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INTRODUCTION TO SENSITIVITY ANALYSIS 87

MANAGEMENT SCIENCE IN ACTION

Assigning Products to Worldwide Facilities at Eastman Kodak
ne of the major planning issues at Eastman is always changing. Thus, the linear programming
O Kodak involves the determination of what prod- model must be used in a dynamic way. For instance,
ucts should be manufactured at Kodak’s facilities when demand expectations change, the model can
located throughout the world. The assignment of be used to determine the effect the change will have
products to facilities is called the ‘world load’. In on the world load. Suppose that the currency of
determining the world load, Kodak faces a number country A rises compared to the currency of country
of interesting trade-offs. For instance, not all manu- B. How should the world load be modified? In addi-
facturing facilities are equally efficient for all prod- tion to using the linear programming model in a
ucts, and the margins by which some facilities are ‘how-to-react’ mode, the model is useful in a more
better varies from product to product. In addition to active mode by considering questions such as the
manufacturing costs, the transportation costs and following: Is it worthwhile for facility F to spend d
the effects of customs duty and duty drawbacks dollars to lower the unit manufacturing cost of prod-
can significantly affect the allocation decision. uct P from x to y? The linear programming model
To assist in determining the world load, Kodak helps Kodak evaluate the overall effect of possible
developed a linear programming model that accounts changes at any facility.
for the physical nature of the distribution problem and In the final analysis, managers recognize that
the various costs (manufacturing, transportation and they cannot use the model by simply turning it on,
duties) involved. The model’s objective is to minimize reading the results and executing the solution. The
the total cost subject to constraints such as satisfying model’s recommendation combined with manage-
demand and capacity constraints for each facility. rial judgement provide the final decision.
The linear programming model is a static repre-
sentation of the problem situation, and the real world Based on information provided by Greg Sampson of Eastman Kodak.

The optimal solution, S ¼ 540 standard bags and D ¼ 252 deluxe bags, was based on
profit contribution figures of $10 per standard bag and $9 per deluxe bag. We are
now told by the Sales Dept. that, because of increased competition they have
reduced prices and the profit contribution for the standard bag has fallen from
$10 to $8.50. Sensitivity analysis can be used to determine whether the production
schedule calling for 540 standard bags and 252 deluxe bags is still best. If it is, solving
a modified linear programming problem with 8.50S +9D as the new objective
function will not be necessary.
Sensitivity analysis can also be used to determine which coefficients in a linear
programming model are crucial. For example, the Accounting Department has
indicated that the $9 profit contribution for the deluxe bag is only a best estimate
and could be lower. The problem for management is that 252 deluxe bags are
currently being produced, based on the $9 profit contribution estimate. If the profit
contribution is actually lower should they stop producing the deluxe bag and switch
production to the standard bag instead? Sensitivity analysis can be used to calculate
how much lower the $9 profit contribution would need to be for the deluxe bag not
to be profitable enough to produce.
Another aspect of sensitivity analysis concerns changes in the right-hand side values
of the constraints. Recall that in the GulfGolf problem the optimal solution used all
available time in the cutting and dyeing department and the finishing department.
What would happen to the optimal solution and total profit contribution if the
company could obtain additional quantities of either of these resources? Sensitivity

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