Operations and Supply Chain Management The Core

MATERIAL REQUIREMENTS PLANNING chapter 9 283
Economic Order Quantity Run Size for an MRP Schedule
exhibit 9.15
WEEK NET REQUIREMENTS PRODUCTION QUANTITY ENDING INVENTORY HOLDING COST SETUP COST TOTAL COST
1 50 351 301 $15.05 $47.00 $ 62.05
2 60 0 241 12.05 0.00 74.10
3 70 0 171 8.55 0.00 82.65
4 60 0 111 5.55 0.00 88.20
5 95 0 16 0.80 0.00 89.00
6 75 351 292 14.60 47.00 150.60
7 60 0 232 11.60 0.00 162.20
8 55 0 177 8.85 0.00 171.05
Exhibit 9.15 shows the MRP schedule using an EOQ of 351 units. The EOQ lot size
in week 1 is enough to meet requirements for weeks 1 through 5 and a portion of week 6.
Then, in week 6 another EOQ lot is planned to meet the requirements for weeks 6 through 8.
Notice that the EOQ plan leaves some inventory at the end of week 8 to carry forward
into week 9.
Least Total Cost
The least total cost (LTC) method is a dynamic lot-sizing technique that calculates the
order quantity by comparing the carrying cost and the setup (or ordering) costs for various
lot sizes and then selects the lot in which these are most nearly equal.
The top half of Exhibit 9.16 shows the least cost lot size results. The procedure to
compute least total cost lot sizes is to compare order costs and holding costs for various
numbers of weeks. For example, costs are compared for producing in week 1 to cover the
requirements for week 1; producing in week 1 for weeks 1 and 2; producing in week 1 to
cover weeks 1, 2, and 3; and so on. The correct selection is the lot size where the ordering
costs and holding costs are approximately equal. In Exhibit 9.16, the best lot size is 335
because a $38 carrying cost and a $47 ordering cost are closer than $56.75 and $47 ($9
versus $9.75). This lot size covers requirements for weeks 1 through 5. Unlike EOQ, the lot
size covers only whole numbers of periods.
Based on the week 1 decision to place an order to cover five weeks, we are now located
in week 6, and our problem is to determine how many weeks into the future we can provide
for from here. Exhibit 9.16 shows that holding and ordering costs are closest in the quantity
that covers requirements for weeks 6 through 8. Notice that the holding and ordering costs
here are far apart. This is because our example extends only to week 8. If the planning
horizon were longer, the lot size planned for week 6 would likely cover more weeks into
the future beyond week 8. This brings up one of the limitations of both LTC and LUC (discussed
below). Both techniques are influenced by the length of the planning horizon. The
bottom half of Exhibit 9.16 shows the final run size and total cost.
Least Unit Cost
The least unit cost (LUC) method is a dynamic lot-sizing technique that adds the ordering
and inventory carrying cost for each trial lot size and divides by the number of units