hundreds of and strategic levels. The operational version of the
different products, with new products frequently KPS is used on a weekly basis to help management
introduced as consumer demand and preferences take decisions on production, packaging, inventory
change. Its products are produced at a number of and distribution. The KPS is also used on a longer
different production plants and the company has a term basis to help develop plans relating to plant
number of operational decisions to take to ensure development, capacity expansion and plant location.
profitability. What quantities of each product should It is estimated that savings of around $4.5 million a
be produced over the next planning period? How year have already been realized from using the
much of each product should be produced at each model and that when completed annual savings of
plant? Which plants should supply which customers around $35–40 million will be achieved.
and sales outlets? How much should we produce for
Based on Gerald Brown, Joseph Keegan, Brian Vigus and Kevin Wood,
stocks/inventory and how much for sales? The com- ‘The Kellogg Company Optimizes Production, Inventory and Distribu-
pany has been developing and using since the late tion’, Interfaces 31 6 (Nov/Dec 2001): 1–15.

Dantzig’s contribution to by the constraints limiting production capacity. The financial analyst’s portfolio prob-
LP was recognized by lem is constrained by the total amount of investment funds available and the maximum
the Mathematical
Programming Society amounts that can be invested in each stock or bond. The marketing manager’s media
through the Dantzig selection decision is constrained by a fixed advertising budget and the availability of the
Award, given every three various media. In the transportation problem, the minimum-time shipping schedule is
years since 1982 to one constrained by the supply of blood available and the demand from hospitals. Thus,
or two people who have
made a significant constraints are another general feature of every linear programming problem.
impact in the field of
mathematical
programming.
2.1 A Maximization Problem

GulfGolf is a small family-run company in the United Arab Emirates. It manufactures
golfing equipment aimed at the increasing demand, primarily from tourists coming for
golfing holidays in the Gulf region. The company has decided to manufacture two new
products: a medium-priced golf bag and a more up-market, expensive golf bag. The
company’s products are priced in US$ given its international customer base. The
company’s distributor is enthusiastic about the new product line and has agreed to buy
all the golf bags the company produces over the next three months.
After a thorough investigation of the steps involved in manufacturing a golf bag,
management determined that each golf bag produced will require the following four
operations:
1 Cutting and dyeing the material needed.
2 Sewing.
3 Finishing (inserting umbrella holder, club separators, etc.).
4 Inspection and packaging.

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