Executive SummaryThe job is to find the optimum wood heap size to minimise costs for CPP. The cardinal issue is that the figure of yearss the river is frozen varies each twelvemonth. and therefore the sum of wood that will be needed in the reserve for the winter will besides change. The solution is the optimum sum of wood that should be stockpiled in order to minimise the costs associated with both buying extra wood later and keeping wood over to the following twelvemonth.
ModelDecision: Pile size. and therefore figure of yearss of available wood. to carry. Objective: Optimize pile size to minimise costs associated with supplying wood. given that the figure of yearss the river is frozen is random.
Constraints: Weekly demand is 4800.
Premises:– The $ 2 carrying fee is paid at the same clip that the $ 8 transportation fee and $ 23 variable cost are incurred.-All logs cut have to travel to carry. can’t send straight to mill -Stockpiling fees given include clip value of money– Given comparatively few historical information points. normal distribution is the most accurate manner to gauge the figure of yearss needed.– Costss remain the same at different volume degrees– Cost of capital remains changeless at 20 %
Using the provided information. we started by ciphering the norm and standard divergence of the figure of yearss the river freezes. Using these figures. we created a normal distribution and so calculated the figure of yearss frozen in our simulation. utilizing the random figure generator. We so multiplied the figure of yearss frozen by the demand per twenty-four hours to cipher the figure of cunits of wood needed in that twelvemonth. Next. utilizing our determination variable of “Cunits of wood” produced. we multiplied the variable costs per unit ( cutting + transporting + carrying fee ) by the sum produced to find the costs associated with bring forthing this sum of wood.
Following. utilizing the sum of remnant wood. or sum of excess wood needed. we calculated the costs associated with buying excess wood. and with hive awaying the wood for a twelvemonth. along with following year’s nest eggs by holding excess wood left over. We so calculated entire costs. and found the norm for our simulations of the entire cost. With this norm. we ran solver to minimise mean costs with the appropriate sum of wood.
Answer ( a ) : Given the historical information. a normal distribution can be used to reasonably simulate # of yearss of river freezing. The sum of wood required to maintain the factory running is the figure of freeze yearss ten demand per twenty-four hours ( 686 ) as shown in the spreadsheet. ( Actual reply varies for each simulation. ) Answer ( B ) : Shown in spreadsheet for simulations of different periods of clip the river is frozen. Answer ( degree Celsius ) : When utilizing our Normal distribution theoretical account. utilizing Solver. we determined the optimum sum of wood to shop was 112. 074. While estimation can non be perfect because we relied on a reasonably limited informations set. we believe that the normal distribution is the most effectual manner to cipher these figures. Answer ( vitamin D ) : The fringy cost of 1 unit of under production = 65 – 33 = 32. Fringy cost of 1 unit of overrun = 33 – 33/1. 2 = 5. 5.
Optimum rate of overrun = 32/37. 5 = 85. 333 %Optimum rate of underproduction = 5. 5/37. 5 = 14. 666 % .
So our optimum production degree should be NORMINV ( . 8533. 145. 14. 05 ) = 109. 458. which is about 159 yearss.
These figures match up nicely with our old estimations. besides based on a normal distribution.