Homework AssignmentHomework AssignmentInventory Control ModelsInventory Control Models

MGMT E-5065 Operations and Logistics ManagementMGMT E-5065 Operations and Logistics Management

Due December 4th

The Toy Manufacturer The Toy Manufacturer

A toy manufacturer uses forty eight thousand ( 48,000 ) wheelsper year for its popular dump truck series. The firm makes itsown wheels which it can produce at a rate of eight hundred ( 800 )per day. The toy trucks are assembled uniformly over the entireyear. Carrying cost is one dollar ( $1.00 ) per wheel a year. Setupcost for a production run of wheels is forty five dollars ( $45.00 ).The firm operates two hundred and forty ( 240 ) days per year.

Problem 1Problem 1

MGMT E-5065MGMT E-5065Operations and LogisticsOperations and Logistics

ManagementManagement

The Toy Manufacturer The Toy Manufacturer

REQUIREMENT

A. Manually compute the optimal production run size.B. Manually compute the total variable costs ( TVC ) for the above production run size.C. Manually compute the length of the production run period.

Office Supply DistributorOffice Supply Distributor

Problem 2Problem 2

A firm buys a projector bulb at the rate of ten ( 10 ) per week.The price charged by the manufacturer varies with the order quantity as follows:

Order Quantity Unit Price

0 - 99 $200.00

100 - 249 $180.00

250 - 499 $150.00

500 or more $130.00

The firm estimates that it pays one hundred dollars ( $100.00 ) foreach order of bulbs. It also believes that it costs eighteen percent( 18% ) per year of a bulb’s unit price to hold it in inventory.

Office Supply DistributorOffice Supply Distributor

REQUIREMENT

A. Determine the most cost-effective number of bulbs to order at one time.

B. Compute the TC ( total costs ) for such an ordering policy as well as the candidate ordering policies.

NOTE: NOTE: Assume a fifty-two ( 52 ) week year.

ABC Company ABC Company

Problem 3Problem 3ABC Company is the exclusive North American distributor of aportable sauna manufactured in Sweden. The saunas cost thecompany two-thousand four-hundred dollars each ( $2,400.00 ) ,and the company estimates the annual carry cost per unit forthis product is five-hundred and twenty-five dollars ( $525.00 ) .Because the saunas must be shipped in a containerized vessel,the fixed ordering cost is fairly high at one-thousand two-hundredand fifty dollars ( $1,250.00 ) . Lead time for delivery is four ( 4 )weeks. ABC Company receives orders for an average of fifteen( 15 ) saunas per week. Customers are willing to place orders forthe saunas when ABC is out of stock. However, the firm estimatesthe cost of keeping a customer’s sauna on backorder is $1,040.00one thousand and and forty dollars per year.

ABC CompanyABC Company

REQUIREMENT

A. Determine the optimal order quantity ( Q* ) for the saunas.

B. Determine the optimal number of backorders ( S* ) .

C. Determine the reorder point ( ROP / R ) for the optimal order quantity.

Note: The firm operates fifty-two ( 52 ) weeks a year.

The Retailer The Retailer

A retailer buys a certain item from a distant supplier. Lead time( L ) is normally distributed with a mean of thirty days ( µ = 30 )and a standard deviation of fourteen days ( σ = 14 ). Daily demand is also normally distributed with a mean of fouritems ( µ = 4 ) and a standard deviation of one and one-half items( σ = 1.5 ) .

Problem 4Problem 4

The RetailerThe Retailer REQUIREMENT

A. Determine the safety stock and reorder point for an eighty-five percent (85%) service level, that is, a 15% risk of a stockout.

B. Determine the safety stock and reorder point for a ninety-five percent (95%) service level, that is, a 5% risk of a stockout.

XYZ CompanyXYZ Company

XYZ Company buys a component from a distant vendor seven (7) times a year. It takes an average of ten (10) days to receive an order from the time it is placed. The units cost three dollars ( $3.00 ) each and have a carry cost of seventy-five cents ( $.75 ). The firm estimates a stockout cost of one dollar ( $1.00 ) per unit. The probability distribution of demand during a ten ( 10 ) day period is as follows:

Demand 144 152 160 168 176 184 192

Probability .01 .04 .20 .50 .20 .04 .01

Problem 5Problem 5

XYZ CompanyXYZ Company

REQUIREMENT

1. Calculate the safety stocks ( SS ) for reorder points 168 and 176 ( units ).2. Calculate the additional annual carry costs ( H ) for the reorder points 168 and 176 ( units ).3. Calculate the annual expected stockout costs ( Cs ) for the reorder points 168 and 176.

Homework AssignmentHomework AssignmentInventory Control ModelsInventory Control Models

MGMT E-5065 Operations and Logistics ManagementMGMT E-5065 Operations and Logistics Management