OpMan exam 2 notes

Annual Inventory Turnover Equation

= 𝐶𝑂𝐺𝑆 / 𝐴𝑣𝑔𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦

COGS

sales - gross profit

Days’ supply of inventory on hand equation

= 𝐴𝑣𝑔 𝐼𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 / 𝐷𝑒𝑚𝑎𝑛𝑑 𝑅𝑎𝑡𝑒 per time period

or

= time period / inventory turnover

average inventory

(inventory 1 + inventory 2) / 2

𝐷𝑎𝑖𝑙𝑦 𝐷𝑒𝑚𝑎𝑛𝑑 𝑅𝑎𝑡𝑒 Equation

cost of goods sold (COGS) / days in year

average inventory level required to hit the target

COGS / inventory turnover

total annual dollar usage of these items

Perform an A-B-C Inventory classification

1. Calculate annual dollar values

   • Multiply Unit Cost by Annual Volume

2. Arrange items from highest DV to lowest

3. Calculate percentages and classify

Re-order point models address uncertainty by including safety stock on top of average demand

True or false?

True

λ (lamda)

Arrival Rate

to find out waiting lines

Mu (μ)

Service Rate

to find out waiting lines

EOQ (Economic Order Quantity)

The order size that minimizes total annual cost (consisting of Holding costs and Ordering (shipping) costs)

order size, shown as “Q”

Useful for giving us order SIZE but not order TIMING

square root of (2DS/H)

where D = Number of Orders, 𝑆 = shipping cost, H = Holding Cost per UNIT per YEAR

3 types of EOQ (Economic Order Quantity) Models

• Simple

• Fixed Carrying Costs with Quantity Discounts

• EOQ with Quantity Discounts (Percentage Holding Costs)

EOQ Model: Fixed Carrying Costs with Quantity Discounts

• Step 1: Find EOQ

• Step 2: Use Total cost formula to compare total costs

  • for one of these, use the EOQ and the other use the quantity of books that qualifies for the discount

• Step 3: Pick which one has least cost

Total cost formula

used in EOQ models for finding Fixed Carrying Costs with Quantity Discounts

TC= ((𝑄 / 2) H)) + ((𝐷 / Q *𝑆)) + (P* D)

P = price of discount

D =Number of Orders

think of it like “𝑇𝑜𝑡𝑎𝑙𝐶𝑜𝑠𝑡 = 𝐶𝑎𝑟𝑟𝑦𝑖𝑛𝑔 Cost + 𝑂𝑟𝑑𝑒𝑟𝑖𝑛𝑔 Ordering + 𝐶𝑂𝐺𝑆”

Orders per year

𝐴𝑛𝑛𝑢𝑎𝑙𝐷𝑒𝑚𝑎𝑛𝑑 (D) / Order size (Q)

𝑇𝑖𝑚𝑒 𝐵𝑒𝑡𝑤𝑒𝑒𝑛 𝑂𝑟𝑑𝑒𝑟𝑠

𝑂𝑟𝑑𝑒𝑟𝑆𝑖𝑧𝑒 (Q) / 𝐷𝑒𝑚𝑎𝑛𝑑 (D)

EOQ Mode: EOQ with Quantity Discounts (Percentage Holding Costs)

H=I(C)

where I = carrying cost percentage

and C = carrying cost

have to plug in percentage holding cost for each discount option for EOQ, not just the first one

Two main questions for inventory management

1. How much inventory to order?

2. When to order inventory?

Reorder Point

tells us best time to reorder before running out

𝑑 × 𝐿𝑇

d = Demand rate (units per day or week)

LT = Lead time in days or weeks

Lead time

total delay between ordering and receiving inventory

ROP when Known standard deviation of lead-time demand

= 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐷𝑒𝑚𝑎𝑛𝑑 + 𝑆𝑎𝑓𝑒𝑡𝑦 𝑆𝑡𝑜𝑐𝑘

• (D * LD) + (𝑧 * 𝜎𝑑𝐿𝑇)

safety stock = 𝑧𝜎𝑑𝐿𝑇

Z is the number of standard deviations (find stockout risk on z table)

𝜎𝑑𝐿𝑇 is the standard deviation of “lead time demand”

𝑆𝑎𝑓𝑒𝑡𝑦 𝑆𝑡𝑜𝑐𝑘

extra stock just in case the order gets delayed or it gets popular (variation in demand)

= 𝑧𝜎𝑑𝐿𝑇

helps meet customer demand, but it costs money to hold…

Service level

the probability that demand will not exceed supply (aka: the probability of having stock still left on your shelves)

stockout

chance of running out of stock

If a stockout has a 5% chance in a given week, what is my service level?

• 95%

ROP when variable demand

• (D * LD) + (𝑧 * 𝜎𝑑 * √𝐿𝑇)

ROP when variable lead time

ROP=(D×LT)+(z×σLT​×D)

Little’s law

The average amount of inventory in a system = to the product of the average rate of inventory leaving the system

(demand rate) and the average time of a unit in the system

Critical Path

the slowest path

will therefore determine the overall finish of the project

makes sense to crash ANY activity on this path if needed

Crashing

shortening/expediting some activities (at a cost) within a project to reduce overall project completion time/cost

usually try to pick one on critical path

Normal time (N T) and Normal cost (N C)

activity time and cost to complete an activity under normal conditions and with the normal time

Crash time (C T) and Crash cost (C C)

shortest possible time to complete an activity and the activity cost associated with the crash time

Project duration in PM

the LONGEST path from start to finish

Add all possible paths and pick the longest

Slack in PM

(Latest Start) − (Earliest Start)

LS = start from the end of the project and time of those activities + one needed

ES = start from beginning of project and only add time of activities before, not the one needed

littles law formulas

Lq = λ * Wq

• waiting in line, people in the queue

L = λ * W

• entire system not just in line (people in system, in bank, being served)

where

• L = customers

• W = wait time

• λ (lamda) = arrival rate

Single-Server Model (M/M/1)

when μ (service rate) present

L = (λ) / ( μ - λ)

Little’s Law vs Queue Model Formulas (M/M/1)

use Queue Model when given service rate (μ)

so if you hear

• utilization

• server processes X per hour

• % of time working (utilization)

• can handle X per hour

• service time

utlization

defined as “P”

“what percentage of time are they busy”

P =λ (lamda) / μ (Mu)

probability

“what is the probability that the line is empty”

P0 ​= 1 − ρ