Unit 6: Linear Programming and Inventory Models (30% of the Assessment) Flashcards
Abbreviation for the amount of inventory a business should order to minimize the total amount of inventory costs
EOQ
Restriction that limits the degree in which a company can pursue its objective
Constraint
The cost resulting from not having an item on the shelf for sale
Shortage costs
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)
linear programming
Any goods held in stock for immediate or future use
inventory
Multiplier of the variable, as in linear equations or inequalities
Coefficient
The cost of replenishing inventory, including receiving logistics
Ordering costs
The number of items needed, typically per year
Demand
The function that seeks to minimize or maximize some quantity
Objective function
The costs of storing inventory, insurance, and managing inventory risk due to damage or theft
Carrying costs
Area of the graph that satisfies all constraints
Feasible region
A mathematical technique that can be used to identify the value of a variable for a given set of constraints.
linear programming
Amount of inventory a business should order to minimize the total amount of inventory costs, including carrying, ordering, and shortage costs.
economic order quantity
Any goods held in stock for immediate or future use.
inventory
Area of the graph that satisfies all constraints.
feasible region
Multiplier of the variable, as in linear equations or inequalities
coefficient
Restriction that limits the degree in which a company can pursue its objective
constraint
The cost of replenishing inventory, including receiving logistics
ordering costs
The costs of storing inventory, insurance, and managing inventory risk due to damage or theft.
carrying costs
The costs resulting from not having an item on the shelf for sale.
shortage costs
The function that seeks to minimize or maximize some quantity.
objective function
The number of items needed, typically per year.
demand
optimization
solving for the optimal (min or max) objective subject (goal) to a set of constraints
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.
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 $8.
Decision Variables = # of Hats & # of Scarves
Profit = 11H + 8S
Production quanities are constrained by the amount of labor hours available
in Knitting and Finishing Depts, 120 and 110, respectively. Each Hat requires
.4 Hrs of Knitting time and .4 Hrs of Finishing. Scarves require .3 Hrs of
Knitting and .2 Hrs of Finishing
-Knitting Constraint: .4H + .3H <= 120
-Finishing Constraint: .4H+.2S<=110
-Non-negativity Constraint: H>=0, S>=0
The “feasible region”
Annual Total Inventory Cost (TIC) equation
Annual Total Inventory Cost (TIC) = Purchasing Costs (DP) + Holding Costs (Q/2H)+ Ordering Costs (D/Q*O)
D= Demand (Units/Year) P=Price ($ 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)
The Qty that results in the Lowest Total Inventory Cost is called the
Economic Order Qty (EOQ)
EOQ=√2DO/hP
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.
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)
Annual Holding Cost Formula
Annual Holding Cost = (Average Inventory Level) * (holding cost per unit per year) = (EOQ/2)*hP
Annual Ordering Cost Formula
Annual Ordering Cost = (Annual Demand) / (Order Quantity) * (Cost per Order) = (D/EOQ)*O
