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Multi-Period Inventory Management

Problem: Managing inventory across multiple periods to minimise holding costs while maintaining sufficient stock.

What if your product is made from materials that are in limited supply and require special or expensive storage facilities? In such a situation, you have to keep purchasing and inventory costs down, but still keep enough stock to meet demand. If you use perishable resources or materials subject to supply limitations, you may encounter problems like this one.

Your production demands vary over thirteen time periods. Raw materials, available at varying costs from three different suppliers, must occasionally be held in sufficient quantity from time period to time period to meet production needs. A holding cost associated with inventory held over further complicates the picture. How can you determine how much inventory to hold and which supplier to use while minimising Total Cost and meeting your customers' demand for the product?

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You know the unit demand for each of the thirteen time periods. For instance, the demand for time period 1 must be met by using some combination of sources 1, 2, and 3. The ending inventory is equal to starting inventory plus the sum of amounts purchased from each source less the unit demand.

You must not only satisfy the demand for each period, but also minimise the amount of inventory held over. Obviously, it's in your interest to purchase as much as possible from your least expensive source, source 1. However, demand in some periods exceeds source 1's capacity.

The objective in the Inventory model is to minimise the total cost and determine how much material to buy from each source in each time period to meet customer demand at lowest purchase and holding cost.

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