Team 27Nick Armstrong, Evan Mohl, Shreeraj Pawar, Sydney Sarachan

Confederated Pulp and Paper Case Write Up

For the question, we determined that we would need to find the appropriate

service level first. Then, that service level, combined with information in exhibit 1 to

derive demand, would give us the appropriate block pile at the start of the winter.

We started with the basic service level equation

SL= CsCs+Ce

Cs, or the cost of being short in inventory, was calculated as the difference

between the cost of cutting the wood and what the farmers charged. The farmers

charged $65. For the cost of supplying wood, we added the unit cost of $47.50 with

$8.00 of shipping (since every piece of timber is shipped). We debated whether to

add the $2 holding charge, but since every piece of wood would be held in the

winter we included it. Thus, Cs =$65-($47.50+$8+$2).

In order to calculate, Ce, we used this equation.

Ce=H∗Qλ

However, we quickly realized we did not have Q, or the total ordering and

holding cost per period. So we used the Q equation

Q=❑√ 2λshWe determined lamda as 4800/week, which was given in the case. We

converted this to a yearly total, dividing by 52 and getting 92.3. We assumed the

case numbers were given in a per year basis as often times they cited annual

numbers. Since S is the supply cost, we simply used $47.50 + $8.00 for $55.50. For

H, we employed the formula H = ic +v. These were all supplied in the case (v=23,

i=20% and c=$2).

Eventually we calculated Q.

Q=❑√ 2∗92.3∗55.523.4=$20.92 per year

We then could solve the Ce equation.

Ce=23.4∗20.9292.3

=$5.3 per year

This gave us all the variables needed for the service level equation.

SL= 7.55.3+7.5

=.585

To then determine at what service level we would find the optimal stocking

level for winter, we created a demand frequency table (see below) from the

historical data given in Exhibit 1. We figured that the difference each year between

the pile in the fall and the pile in the spring replicated demand, since that’s what was

sold. We then arranged each year by demand and calculated the cumulative

probability. The place where optimal service leveled equaled cumulative probability

would give us the amount to pile up in the winter. Because the .585 service level

falls between the cumulative probabilities of 0.5 and 0.66, we want to stock up to

ensure we cover the service level. As a result, we chose the 1982-83 year with a

demand of 88,000. So, the company should be sure to pile up 88,000 units of the

timber in the winter.

Frequency Demand table

Year Pile: Fall Pile: Spring DifferenceRe-ordered Difference

ProbabilityCumulative Probability

1982-83 100 12 88 82 0.1666666 0.1666666

1983-84 100 a 112 85 0.1666666 0.333333

1984-85 125 40 85 86 0.1666666 0.5

1985-86 113 27 86 88 0.1666666 0.666666

1986-87 110 5 105 105 0.1666666 0.833333

1987-88 110 28 82 112 0.1666666 1.0