Flag ACKGROUND

SMP&P is a fully integrated paper company with extensive holdings in woodlands, several large mills,
and nationwide distribution facilities. The company manufactures a wide variety of paper products
under its own brand name, and a more limited product line under contract for private distributors.
SMP&P’s oldest mill, Bayou 1, is located in Pass Christian, Mississippi and produces four major
products; book paper, coarse paper, container board and food board. The flow of materials through
the mill is illustrated below:

CHIPPING

KRAFT
PULPING

BEATING

MACHINING

hardwood

BLEACHING

softwood

SEMI-CHEMICAL PULPING

book paper

coarse paper

container
board
food board

PROCESS DESCRIPTION

The milling process begins with chipping in which two different grades of hardwood and one type
grade of softwood are used as inputs. After chipping, the hardwood outputs enter Kraft pulping or
semi-chemical pulping. The softwood and hardwood outputs from chipping enter the Kraft pulping
operation. Some of the hardwood outputs from chipping transverse through semi chemical pulping
process. No softwood chipping outputs can enter semi chemical pulping. From Kraft pulping, some
products enter the bleaching stage while others go directly through beating. Semi-chemical pulping
products go directly to the beating stage process. The outputs of the beating process are inputs into
machining which produces the four major products, book paper, coarse paper, container board and
food board.

Hardwood and softwood inputs for chipping are available from internal company sources in limited
quantities. Additional quantities can be purchased at a slightly higher cost. The related availability’s
and costs are as follows:

INTERNAL SOURCES
INTERNAL
IN TONS PER YEARCOST

EXTERNAL

WOOD TYPE

Hardwood - grade 1 110,000 tons per year
Hardwood - grade 2 88, 500 tons per year
Softwood
160,000 tons per year

COST

$18 per ton
$18.10 per ton
$19 per ton

$18.65 per ton
$18.20 per ton
$ 20.95 per ton

When required, up to 15,000 tons per year of softwood Kraft pulp can be purchased. Quantity
discounts are available on these purchased quantities so that the first 5000 tons/yr. would cost $57/ton
while the second 10,000 tons/yr. cost $53/ton. This purchased pulp cannot be bleached and is used as
an input into the beating process.

The following process yields (tons output/tons input) and capacities (tons input/year) were provided by
the operations manager:

PROCESS

Chipping
Kraft Pulping
Semi- Chemical Pulping
Bleaching
Beating
Machining

HARDWOOD - 1

.969
.88
.765
.90
.99
.98

YIELDS
HARDWOOD - 2

.942
.88
.755
.90
.99
.98

SOFTWOOD CAPACITIES

.98
.88

.825
.99
.98

700,000
130,000
125,000
170,000
300,000
285,000

MARKET DEMANDS & OTHER REQUIREMENTS

The four final products must be composed of at least 25% of grade 1 hardwood and at least 50%
softwood. At least 10% of the composition must consist of outputs from the bleaching process. Due
to contractual requirements a minimum of 33,400 tons of coarse paper, 117,800 tons of container
board and 61,500 tons of food board must be produced in the upcoming year. SMP&P marketing has
determined that all of the book paper that can be produced will be sold as well as any excess of the
other three products above there minimum requirement.

OPERATIONAL COSTS

Company records show that variable operating cost ($/ton output) for each process are defined as
follows:

PROCESS

Chipping
Kraft Pulping
Semi- Chemical Pulping
Bleaching
Beating
Machining

Book paper sells for $210 per ton, $ 125 per ton for coarse paper, $133 per ton for container board and
$128 per ton for food board.

OPERATING COST

$ 2.40 per ton
$ 13.12 per ton
$ 18.98 per ton
$ 6.03 per ton
$ .77 per ton
$ 7.16 per ton

QUESTIONS

A. Develop and solve a linear programming model to determine output and input requirements
which will maximize profits.

B. Senior management is considering implementing modifications to the Bayou 1 plant to
increase
output capacity. Due to budget constraints only one operation or process can
be modified.
The cost of increasing capacity is approximately the same for each operation
and would result an
increase of capacity by 10%. Which operation (process) would you
recommend to increase capacity. Support your answer with analysis.