On the Effectiveness of Zero-Inventory-Ordering Policies for the Economic Lot-Sizing Model with a Class of Piecewise Linear Cost Structures

Lap Mui Ann Chan (), Ana Muriel (), Zuo-Jun Shen () and David Simchi-Levi ()
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Lap Mui Ann Chan: School of Management, University of Toronto, Toronto, Ontario, Canada M5S 3E6
Ana Muriel: Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, Massachusetts 01106
Zuo-Jun Shen: Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611
David Simchi-Levi: The Engineering Systems Division and the Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142

Operations Research, 2002, vol. 50, issue 6, 1058-1067

Abstract: We consider an economic lot-sizing problem with a special class of piecewise linear ordering costs, which we refer to as the class of modified all-unit discount cost functions. Such an ordering cost function represents transportation costs charged by many less-than truckload carriers. We show that even special cases of the lot-sizing problem are NP-hard and therefore analyze the effectiveness of easily implementable policies. In particular, we demonstrate that there exists a zero-inventory-ordering(ZIO) policy, i.e., a policy in which an order is placed only when the inventory level drops to zero, whose total inventory and ordering cost is no more than 4/3 times the optimal cost. Furthermore, if the ordering cost function does not vary over time, then the cost of the best ZIO policy is no more than 5.6/4.6 times the optimal cost. These results hold for any transportation and holding cost functions that satisfy the following properties: (i) they are non decreasing functions, and (ii) the associated cost per unit is non increasing. Finally, we report on a numerical study that shows the effectiveness of ZIO policies on a set of test problems.

Keywords: Analysis of algorithms--computational complexity; economic lot-sizing problem; Inventory/production--approximations for economic lot-sizing problem; Transportation--less than truckload cost (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (29)

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