Promise Date Policies in Inventory Theory.
NEW YORK UNIV N Y COURANT INST OF MATHEMATICAL SCIENCES
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The notion of a promise date policy is introduced into an n-period inventory model. The considered period consists of the arrival of a replenishment stock, receipt of a deterministic demand, followed by the issuance of promise dates to all new orders and then the shipment of available stock against outstanding orders promised for the given or earlier periods. The demand schedule is associated with an n x n matrix called an urgency structure. An n x n x n real array is called a promise date policy only if stated conditions are satisfied. The set of all such arrays is denoted by the symbol omega. A policy is said to satisfy the FIFO property if promise dates are assigned to orders in the sequence of their receipt. The set of FIFO policies is denoted. The deferred demand schedule determines a quantity called the net stock level at the end of the subject period. The cost of holding stock through the end of the period is determined as well as the total amount of all unshipped orders promised in the given or learlier periods. The shortage cost is found for a fixed replenishment schedule, the total cost is then computed. An optimal promise date policy is one which minimizes this cost over all policies omega. The set of all deferred demand schedules corresponding to all policies omega is denoted. The set of deferred demand schedules corresponding to omega policies is shown to consist of all elements in satisfying an additional condition The search for optimal policies can then be carried out. Author
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