PRODUCTION/OPERATIONS MANAGEMENT

Michael J. Showalter, Feature Editor, Florida State University

IN SEARCH OF THE CORRECT--AND TEACHABLE--MRP TABLEAU

by Warren W. Fisher Stephen F. Austin State University

A few days ago, I was visited by a representative from the publisher of the textbook that I use in my introductory POM course. He asked me how I liked the book, which is one of the more widely adopted ones on the market, and I said that it was fine except for using an incorrect procedure to calculate MRP tableaus. The conversation reminded me of something that I noticed when I was reviewing POM books to make the choice for my course: most of the popular books contain MRP calculations that are either incorrect, incomplete, or both!

Now I don't claim to be an expert on MRP, but I have taught it in the classroom for over twelve years at four different universities (mostly as a required core class for BBA majors), and that experience has given me a pretty good idea of what you can and can't get students to understand. It's hard enough even under ideal circumstances to get the typical student in this type of class to grasp MRP, but put an illogical tableau on the board and you will lose everyone. Worse, if you somehow manage to get one of the improper procedures to sink in, the student(s) will leave college ``knowing'' the wrong approach.

This paper is an effort to clear the air about the MRP tableau. It illustrates several different ways of approaching the tableau, including those that do and do not make sense. I hope that the paper will be read by authors and prospective authors of POM textbooks, and that the result will be an overall improvement in the quality of instruction in POM classes.

The "Right" Way

Most of us would recognize the American Production and Inventory Control Society (APICS) as the definitive authority on modern practice with respect to POM. APICS publishes study guides on MRP (e.g., [1]), among other subjects, and it seems safe to assume that those guides accurately represent current practice.

The following definitions are given in [1] and are generally used in the same manner in all textbooks: gross requirements are expected needs, scheduled receipts are future receipts expected from orders that have already been placed, net requirements are gross requirements that cannot be satisfied from inventory or scheduled receipts, planned order receipts are future receipts expected from orders that have not yet been placed, and planned order releases are orders that should be placed in order to obtain the planned order receipts. The rub comes with ``on hand,'' which can be interpreted in several different ways. It can, for example, be on hand as of the period end, but period beginning can also be used if done correctly. Several other variations are possible and are described below.

The tableau labeled Format 1 (with the rows sometimes rearranged) is the most common format used in a recent APICS study guide [1, pp. 3-7 and elsewhere]. Please note that I have changed the numbers to make a more concise example. It uses on hand as of period end, which is calculated as on hand from the previous period plus scheduled (but not planned) receipts and minus gross requirements. One advantage of this format is that the entire on hand row can be calculated without respect to the lot sizing rule in effect. A second pass is then made to determine net requirements, planned order receipts, and planned order releases in the usual manner. A disadvantage of this approach is that the negative on hand balances are not actually expected to occur! In reality, the planned receipts will (hopefully) arrive when indicated and will prevent backorders from occurring. Further, it is difficult to tell whether net requirements are correct, since (except for the first one in a given tableau) they are not equal in magnitude to the negative on hand quantities.

Format 2 is similar to Format 1 and comes from the same reference [1, pp. 3-5]. In it, the on hand quantities include planned receipts and are calculated in a single pass in this manner: first, one calculates on hand for a given period in the same manner as in Format 1. If the result is zero or greater, you go on to the next period. If the result is negative, you post a planned receipt (and release), then adjust the on hand quantity to reflect the receipt. This allows the entire tableau to be completed in a single pass and is very straightforward in the case of lot-for-lot and fixed quantity ordering, but it gets a little messy otherwise. Format 2a illustrates the effective computations in Format 2 by lining out the negative numbers. Note especially that the net requirements are easy to verify, since they are the absolute value of the (lined-out) negative on-hand balances. Although quite easy to understand, Format 2a is very hard to find in print (maybe the strike-outs are too hard to typeset).

Although not illustrated in [1], Format 2b is a straight-forward way to present the same information as Format 2 using beginning on hand inventory (which eliminates the need for on hand now). Like Format 1, however, there is no longer a close correspondence between on hand and net requirements.

Current Textbook Formats

In a rather unscientific approach at determining the state of the current textbook art, I grabbed the most recent review copies of nine major POM textbooks from my shelves. By ``major,'' I mean big (mostly 800+ pages), shiny books by well-known authors, most of which are in the second or subsequent edition. One was a 1991 edition, two were 1992, and the rest were 1993 or 1994. I checked several of the books' earlier editions and found the procedures there essentially identical to the current versions, so the procedures described herein do not appear to be evolving. Though certainly not 100% of the market, I feel confident that the sample is representative, especially since it contains the flagship offering from each of several of the largest publishing companies. Since my objective is to clear the air rather than to point fingers, I will refer to the nine texts only as A, B, ... , I. Further, none of the following examples actually appear in any of the books. Instead, I have applied the procedures illustrated in each text to the data from Format 1 (or as close to that as the respective format will allow).

