The purchasing manager for the Pacific Steel Companymust determine a policy for ordering coal to operate 12converters. Each converter requires exactly 5 tons of coalper day to operate, and the firm operates 360 days per year.The purchasing manager has determined that the orderingcost is $80 per order, and the cost of holding coal is 20% ofthe average dollar value of inventory held. The purchasingmanager has negotiated a contract to obtain the coal for$12 per ton for the coming year.a. Determine the optimal quantity of coal to receive in eachorder.b. Determine the total inventory-related costs associatedwith the optimal ordering policy (do not include the costof the coal).c. If five days’ lead time is required to receive an order ofcoal, how much coal should be on hand when an order isplaced?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section7.3: Pricing Models
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The purchasing manager for the Pacific Steel Company
must determine a policy for ordering coal to operate 12
converters. Each converter requires exactly 5 tons of coal
per day to operate, and the firm operates 360 days per year.
The purchasing manager has determined that the ordering
cost is $80 per order, and the cost of holding coal is 20% of
the average dollar value of inventory held. The purchasing
manager has negotiated a contract to obtain the coal for
$12 per ton for the coming year.
a. Determine the optimal quantity of coal to receive in each
order.
b. Determine the total inventory-related costs associated
with the optimal ordering policy (do not include the cost
of the coal).c. If five days’ lead time is required to receive an order of
coal, how much coal should be on hand when an order is
placed?

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