INTERFACES Copyright © 1979, The Institute of Management SciencesVol. 9, No. 2, Pt. 1, February 1979 OO92-21O2/79/O9O2/OOOl$O1.25

USING MRP AND EOQ/SAFETYSTOCK FOR RAW MATERIALS INVENTORY CONTROL:

DISCUSSION AND CASE STUDY

Matthew J. LiberatoreIndustrial Chemicals Group

FMC CorporationChemical Research and Development Center

Box 8Princeton, New Jersey 08540

ABSTRACT. The MRP and EOQ safety stock model approaches are re-viewed relative to raw materials inventory control. Useful methods for develop-ing order quantities, lead time demand distributions, and other parameters arepresented. Ways to use and combine these approaches are considered. Inconclusion, a case study in chemical process operation is presented.

Introduction

With the advent of the Material Requirements Planning (MRP) revolution, it hasbecome necessary to develop criteria for selecting and changing available techniques forraw materials inventory control. The purpose of this paper is to explore the utility of thetwo principal techniques, MRP and Economic Order Quantity/Safety Stock (EOQ/SS).A chemical process operation case study is used, as the MRP approach for fabricationindustries has been discussed elsewhere [3].

EOQ/SS

EOQ/SS is particularly applicable if the product utilizing the raw materials has asimple process structure and is produced continuously over time at a fairly uniform rate.A simple example is a chemical process which requires only a few major ingredients (interms of usage levels) to yield a finished product. Ideally, the economic running sizes arewell known, and the budgeted production rate is relatively constant over long timeperiods, although process downtime does occur. The case for EOQ/SS is enhanced if theprocess machinery is used to make only a few different products, limiting scheduling andtime-phasing complications. In such situations there are two decisions which must bemade: the order size and the policy to protect against lead time and usage fluctuations.

Shipment size

Many materials are often ordered in bulk only once a year or once a quarter. Thefixed cost used in EOQ calculations should then represent the cost of processing a re/ea.$efor a truck or rail car. Normally, $ 10-20 per release is appropriate. The order quantityresulting from the direct application of the EOQ formula often must be adjusted to fullcarloads or truckloads. This is especially true for bulk commodity chemicals which havelow value per pound and relatively high freight cost per pound. The general problem can

INVENTORY/PRODUCTION — APPLICATIONS; INDUSTRIES — CHEMICAL

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be handled by comparing the sum of annual ordering, holding, and freight costs at thetraditional EOQ and the freight break-even points and for multiple car/truck loads (ifapplicable).

Safety stockUsage. Changing usage pattems in a generally stable continuous process operation

can result for several reasons: (1) changing process efficiencies, (2) adjusting theproduction rate in response to changing market conditions, and (3) process down time.This demand variation can be captured in several ways. For instance, daily productionsheets can yield an historical raw material usage distribution by utilizing the processcoefficients. Use this approach if it is reasonable to assume that materials requirementswill fiuctuate in a similar fashion during the upcoming quarter.

Alternatively, analyze forecasted/budgeted materials usage over the next quarterand determine the implied daily usage rates. If the variation in these is small, use theaverage or maximum as a point estimate of daily usage. This approach is preferable if theusage rates are known to be fairly stable because there is (say) a limited range ofeconomic production rates.

Lead time. Lead time equals the order processing delays for both the supplier andreceiver plus the transit time. Order processing time may consist of: (1) notification timefor release of cars or trucks, (2) time before material can be produced, and (3) paperworkdelay. The time for (1) and (3) can usually be reduced to a point estimate, while point (2)is normally a range. Thirty recent observations are adequate to develop a transit timeprobability plot.

We wish to indicate (somewhat parenthetically) that lead time performance evalua-tions are useful in other contexts. For instance, they can enable purchasing agents toquantify the level of service provided by the vendors. If multiple suppliers are utilized,this information can be a significant input into contract negotiations over price andpercentage allotment.

The lead time demand distribution (LTDD). Knowing both the raw materialsdemand and lead time probability distributions, we can perform a Monte Carlo simula-tion to obtain the LTDD. A simple APL program can be written to perform the simulationusing the discrete probability frequency distributions. (A sample program and terminalsession will be sent to the reader upon request.)

