Dynamic Lot Sizing The dynamic lot-size model in inventory theory, is a generalisation of the Economic Order Quantity (EOQ) model that takes into account that demand for a product varies over time.

Dynamic lot sizing sometimes refers to as Time-Varying Demand as well. In contrast to EOQ model where demand is constant, in the time-varying deterministic demand model, demands of various periods are unlike. The variations depend on different reasons. For example, production on a contract, which requires that certain quantities are delivered on specified dates. Note that we are still considering deterministic demand, i.e., all variations are known in advance. In the basic models, lead-time is disregarded. When dealing with lot sizing for time-varying demand, it is generally assumed that there are a finite number of discrete time steps, or periods. A period may be, for example, a day or a week. We know the demand in each period, and for simplicity, it is assumed that the period demand takes place at the beginning of the period. There is no initial stock. When delivering a batch, the whole batch is delivered at the same time. The holding cost and the ordering cost are constant over time. No backorders are allowed. We shall use the following notation:

Var Definition = number of periods, = demand in period i, = 1, 2, ..., , = ordering cost, = holding cost per unit and time unit.

Problem

Costco has received the following demands for a product this year:

Month 1 2 3 4 5 6 7 8 9 10 11 12

Demand 300 700 800 900 3300 200 600 900 200 300 1000 800

Suppose ordering cost (OC) is $504 and holding cost (HC) of one unit of product in a year is $3.

There is no shortage cost. Backordering is not allowed in this model.

To achieve the minimum total cost (ordering cost + holding cost), how many times the company should place orders in a year? In each order, how many products should be ordered? What is the total cost in a year?

Q1 (2 marks) Given that the total demand of the whole year is 10,000 products, suppose the company is going to use the EOQ model for the accumulated demand of one year (10,000). In other words, ignore the monthly demand.

Compute: Optimal order quantity (Q*) Total cost Frequency of orders Time between orders