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A telecommunication company (CALLME TEL Co., Ltd) receives and processes customers’ orders.

Orange Co., Ltd is an important customer, who mostly places orders every 2 months. Medium quantity of successful order in the “shall-placing-order-month” total is 500 units. (occasionally it also places small number of orders every month)

(the Orders came in different days in the “shall-placing-order-month”, for various phone models of different quantities. The total successful quantity of all models sums to about 500 units in the month)

Because of different reasons (delivery, stock, pricing, etc.), the order success rate remains on 30%.

From an order received from Orange, to the order is confirmed as successful, it takes 5 to 60 days (depends on processing time of individual orders).

As the customer Orange may place orders to CALLME’s competitors too. CALLME’s manager wants to detect if the orders came from Orange is declining early.

CALLME’s manager thinks, CALLME shall maintain a safe order level from Orange (orders being progressed).

How to calculate the safe order level? (any other information required for the calculation)

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    $\begingroup$ Would you please, give a simple example of what you are looking for? $\endgroup$
    – A.Omidi
    Commented Feb 26, 2023 at 9:07
  • $\begingroup$ @ A.Omidi, thank you for the kind comment. Above is a real case I have in my work - the company wants to know what's the quantity of order in hand, to get to know the customer is taking our company as the main supplier (i.e. if the quantity of orders in our hand drops to certain level, it may indicate the customer is shifting the purchase to other supplier(s). Sutanu's reply below is inspiring. I just need more time to understand it before next follow-up. $\endgroup$
    – Mark K
    Commented Feb 27, 2023 at 1:30

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It's part of inventory control, subject of research & practice within large supply chain domain. Though in grad school, inventory management is a topic as part of operations research. Inventory management is therefore an intersection between optimization, statistics (probability distribution of orders and lead time), processes (fulfillment) and maybe Machine learning (to predict seasonal/cyclical likelihood of incoming orders).
Though literature on this subject is vast and easily available (just google inventory+safety stock+service level) for dive-down, I usually find links that aggregate content and present as quick guide quite useful like this. While scenarios will impact calculation but generally what you are asking can be interpreted in a similar way to safety stock metric used in inventory management. General formulation is
Safety stock =$z\sqrt{L_{\mu}^2D_{\sigma}^2+ L_{\sigma}^2D_{\mu}^2 }$
where $z$ is z-score for service level (your case is 70%) and L is lead time, D is demand indexed by $\mu$: average lead time/average demand and $\sigma^2 $ is their corresponding variance.

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