Q$1.$ Production Planning $($Regular $+$ Overtime$)$

Scenario:

A workshop plans production using regular and overtime hours to meet monthly demand.

Month Demand Regular Capacity

Jan $400350$

Feb $450400$

Mar $500400$

Costs:

$-$ Regular cost: $$50/$unit

$-$ Overtime cost: $$70/$unit

$-$ Max $100$ units overtime allowed per month

A$.$ How many units should be produced using overtime each month?

B$.$ What is the total production cost for $3$ months?

Q$2.$ Inventory Carrying

Scenario:

A store receives shipments of fans and carries inventory at a cost each month. Demand and supply data are

below.

Month Demand Supply Received

Jan $300350$

Feb $320320$

Mar $310330$

Carrying cost $=$ $$2$ per unit$/$month

No stockouts allowed

A$.$ How many units are carried as ending inventory each month?

B$.$ What is the total inventory carrying cost for $3$ months?

Q$3.$ EOQ Model

Scenario:

An item has the following parameters for annual demand, ordering cost, and holding cost.

$-$ Annual demand: $10,000$ units

$-$ Ordering cost: $$100/$order

$-$ Holding cost: $$2$ per unit$/$year

A$.$ What is the Economic Order Quantity $($EOQ$)?$

B$.$ How many orders will be placed per year?

Q$4.$ Simple Forecasting $($Moving Average$)$

Scenario:

Sales data $($units$)$ for the past $4$ months are given below.

Month Sales

Jan $200$

Feb $220$

Mar $210$

Apr $230$

A$.$ What is the $3-$month moving average forecast for May?

B$.$ What is the forecast error for April using $3-$month MA$?$

Q$5.$ Labor Cost Planning

Scenario:

A factory pays different rates for labor hours. The required and available hours are below.

Month Required Hours Regular Hours Overtime Limit

Jan $1,000800200$

Labor cost per hour:

$-$ Regular: $$12/$hr

$-$ Overtime: $$18/$hr

A$.$ How many hours should be done using overtime?

B$.$ What is the total labor cost for January?

Q$6.$ Reorder Point $($ROP$)$

Scenario:

A product has the following parameters regarding lead time, daily demand, and safety stock.

$-$ Lead time: $5$ days

$-$ Daily demand: $100$ units

$-$ Safety stock: $200$ units

A$.$ What is the reorder point $($ROP$)?$

B$.$ If current inventory is $600$ units, when should an order be placed?

Q$7.$ Production with Inventory Holding

Scenario:

Monthly production and demand data for a product are shown below.

Month Demand Production

Jan $400450$

Feb $420400$

Mar $440450$

Holding cost $=$ $$3/$unit$/$month

No shortages allowed

A$.$ What is the ending inventory at the end of each month?

B$.$ What is the total holding cost for the $3$ months?

Q$8.$ Break$-$Even Analysis

Scenario:

A product incurs fixed and variable costs as shown below. The company wants to find the break$-$even point.

Cost Type Amount

Fixed Costs $$10,000$

Variable Cost $$30$ per unit

Selling Price $$50$ per unit

A$.$ What is the break$-$even volume $($units$)?$

B$.$ What is the total revenue at the break$-$even point?

Q$9.$ Machine Utilization

Scenario:

A machine is available $160$ hours per month. The following hours were recorded:

Activity Hours

Running Time $130$

Idle Time $?$

A$.$ Calculate the machine utilization rate $($in $\%).$

B$.$ Calculate the machine idle time $($hours$).$

a