Page 172 - Orlicky's Material Requirements Planning

CHAPTER 8 Lot Sizing 151

Least Total Cost (LTC)

The LTC technique is based on the rationale that the sum of setup and inventory carry-
ing costs (total cost) for all lots within the planning horizon will be minimized if these
costs are as nearly equal as possible, the same as under the classic EOQ approach. The
LTC technique attempts to reach this objective by ordering in quantities at which the
setup cost per unit and the carrying cost per unit are most nearly equal. A second look at
Figure 8-6 will show that the LUC technique chose a quantity at which setup cost per unit
($2.22) significantly exceeded carrying cost per unit (22 cents).
Because it seeks the equality of these costs, the LTC technique is able to avoid the
relatively laborious computation procedure of the LUC approach and can proceed
toward its goal in a more direct fashion. The vehicle for this is computation of the so-
called economic part-period (EPP). The part-period measure is analogous to a man-year
or a passenger-mile. It is one unit of the item carried in inventory for one period. The
part-period is a convenient expression of inventory carrying cost for purposes of com-
parison and tradeoff; that is, it can be said that to carry a quantity of an item in invento-
ry for a certain period of time will “cost” times the number of part-periods. The EPP is
defined as that quantity of the inventory item which, if carried in inventory for one peri-
od, would result in a carrying cost equal to the cost of setup. It is computed simply by
dividing the inventory carrying charge per unit per period IpC into setup cost S. In our
example, this is EPP S/IpC 100/0.02 50 100.
The LTC technique selects the order quantity at which the part-period cost most
nearly equals the EPP. An example of LTC computation appears in Figure 8-8. The quan-
tity chosen for the first lot would be 85 because the 130 part-periods that it would cost
most nearly approximate the EPP of 100. This order would cover requirements of periods
1 through 5, and the second order of 65 would cover requirements of periods 6 through
9. This is shown in Figure 8-9.
The LTC approach to lot sizing generally is favored over the LUC approach, but the
arguments its advocates put forward, as well as results of limited simulations, are not
entirely convincing. The LTC logic has a flaw of its own in the premise that “the least total

FIGURE 8-8
Carried in
Net inventory Prospective Part-periods
Computation of Period Requirements (periods) lot size (cumulative)
least total cost.
1 35 0 35 0
2 10 1 45 10
3 0 2
4 40 3 85 130

FIGURE 8-9
Period 1 2 3 4 5 6 7 8 9 Total
Least total cost.
New Requirements 35 10 40 20 5 10 30 150
Planned-Order Coverage 85 65 150