Operations Management 2


Inventory Management

$$TC = CD + QH/2 + (D/Q) \times S$$

Minimizing TC gives us-

NewsVendor Model

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

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

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

Multiperiod inventory model


Scheduling Algorithms

Queueing Theory [WIP]