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Rolling planning horizons: Error bounds for the dynamic lot size model. (English) Zbl 0631.90018

The authors consider an inventory situation where demand occurs and ordering is done periodically, with both demand and the cost of ordering open to change from period to period, and where at any stage these are only known for the next t periods. The goal is to minimize (present) costs over the next t periods.
The problem studied is: suppose demand and ordering costs are only known for the next T periods, \(T<t\); what is the cost for acting as if the planning horizon is T, not t? A bound on the value of perfect information for periods greater than T, \(E_ k(T)\) is defined (the significance of k is too involved to describe here) and an algorithm to calculate \(E_ k(T)\), with running time \(0(T^ 2)\), is given, computer simulation results are presented which show that in many cases the value of T needed to make \(E_ k(T)=0\), c.e., information about time periods greater than T is valueless, can be much greater than the value of T which will make \(E_ k(T)\) small.
The inventory situation studied is one where holding costs are linear, ordering costs are linear plus a set-up cost, and where no backlogging is allowed. A companion article concerning the case where backlogging is allowed is promised for the future.
Reviewer: E.Boylan

MSC:

90B05 Inventory, storage, reservoirs
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