Article Preview
TopIntroduction
The problem studied is a 
type of inventory control system (Hadley & Whitin, 1963) for a single item, which is subject to sporadic demand that is also highly variable in size. Item replenishment occurs after a fixed period of time 
(lead time) and there is a fixed ordering (or setup) cost 
plus a unit cost
. Units carried in excess of demand incur a holding cost of 
per unit and demand not satisfied is backordered and incurs a penalty cost of 
per unit. The objective function is to minimize the expected value of the sum of carrying, backordering and ordering costs. Although most problems of this nature can be solved optimally, when mean demand and its frequency of occurrence are small and backordering costs are high, it takes a very long time (days) to find the optimal solution, indicating that we still need heuristics. The goals of this research - none of which have been addressed before - are as follows:
- 1.
Using the expected total cost as the criterion, compare the performance of two popular heuristic lot sizing rules (Wagner, 1975) with the corresponding optimal solutions.
- 2.
Perform sensitivity analysis on ordering costs, carrying costs, and the symmetry of the distribution of demand. Show how each affects the performance of the heuristics.
- 3.
Use as much actual data as possible.
For the problem discussed, when the ordering decisions are restricted to demand occurrences, a policy of type 
will minimize the undiscounted expected cost over an infinite horizon (Beckmann, 1961; Vienott & Wagner, 1965; Iglehart, 1963; Archibald & Silver, 1978; Ehrhard, 1979). Accordingly, when inventory on hand plus on order minus backorders, 
is less than or equal to
, a replenishment order of size 
is placed (Silver & Peterson, 1985).
In studies dealing with the spare parts inventory control problem, various assumptions have been made with respect to demand. However, the most commonly used were the Poisson distribution (Schultz, 1987; Gelders & Van Looy, 1978; Hadley & Whitin, 1963) and the normal distribution (Croston, 1972; Bartakke, 1981; Porteus, 1985; Vereecke & Verstraeten, 1994; Sani & Kingsman, 1997).
A few (Dunsmuir & Snyder, 1989; Segerstedt, 1994; Yeh, 1997) have used the gamma distribution, for demand size and occurrence, after observing that most spare parts inventories typically possess positively skewed frequency profiles with a large spike at zero.