The model is developed under the following assumptions:
1. Demand is deterministic at a constant rate and known.
2. Shortages are allowed and fully backlogged.
3. Lead time is constant.
4. Planning horizon is infinite.
5. Replenishment rate is infinite.
3. Mathematical formulation
In this section, some inventory models are developed for each possible case. Our purpose is to minimize the total cost
function. The total variable cost per cycle C(t1, T) can be expressed as