Sample questions for Midterm $($this will be revised to add more problems$)$

$(1)$ The actual demand for a product in the months of March, April May and June are

respectively $15,16,18$ and $20($in $1000$ dollars$).$ Make forecast for July using

$($i$)$ a simple three$-$period moving average $(5),$

$($ii$)$ weighted three$-$period moving average with weights, $,$ and and $(8)$

$($iii$)$ exponential smoothing model with $,$ and a March forecast of $14.(12)$

$(2)$ The following is the demand data for three years for a product of three seasons:

year$124,45,34$

year $230,50,38$

year $338,58,42$

Construct the seasonal indexes for the three season; use Excel to construct the

regression model.

$(3)$ For a manufacturer, the beginning and ending inventory are respectively $$30,000$

and $$40,000.$ Find inventory turnover ratio for that year if the annual revenue for

that year is $$1,400,000$ given that company uses an average markup of $35\%.$

$($Hint: first find the COGS$)(8)$

$(4)$ Consider a trend model with seasonal effects $($FOUR seasons$),$ The trend model

is given by ; the seasonal factors are. Historically for season $1$ of year $2001.$

Make a seasonalized forecast for the four seasons of year $2016.$

$(5)$ If the annual revenue of a company is $$400,000$; find the following

$($a$)$ overall cost if the company is on record with a overall productivity of $1\mathrm{.}25(5)$

$($b$)$ Cost of labor if the labor productivity is $4\mathrm{.}5(5)$

$(6)$ A retailer uses continuous review method to manage its inventory. A certain

product has a daily demand of $25$ units; the retailer operates the store $360$ days a

year. The purchase price of the product is $$40$; holding cost is determined to be

$15\%$ of cost$.$ Ordering cost is determined to be $$93\mathrm{.}4.$ Do$/$answer the following.

$($i$)$ What is the annual demand? $(5)($ii$)$ What is the optimal order quantity? $(15)$

$($iii$)$ What is the maximum inventory? Calculate the average inventory and the

total annual holding cost. $(10)$

$($iv$)$ What would be your estimate of annual ordering cost based on your

calculations so far? You have to briefly state the rationale. $(5)$

$($v$)$ Annually, how many times are orders placed? $(5)$

$($vi$)$ Given that the lead time is FOUR days, what would be the ROP under

constant demand rate assumption? $(5)$

$($vii$)$ What is the probability of being stock out during lead time if you used your

answer in $($vi$)$ as ROP? What is the service rate if ROP is $136?(5+10)$

$($viii$)$ Calculate the ROP and safety stock for a service rate of $97\mathrm{.}5\%.(15)$

$($ix$)$ What is the average maximum and minimum inventory levels with the

policy of using safety stock? Calculate the average inventory and the

increment in holding cost due to safety stock. $(10)$

$(7)$ Using a continuous review model a manager orders $580$ units every time he$/$she

places an order. The ROP is such that the average safety stock is $180$ units. If

the holding cost, $h,$$$1\mathrm{.}50$ per unit per year.

$($i$)$ What is the annual holding cost, $HC.$

$($ii$)$ What is the holding cost incurred due to safety stock.