Page 116 -

96 CHAPTER 3 LINEAR PROGRAMMING: SENSITIVITY ANALYSIS AND INTERPRETATION OF SOLUTION

MANAGEMENT SCIENCE IN ACTION

Evaluating Options for the Provision of School Meals in Chile
he National School Assistance and Scholarship minimize cost but at the same time satisfy the
TBoard (JUNAEB) in Chile is a public sector various constraints required. In the late 1990s
agency tasked with responsibility for a variety of JUNAEB developed an LP model to help with
public welfare programmes aimed at encouraging the decision problem. Sensitivity analysis is carried
better student performance and academic attain- out on the optimal solution routinely. Examples
ment, reducing pupil absenteeism, truancy and drop include:
out rates. Chile is a developing country with a pop-
• looking at the effect on total cost (the objective
ulation of over 15 million and sees education as a
function) of changing the quality of meals to be
key element of its development strategy. The country
provided;
has around 14 000 primary and secondary level
schools but with over 90 per cent of this provided, • assessing the effects on the solution of changing
or supported, by the government. Unsurprisingly, the specified nutritional content of meals;
there are high levels of poverty – 30 per cent of • evaluating the effect of assigning more contracts
children are estimated to live below the official pov- to those firms which have better overall
erty level – with subsequent effects on children’s performance ratings. In this case, JUNAEB
education. JUNAEB is responsible for ensuring the concluded that contracts could be awarded to
provision of free school meals across Chile and has firms so that firms were 40 per cent better
an annual budget of around US$140m to feed qualified than those in the original solution. This
around 1.2 million school children. JUNAEB con- added only 4 per cent to the original objective
tracts out the actual catering service provision to function cost.
private sector companies. This is done through a
The LP model is rated as highly successful and the
rolling cycle of three-year contracts covering one-
sensitivity analysis particularly so, allowing different
third of schools each time. Private companies are
scenarios to be easily explored and evaluated. The
invited to bid for the catering contracts through an
model is estimated to have improved the price/qual-
auction process, where JUNAEB specifies the quan-
ity ration of school meals with annual savings of
tity and quality of services to be provided in each
about $40 million – the cost of feeding 30 000
geographical area. JUNAEB uses a number of cri-
schoolchildren.
teria to assess the bids received, including an
assessment of the overall quality of the firm bidding;
Based on Rafael Epstein, Lysette Henriquez, Jaime Catalan, Gabriel
the nutritional requirements of the specified meals;
Y. Weintraub and Cristian Martinez, ‘A Combinational Auction
quality standards; operating conditions. JUNAEB Improves School Meals in Chile’ Interfaces 32 6 (Nov/Dec 2002):
seeks to identify the combination of bids that will 1–14.
NOTES AND COMMENTS

1 If two objective function coefficients change is closely related to the concept of a dual price.
simultaneously, both may move outside their The shadow price associated with a constraint is
respective ranges of optimality and not affect the the change in the value of the optimal solution per
optimal solution. For instance, in a two-variable unit increase in the right-hand side of the
linear programme, the slope of the objective constraint. In general, the dual price and the
function will not change at all if both coefficients shadow price are the same for all maximization
are changed by the same percentage. linear programmes. In minimization linear
2 Some texts associate the term shadow price with programmes, the shadow price is the negative of
each constraint. The concept of a shadow price the corresponding dual price.

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has
deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.