Multi Period Model
A multi-period model is an inventory or supply-planning model that divides the planning horizon into multiple linked time periods. Inventory carryover and material balance constraints connect each period, so ending stock becomes the next period's beginning stock. It optimizes what, how much, and when to order across time while balancing ordering, holding, backlog, transportation, and shortage costs under dynamic demand and variable lead times.
On a manufacturing shop floor, multi-period planning starts with beginning inventory, then adds production receipts and supplier deliveries, subtracts work-order consumption, and calculates ending inventory for each period. This time-phased balance tells planners whether a raw-material lot should be released now or deferred to avoid excess WIP and holding costs, especially when demand is seasonal or production spans multiple shifts. In warehousing, the same structure supports reorder timing, safety-stock targets, and space planning by comparing expected receipts against storage capacity and future withdrawals. The model is typically embedded in ERP/MRP or MILP optimization, coordinating supplier selection, lead times, minimum order quantities, and limited storage across parts and periods. In rolling implementation, it is solved each period, only the first-period action is executed, and the horizon shifts forward as new data arrives.
What is the key state variable in a multi-period inventory model?
Ending inventory in one period becomes beginning inventory in the next period, making inventory the main linking variable across time.
What mathematical form do these models usually take?
They are commonly formulated as LP, MILP, MINLP, or stochastic optimization models, depending on whether demand, lead time, supplier choice, and capacity are deterministic or uncertain.
Why is a multi-period model preferred for manufacturing planning?
Production and procurement decisions have intertemporal effects; multi-period models capture trade-offs across demand fluctuations, lead times, and capacity limits.