# Operations Management 2

## Inventory Management

• Total Cost (per year) = Purchase Cost + Holding Cost + Ordering Cost
• Total Cost = CD + Average inventory size * H + Number of Orders * Ordering cost
$$TC = CD + QH/2 + (D/Q) \times S$$

Where,
• Q : Order Size (Variable)
• C : Cost per item
• D : Annual Demand / Rate of demand
• H : Holding Cost (i*C)
• S : Ordering Cost

Minimizing TC gives us-
• $Q^* = \sqrt{\dfrac{2DS}{H}}$
• $T^* = CD+\sqrt{2DSH}$

## NewsVendor Model

• P (Selling Price) = 40
• w (Wholesale Price) = 30
• S (Salvage Price) = 10
• Cu (Underage Cost) = P - w = 10
• - Cost of stocking one less item
• Co (Overage) = w - S = 20
• - Cost of stocking one more item

Profit $= Cu \times P(D>Q)$ where $P(D>Q)$ is the probability that demand is greater than $Q$.

Go on stocking as log as--
$Cu \times P(D>Q) \geq Co \times P(D \leq Q)$
$Cu \times (1-F(Q)) \geq Co \times F(Q)$
$\boxed{F(Q) \leq \dfrac{Cu}{Cu + Co} = \dfrac{P-w}{P-S}} = 0.33$

$E[demand] = E[sales] + E[lost sales]$
$E[\text{left over stock}] = Q - E[sales]$
> Where Q is the decided quantity to be restocked

$\text{Fill rate} = \dfrac{E[Sales]}{E[Demand]}$

$E[Profit] = Profits - Losses$
$E[Profits]= Cu \times E[Sales] - Co \times E[\text{left over stock}]$

## Multiperiod inventory model

Cases:
• Demand is uncertain
• Demand and lead time both are uncertain

## Scheduling Algorithms

• [ ] FCFS
• [ ] SPT : Shortest Processing Time
• [ ] EDD : Earliest Due Date
• [ ] SWPT : Smallest weighted processing time
• [ ] Critical Ratio Heuristic
• [ ] Hogson's Algorithm

• [ ] M/M/1
• [ ] M/M/S

## References

• Class notes. [Add book references here]