[CONFEDERATED PAPER AND PULP BY TEAM 13] 1 The size of the block pile needed at the start of the coming winter is dependent on both inventory needed to meet expected demand (rate of consumption of wood) and inventory (safety capacity) needed to handle a certain service level given the expected length of time the river stays frozen (lead time for arrival of inventory). Given that demand varies historically (strong correlation with days of freezing) and there is a fluctuation in lead times due to variability in number of freeze days, the calculation for necessary amount of stockpiled wood in the winter is based on the formula: (

)

)

√(

(

[ ])

(

can be understood as the historical average demand per freeze-day and L as the ) is the mean Lead Time historical average number of freeze days. Hence, ( Demand, which represents the average demand expected during freeze days. Based on ) Exhibit 1, ( . The latter half of the larger equation represents the additional inventory needed to meet expected demand based on a calculated optimal service level that takes into both the cost of stock out and the cost of holding excess inventory (See Exhibit 2 for calculations). Based on a calculated optimal service level of approximately 98.83%, which corresponds to a Z-value of 2.263, the level of safety capacity needed is: ( (

√(

)

√( )

(

(

[ ]) )

Therefore, necessary size for the block pile at the start of coming winter given an expected demand based on historical average (and standard deviation) and an optimal service level of 98.83% (which intuitively makes sense because stock out costs are much higher than excess inventory holding costs) is:

In order to avoid stocking out and meet demand, Confederated Pulp & Paper need to have a block pile at the start of the coming winter of 110,851 cunits.

Kenneth Mao, Alex Muckerman, Ameen Aftab, Jinjin Zhao, Christine Pavia

[CONFEDERATED PAPER AND PULP BY TEAM 13] 2 Exhibit 1. [Historical] Average Demand based on Average Number of Freeze Days Year (End) 79 80 81 82 83 84 85 86 87 88 Mean SD

Pile Size (Fall)

100000 100000 125000 113000 110000 110000 109666.67 9309.49

Pile Size (Spring)

Demand

12000 88000 -12000 112000 40000 85000 27000 86000 5000 105000 28000 82000 16666.67 93000 18758.11 12361.23

Freeze Days 142 151 120 148 144 170 138 146 159 130 144.8 14.05

Demand Per Freeze Days

Weighted Demand Per Freeze Days

611.11 658.82 615.94 589.04 660.38 630.77 627.68 28.12

88488.89 95397.65 89188.41 85293.15 95622.64 91335.38 90887.69 4071.87

Important Notes:   

Demand was calculated based on the difference in pile sizes from the beginning of fall to the beginning of spring. We chose to the average value of freeze days from 1979 to 1988 for a better estimation (larger sample size) rather than from 1983 to 1988 only. The historical average demand per freeze-day ( ) is 627.68 and the historical average number of freeze days is 144.8. Multiplying the two together gives us the level of inventory we would expect to hold given no variability in demand and instant response time from a supplier. This is unrealistic given P’s situation, so a safety capacity needs to be taken into in which the reliability of supply time (in this case river usage based on non-frozen days) needs to be calculated.

Kenneth Mao, Alex Muckerman, Ameen Aftab, Jinjin Zhao, Christine Pavia

[CONFEDERATED PAPER AND PULP BY TEAM 13] 3 Exhibit 2. Calculating Safety Capacity Z-Value Optimal service level is determined by the ratio of:

Cs is the cost of stock out and Ce is the cost of holding excess inventory. Cs can be calculated based on what P would have to pay local suppliers minus what regular supply costs (cost per unit + shipping + stack/unstack). (

)

Ce is dependent on holding costs, the optimal inventory quantity that minimizes total inventory costs (balances both holding and ordering costs), and expected demand ( ).

Holding cost per unit per year is calculated as follows: (

)

(i, c, v are given in case as cost of capital, variable cost, cost of stacking + un-stacking) The optimal quantity level of inventory such that holding and ordering costs is: √

The term “S” is the cost of replenishing an order, which we assumed to be equivalent to the cost of replenishing a single cunit. The total cost of supplying a cunit (plus shipping) is $55.50 (= $47.5 + $8.00). √

The cost of holding excess units can be calculated as follows:

Kenneth Mao, Alex Muckerman, Ameen Aftab, Jinjin Zhao, Christine Pavia

[CONFEDERATED PAPER AND PULP BY TEAM 13] 4 Given the values now for Cs and Ce, the optimal service level can be calculated:

This intuitively makes sense because of the extremely high stock out costs in relation to excess holding costs of a single cunit for the year. A higher SL is preferred. 98.83% corresponds to a Z-value of 2.263. This allows us to calculate the additional inventory needed to meet a total service level of 98.83%. ( (

√(

)

√( )

(

(

[ ]) )

Kenneth Mao, Alex Muckerman, Ameen Aftab, Jinjin Zhao, Christine Pavia