Basic EOQ with stochastic parameters
From Supply Chain Management Encyclopedia
Russian: Экономичный размер заказа при случайном спросе
Notations
- – order quantity;
- – economic order quantity ;
- – number of orders per year;
- , – annual demand;
- – cost of unit of resource;
- – inventory costs per year (%);
- – marginal inventory costs per year;
- – rate of production;
- – demand rate;
- – lead-time;
- – inventory;
- – standard deviation of demand;
- – delivery time;
- – standard deviation;
- – deficit risk;
- – service level;
- – reorder point;
- – safety stock;
- – surplus costs;
- – shortage costs;
- – profit.
Economic order quantity: .
Standard normal distribution:
,
where - deviation from mean; s – standard deviation, x – demand, – average demand.
safety stock: ;
reorder point: ;
standard deviation during delivery time:
– with constant leadtime L.
or – when varies with mean L and standard deviation sl;
the number of un satisfied customers:
or ;
order quantity:
;
risk:
.
optimal order quantity in one-period model [1]:
,
where .
References
- ↑ Методы оптимизации управления и принятия решений: примеры, задачи, кейсы: учебное пособие. -- М.: Дело, 2007.