Problem $16-12($Algo$)$

Your company assembles five different models of a motor scooter that is sold in specialty stores in the United States. The company uses the same engine for all five models. You have been given the assignment of choosing a supplier for these engines for the coming year. Due to the size of your warehouse and other administrative restrictions, you must order the engines in lot sizes of $1,040$ each. Because of the unique characteristics of the engine, special tooling is needed during the manufacturing process for which you agree to reimburse the supplier. Your assistant has obtained quotes from two reliable engine suppliers and you need to decide which to use. The following data have been collected:

Requirements $($annual forecast$)12,480$ units

Weight per engine $25$ pounds

Order processing cost $ $215$ per order

Inventory carry cost $20$ percent of the average value of inventory per year

Note: Assume that half of the lot size is in inventory, on average $(1,040-$: $2=520$ units$).$

Two qualified suppliers have submitted the following quotations:

ORDER QUANTITY SUPPLIER $1$ UNIT PRICE SUPPLIER $2$ UNIT PRICE

$1$ to $1,499$ units$/$order $$556$ $$554$

$1,500$ to $2,999$ units$/$order $552554$

$3,000+$ units$/$order $550548$

Tooling costs $$25,900$ $$22,000$

Distance $115$ miles $100$ miles

Your assistant has obtained the following freight rates from your carrier:

Truckload $(42,000$ pounds each load$)$: $$0\mathrm{.}80$ per ton$-$mile

Less than truckload: $$1\mathrm{.}20$ per ton$-$mile

Note: Per ton$-$mile $=2,000$ pounds per mile

a$-1.$ Calculate the total cost for each supplier.

Note: Round your answers to the nearest whole number.

a$-2.$ Which supplier would you select?

multiple choice $1$

Supplier $2$

Supplier $1$

b$-1.$ If you could move the lot size up to ship in truckload quantities, calculate the total cost for each supplier.

Note: Do not round intermediate calculations. Round "Required lot size for truckload" and final answers to the nearest whole number.

HINT: Use $($full$)$ truckload cost rates and the lowest $($feasible$)$ unit cost for all calculations. For example, if there are $8\mathrm{.}3$ orders per year, don$$t split the $8\mathrm{.}3$ orders into $8$ full truckloads and $0\mathrm{.}3$ less than truckloads $-$ use the full truckload rate for all $8\mathrm{.}3$ orders. For annual purchase cost, don$$t use two different unit costs for the $8$ complete orders and the $0\mathrm{.}3$ partial orders $$ use the lowest $($feasible$)$ unit cost for all $8\mathrm{.}3$ purchase orders based on the lot size needed for a full truckload.

b$-2.$ Would your supplier selection change?

multiple choice $2$

Yes

No