First the good news: several of the textbooks do indeed use one of the APICS formats or something quite similar. Text A uses a procedure identical to Format 1 except that Text A leaves out the planned order receipts row. Text B is identical to Format 2, while Text C also matches Format 2 except for leaving out the net requirements row. Unfortunately, Text C suffers from the additional problem that there are no simple examples, i.e., without safety stock and with lot-for-lot ordering.

With Text D, we begin to see more serious problems. It uses Format 3, which has no column for beginning on hand even though there obviously is some. (Note that I have adjusted the data from the previous formats in order to make the tableau as similar to the others as possible.) Worse, the computations match Format 2b, but the tableau fails to strike out and change the on hand balance. That is, for example, period 3's on hand is left negative, but it is treated as if it were zero for purposes of calculating period 4! Among the most annoying texts are several that attempt to use beginning rather than ending inventory on hand. Unfortunately, all of these have problems in addition to the inherent complexity of this approach as noted above. Text E, for example, uses Format 4, which has on hand now removed in favor of using beginning inventory. (I have added the on hand now quantity from the previous formats to the first period's scheduled receipts in order to make the tableau as similar to the others as possible.) Note that on hand for periods two through four correctly match the (ending) on hand for periods one through three in Format 2. However, Text E makes the assumption that scheduled receipts are added to beginning on hand in the period in which they arrive! I'd like to know how that can happen in real life! Texts F and G are similar to E but add extra confusion by including a column for on hand now, which of course would always have to match period one's beginning on hand. But waitþText G puts a final nail in the coffin of understandability by using Format 2 (with ending on hand) throughout its section on lot sizing in the same chapter!

Text H uses Format 5, in which both on hand now and scheduled receipts have been removed. Further, none of its examples have a non-zero on hand balance, so it evades the issue of whether to use beginning or ending inventory. At least there is merit in simplicity . . . .

The final book, Text I, puts the rest to shame in its ability to confuse the student. Like Texts F and G, it has both the assumption of beginning on hand and the use of on hand now, but it excludes the scheduled receipts row. Blank cells, however, are used in some places to represent zeros and in others to represent ``the same as the nearest non-zero cells to the left and right.'' Last but not least, it leaves the rightmost gross requirement in most tableaus hanging, i.e., the computations are incomplete for the last period.

I did not set out to review POM software for this project, but most of what I can recall uses one of the formats described above. One exception is illustrated in Format 7, which leaves off both net requirements and planned order receipts. However, it adds a row labeled þlot-for-lot,þ which contains what planned order releases would be if lot-for-lot ordering were done. This is of great usefulness if one is calculating lot sizes by part-period or one of the other methods that requires looking across several periods. In fact, most of the texts that discuss lot sizing do so with a partial tableau that contains information equivalent to the lot-for-lot row in Format 7.

Recommendations

I personally find Format 2a the easiest to explain as a beginning lesson on the MRP tableau. If the more complex lot sizing rules are to be taught, Format 1 or 7 or some variation thereof would probably work best, since it becomes necessary to have something equivalent to the ``lot-for-lot'' row in Format 7. Format 8 is an alternate implementation of the Format 2a calculations and illustrates one way to create an MRP tableau in a spreadsheet without generating a circular reference, at least in the cases of fixed order quantity and lot-for-lot ordering. In it, ``unadjusted'' on hand for a given period is first calculated as the previous period's ``adjusted'' on hand plus scheduled receipts and minus gross requirements. Next, net requirements are generated if the unadjusted on hand is negative, and the lot sizing rule is applied to generate planned order releases and receipts. Finally, the ``adjusted'' on hand is calculated as the unadjusted quantity plus any planned order receipts.

Lastly, I would recommend that all POM textbook authors and faculty teaching POM include rows for on hand now and scheduled receipts. It is conceivable that a factory could run MRP without safety stock and complex lot sizing rules, but no real system can exist without on hand and on order quantities.

Reference

[1] American Production and Inventory Control Society, Inc., , APICS, Falls Church, VA, 1985.

WARREN W. FISHER is an Associate Professor and Chairman of the Management and Marketing Department at Stephen F. Austin State University. Besides teaching production/operations management, he conducts research on related topics, including mathematical modeling, computer simulation, maintenance systems, and microcomputer applications. He received his Ph.D. in operations and logistics management from the University of Texas at Austin. Dr. Fisher is a member of the Society for Computer Simulation, The Institute of Management Sciences, Decision Sciences Institute, Operations Research Society of America, Production and Operations Management Society, and The Honor Society of Phi Kappa Phi.