QUESTION 1:
An Inventory Management Decision Model:
Inventories represent a considerable investment for every organization: thus, it is important that they be managed well. Excess inventories can indicate poor financial and operational management. On the other hand, not having inventory when it is needed can also result in business failure. The two basic inventory decisions that managers face are how much to order or produce for additional inventory, and when to order or produce it to minimize total inventory cost, which consists of the cost of holding inventory and the cost of ordering it from the supplier.
Holding costs, or carrying costs, represent costs associated with maintaining inventory. These costs include interest incurred or the opportunity cost of having capital tied up in inventories; storage costs such as insurance, taxes, rental fees, utilities, and other maintenance costs of storage space; warehousing or storage operation costs, including handling, recordkeeping, information processing, and actual physical inventory expenses; and costs associated with deterioration, shrinkage, obsolescence, and damage. Total holding costs are dependent on how many items are stored and for how long they are stores. Therefore, holding costs are expressed in terms of dollars associated with carrying one unit of inventory for one unit of time.
Ordering costs represent costs associated with replenishing inventories. These costs are not dependent on how many items are ordered at a time, but on the number of orders that are prepared. Ordering costs include overhead, clerical work, data processing, and other expenses that are incurred in searching for supply sources, as well as costs associated with purchasing, expediting, transporting, receiving, and inspecting. It is typical to assume that the ordering cost is constant and is expressed in terms of dollars per order.
For a manufacturing company that you are consulting for, managers are unsure about making inventory decisions associated with a key engine component. The annual demand is estimated to be 15,000 units and is assumed to be constant throughout the year. Each unit costs $80. The companys accounting department estimates that its opportunity cost for holding this item in stock for one year is 18% of the unit value. Each order placed with the supplier costs $220. The companys policy is to place a fixed order for Q units whenever the inventory reaches a predetermined reorder point that provides sufficient stock to meet demand until the suppliers order can be shipped and received.
As consultant, your task is to develop and implement a decision model to help them arrive at the best decision. As a guide, consider the following:
a. Define the data, uncontrollable inputs, and decision variables that influence total inventory cost.
HINTS:
Uncontrollable Inputs:
Annual demand (units) =
Parameters:
Order costs per order =
Unit cost ($ per unit) =
Carrying cost rate =
Carrying cost per unit =
Decision Variable:
Order Quantity=?
b. Develop mathematical functions to compute the annual ordering cost and annual holding cost based on average inventory inventory to find the total cost.
Annual ordering cost = Annual Demand*Order cost/Order quantity
Annual holding cost = Carrying cost rate*Unit cost*Order quantity/2
Total annual cost = Annual ordering cost + annual holding cost
c. Implement the model on a spreadsheet!
d. Set up Data Table (two columns): Order Qty and Order Qty Cost ($)
e. Use Solver to verify Order Quantity with smallest Total Cost.
Question 2
The International Chef, Inc. markets three blends of oriental tea: premium, Duke Grey, and breakfast. The firm uses tea leaves from India, China, and new domestic California sources.
Tea Leaves ( Percent)
Quality Indian Chinese California
Premium 40 20 20
Duke Grey 20 30 40
Breakfast 40 40 40
Net profit per pound for each blend is $.050 for premium, $0.30 for Duke Grey, and $0.20 for breakfast. The firm's regular weekly supplies are 20,000 pounds of Indian tea leaves, 22,000 pounds of Chinese tea leaves, and 16,000 pounds of California tea leaves. Develop and solve a linear optimization model to determine the optimal mix to maximize profit, and write a short memo to the president, Kathy Chung, explaining the sensitivity information in language that she can understand.