Inventory Problem

• A decision theoretic problem about stocking a particular product.
• The decision maker observes the level of stock available (and possibly the stock that is already on order) and decides whether to order more.
• The level of stock is the inventory.
• Inventory problem is about when and how much to order.
• Typically, the inventory problem is a tradeoff between the carrying (or holding) cost and the ordering cost.

Deterministic Inventory Models

• Inventory control deals with ordering and stocking policies for items used in manufacture of industrial products.
• In every manufacturing environment about 80% of the items are bought from outside and the rest is manufactured and assembled into the final product.
• The annual demand and various costs in a deterministic multi-period inventory model is known with certainty.
• The important decision in inventory problems is ‘How much to order?’
• The quantity is denoted by Q.
• Items bought from vendors have the following costs associated with the purchase:

  • Cost of the product (C) This is represented as C Rs/unit. Since the annual demand for the item is known and has to be met, this cost does not play a part in determining the order quantity. The only effect of the unit price C in the order quantity is when there is a discount by which the unit price reduces by a known fraction.

  • Ordering cost per order ($C_o$)

    This is represented as Rs/order. The essential costs that contribute to this cost component are: Cost of people, stationery, communication and follow-up, transportation, inspection and counting, rework and

  • Carrying cost for holding the items ($C_c$)

    This is represented as Rs/unit/year. The costs that contribute to carrying the items are: Cost of capital, people, space, power and utility, special facilities (e.g. air conditioners, chillers, etc.), pilferage, obsolescence Sometimes when the cost of capital dominates the rest of the costs, carrying cost is expressed as $C_c = iC$ , where C is the unit price in Rs and i, the interest rate (cost of capital) in %/year.

  • Shortage cost (backorder costs) ($C_s$)

    This is represented as Rs/unit/year. Here we mean backordering indicating that any unfulfilled demand is met subsequently.

    The necessary costs that contribute to shortage cost are:

    • Loss of customer goodwill
    • Cost of losing a customer
    • Loss of profit associated with not delivering the product.

    The components of the shortage cost are not easy to measure. Usually shortage cost is given a large value to minimize the occurrence of shortage in planning stage of the inventory.

Economic Order Quantity (EOQ) model

Assumption:

Lead Time = 0

Parameters:

Annual Demand = D/year

Order Cost = $C_o$