$($a$)$ For one of its popular computer models, Agility Manufacturing is trying to optimize the

lot sizes for its assembly orders given the requirements in Table $3.$ The following

information has been put together by its Inventory Management Department: Setup cost:

$$\frac{300}{?}$ order; Inventory carrying cost: $$\frac{1}{?}$ unit$/$week; Inventory on hand: $0$ units.

Table $3$

Determine the optimum lot sizing for the company using the Wagner$-$Whitin algorithm.

Assume that the period ending inventory incurs the inventory carrying cost. Specify the

lot sizes over the six weeks and the total cost of the solution.

$(15$ marks$)$

$($b$)$ Consider the sales data in Table $4$ for the previous five months:

Table $4$

$($i$)$ Compute the exponential smoothing values for the above sales data using alpha

value of $0\mathrm{.}20$ and find the forecast for the sixth month. Assume first period

forecast to be $450.$

$($ii$)$ Find the mean absolute deviation $($MAD$)$ for this forecast.

$(10$ marks$)$

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