Que$4$stion $9$: Demand Forecasting

A retailer forecasts demand for a product using $a4-$month moving average. The historical

monthly demand $(in$ units$)$ for the last $6$ months $is$:

Formula for $4-$Month Moving Average Forecast

Forecast for month $t=\frac{D_{t-1}+D_{t-2}+D_{t-3}+D_{t-4}}{4}$

where $D_{t-1},D_{t-2},D_{t-3},D_{t-4}$ are the demands for the four months prior $to$ month $t.$

Tasks

$(a)$ Calculate the $4-$month moving average forecast for July. Round $to$ two decimal

places.

$(b)If$ the actual demand for June was $740$ units and the forecast for June $(madein$

May$)$ was $675\mathrm{.}00$ units, calculate the forecast error for June. Round $to$ two decimal

places.

Note: Show all calculations step$-by-$step. Forecasts cannot $be$ calculated for the first

four months due $to$ insufficient data. Question $10$: Aggregate Production Planning

A company forecasts the following demand for its product over the next $3$ months:

Additional Information

Regular production capacity $=1,250$ units $\frac{?}{?}$ month

Regular production cost $=$$$45$ per unit

Beginning inventory $=200$ units

Inventory holding cost $=$$$2\mathrm{.}50=480$ minutes$(CT)=$ Total available time per shift $$ Units required per shift

Minimum number $of$ workstations $=$ Total task time $$ Cycle time $(roundedup)$

Tasks

$(a)$ Calculate the cycle time required $to$ achieve the desired output rate. Round $to$ two

decimal places.

$(b)$ Determine the minimum number $of$ workstations needed without exceeding the

cycle time.

Note: Show all calculations clearly.

Question $12$: Safety Stock Calculation

A retailer manages inventory for a product with $an$ annual demand $of12,000$ units. The

lead time for restocking $is15$ days, and the company operates $360$ days per year. The

standard deviation $of$ daily demand $is6$ units.

Given Data

Annual demand $(D)=12,000$ units

Lead time $(L)=15$ days

Operating days per year $=360$ days

Standard deviation $of$ daily demand $({}_d)=6$ units Question $14$: Material Requirements Planning

A company produces a product requiring two components, A and $B,$ with the following

details:

Additional Information

Planned production for week $6=120$ units

Current inventory: $A=100$ units, $B=80$ units

Tasks

$(a)$ Calculate the gross requirements for components A and $B$ for week $6.$

$(b)$ Determine the net requirements for components A and $B,$ considering current $in-$

ventory, and the week $in$ which orders must $be$ placed $to$ meet week $6$ production.

Note: Show all calculations clearly. Assume $no$ safety stock. Question $15$: Quality Control

A manufacturing process produces items with a defect rate $of4\%.$ A sample $of200$ items

$is$ inspected daily.

Formulas

Expected number $of$ defects $=$ Sample size $$ Defect rate

Standard deviation $of$ defects $=\sqrt[\phantom{2}]{\text{S}\text{a}\text{m}\text{p}\text{l}\text{e}\text{s}\text{i}\text{z}\text{e}\text{D}\text{e}\text{f}\text{e}\text{c}\text{t}\text{r}\text{a}\text{t}\text{e}(1-\text{D}\text{e}\text{f}\text{e}\text{c}\text{t}\text{r}\text{a}\text{t}\text{e})}$

Tasks

$(a)$ Calculate the expected number $of$ defects $in$ the daily sample. Round $to$ two decimal

places.

$(b)$ Calculate the standard deviation $of$ the number $of$ defects. Round $to$ two decimal

places.

Note: Show all $4$calculations clQuestion $17$: Just$-In-$Time $(JIT)$ Inventory

A company implements a JIT system for a component with a daily demand $of50un$