Unit 6: Linear Programming and Inventory Models (30% of the Assessment)

Question 1

Abbreviation for the amount of inventory a business should order to minimize the total amount of inventory costs

Answer 1

EOQ

Question 2

Restriction that limits the degree in which a company can pursue its objective

Answer 2

Constraint

Question 3

The cost resulting from not having an item on the shelf for sale

Answer 3

Shortage costs

Question 4

A mathematical technique that can be used to identify the value of a variable for a given set of constraints

(no powers, square roots, or multipliers in the equation)

ex: Y=b1X1+b2X2
Y=2X1+5X2+10X3+7X4 where X1, X2, X3, & X4 are decision variables

(#s after letters would be placed to the bottom right of the letter if I knew how to do that on here)

Answer 4

linear programming

Question 5

Any goods held in stock for immediate or future use

Answer 5

inventory

Question 6

Multiplier of the variable, as in linear equations or inequalities

Answer 6

Coefficient

Question 7

The cost of replenishing inventory, including receiving logistics

Answer 7

Ordering costs

Question 8

The number of items needed, typically per year

Answer 8

Demand

Question 9

The function that seeks to minimize or maximize some quantity

Answer 9

Objective function

Question 10

The costs of storing inventory, insurance, and managing inventory risk due to damage or theft

Answer 10

Carrying costs

Question 11

Area of the graph that satisfies all constraints

Answer 11

Feasible region

Question 12

A mathematical technique that can be used to identify the value of a variable for a given set of constraints.

Answer 12

linear programming

Question 13

Amount of inventory a business should order to minimize the total amount of inventory costs, including carrying, ordering, and shortage costs.

Answer 13

economic order quantity

Question 14

Any goods held in stock for immediate or future use.

Answer 14

inventory

Question 15

Area of the graph that satisfies all constraints.

Answer 15

feasible region

Question 16

Multiplier of the variable, as in linear equations or inequalities

Answer 16

coefficient

Question 17

Restriction that limits the degree in which a company can pursue its objective

Answer 17

constraint

Question 18

The cost of replenishing inventory, including receiving logistics

Answer 18

ordering costs

Question 19

The costs of storing inventory, insurance, and managing inventory risk due to damage or theft.

Answer 19

carrying costs

Question 20

The costs resulting from not having an item on the shelf for sale.

Answer 20

shortage costs

Question 21

The function that seeks to minimize or maximize some quantity.

Answer 21

objective function

Question 22

The number of items needed, typically per year.

Answer 22

demand

Question 23

optimization

Answer 23

solving for the optimal (min or max) objective subject (goal) to a set of constraints

Question 24

Consider a company that produces Hates and Scarves
Produce a mix of products (Hats and Scarves) to Maximize Profit where Profit
per Hat is $11 and Profit per Scarf is $8.
Production quantities are constrained by the amount of labor hours available in Knitting
and Finishing Departments, 120 and 110, respectively.
Each Hat requires .4 Hrs of Knitting time and .4 Hrs of Finishing Scarves
require .3 Hrs of Knitting and .2 Hrs of Finishing.

Answer 24

Step 1: Identify the Decision Variables
Step 2: Identify the Objective
-Translate Objective into Mathematical form
Step 3: Identify Constraints
-Translate Constraints into Mathematical Form
Step 4: Apply an LP Solution Software
-Excel Solver or other software products

Pull out the optimization pieces. What is the objective function? What is the
set of constraints?

-Produce a mix of products (Hats and Scarves) to Maximize Profits where
Profit per Hat is $11 and Profit per Scarf is $8.
Decision Variables = # of Hats & # of Scarves
Profit = 11H + 8S

Production quanities are constrained by the amount of labor hours available
in Knitting and Finishing Depts, 120 and 110, respectively. Each Hat requires
.4 Hrs of Knitting time and .4 Hrs of Finishing. Scarves require .3 Hrs of
Knitting and .2 Hrs of Finishing
-Knitting Constraint: .4H + .3H <= 120
-Finishing Constraint: .4H+.2S<=110
-Non-negativity Constraint: H>=0, S>=0

The “feasible region”

Question 25

Annual Total Inventory Cost (TIC) equation

Answer 25

Annual Total Inventory Cost (TIC) = Purchasing Costs (DP) + Holding Costs (Q/2H)+ Ordering Costs (D/Q*O)

D= Demand (Units/Year)
P=Price ($ per Unit)
Q= Order Qty (Units)
H= Holding Costs per Unit per Year
   -H=h*P where h= Holding Cost % per Unit per Year
O=Ordering Cost ($ per Order)

(Note: Demand (D) and H (h*P) must be the same Time units (Daily, Monthly, or Yearly)

Question 26

The Qty that results in the Lowest Total Inventory Cost is called the

Answer 26

Economic Order Qty (EOQ)

EOQ=√2DO/hP

Question 27

A grocery purchases three kinds of Cheese. Prices are respectivelyl: Panela at $3.75/lb,
Goat Cheese at $7.10/lb and Oaxaca at 4.50/lb. Daily Demand for each cheese is
45, 22, and 63 lbs respectively. The cost to prepare and place an Order for any kind
of cheese is $2 per Order. These Cheeses are perishable so the Holding Cost is estimated
to be at 0.5% of the purchase Price.

Answer 27

Step 1: Compute the Economic Order Qty (EOQ):
-Note: Ensure the Demand and Holding Costs are in the same Time units. When not specified, assume Annual.

EOQ=√2DO/hP (formula)

EOQ=√2(22365)2/(.0057.10) =951 (after rounding)

Step 2: Compute the Total Annual Inventory Costs (TIC)

Formula: Annual Total Inventory Cost (TIC) = Purchasing Costs (DP) + Holding Costs (Q/2H)+ Ordering Costs (D/Q*O)

22*365*7.10=57,013
\+
951/2*.005*710=16.88
\+
(22*365/951)*2
=57047 (rounded up)

Question 28

Annual Holding Cost Formula

Answer 28

Annual Holding Cost = (Average Inventory Level) * (holding cost per unit per year) = (EOQ/2)*hP

Question 29

Annual Ordering Cost Formula

Answer 29

Annual Ordering Cost = (Annual Demand) / (Order Quantity) * (Cost per Order) = (D/EOQ)*O