If we use a point estimate of demand, we need only multiply each term in the leadtime probability distribution by the constant demand to get the LTDD. If lead time isconstant (say N days) and demand can be fitted by normal distribution, the LTDD isnormal with mean equal to A' times the mean demand and variance equal to A? times thedemand variance.

Chance of stock-out. Typically this is set at a very low level since the consequenceof a stock-out is usually the shutdown of a production process. The cost and availabilityof emergency ordering (e.g., less than truckload shipments and air freight), as well as thecost of shutting down the production line, must be compared to the cost of holdingadditional inventory in setting the protection level.

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iUIRP

MRP is particularly applicable for complex process structures where raw materialdemands are large, nonuniform, and dependent on scheduled product completion dates.A simple example is a made-to-order chemical economically produced in a sequence ofwell-defined batch sizes, each of which utilizes many raw materials. To facilitate ourdiscussion of the applicability of MRP, we need to define the basic steps of thisapproach. More detail can be found in [3].

The iUIRP approach

The nucleus of the MRP modeling structure is the translation of scheduled productcompletion dates into amount and timing of gross materials requirements by "explod-ing" the various subprocesses. It is easiest to proceed from the top to bottom of theprocess structure. The steps are:

(1) Determine gross requirements over the planning horizon.(a) Develop a standard conversion table yielding number of input units per

output for each process.(b) At each level determine the number and type of input units required for the

next higher level and the process time between levels.(c) Once we have climbed down the "process tree" the amount and desired

receipt date for each raw material are known.(2) Determine net requirements over time by incorporating materials on hand and

scheduled for delivery.(3) Determine raw material lead times as previously discussed. In general, the

maximum reasonable lead time should be used if there are significant fluctuations.(4) Group requirements into orders. There are two basic approaches.

(a) Ad hoc — usually several options are presented in canned MRP packages.For example, order one carload at a time, combine every three periods'demands into an order, and so forth.

(b) Analytical — strangely enough, this option is usually not provided instandard MRP routines. If the fixed order processing costs are significant,utilize a dynamic lot-size algorithm such as the Wagner-Whitin model [4]or one of its variations (e.g., see Blackburn and Kunreuther [1] orLiberatore [2]) to determine the size and timing of orders. Adjust to fullcarloads as necessary.

Some problems in applying iVIRP to process industries

(1) Standard conversion factors for each chemical process must be utilized toaccomplish the "materials explosion." However, the actual proportion may vary withthe quality of the materials and other factors. In addition, there may be quality differ-ences required by certain customers and these may not be achieved during every run.This may require many more process structures to be defined, implying data storage andcomputational difficulties.

(2) A key assumption of MRP is that the production schedules (over the planninghorizon) are known with certainty. Clearly, outages and inventory buildups can resultfrom schedule changes. These effects can be minimized by maintaining some safety

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stock during the production cycle and in finished goods. Research in this area is just nowgetting underway (e.g., see Whybark and Williams [5]).

(3) A more fundamental problem arises in the modeling of the chemical processitself. For example, many chemical processes have by-products which have economicvalue or are recycled into the main process. This complicates the determination of bothinput/output coefficients and the value per unit output, and produces process treestructures whose stages are interdependent.

(4) MRP cannot always safely ignore machine assignment and capacity utilizationissues. For example, if there is peaking of orders it is necessary to adjust the schedule tosmooth production and take advantage of the economics of longer run lengths and largerbatch sizes.

(5) If production due dates are based on uncertain sales forecasts and process leadtimes are long, the MRP approach may lock the process into a schedule which allowslittle flexibility to adjust to a changing order pattern.

One conclusion is that the subset of chemical processes amenable to the MRPapproach needs further definition along the lines suggested above. Another is that weshould strive for a hybrid system of production planning which captures the benefits oftime phasing while minimizing the impact of uncertainty in the planning horizon.

Applying a hybrid approach: a case study in chemicai processingConsider the following case study which resulted from my inventory control audit

of RVIC's Industrial Chemical Group plants. It centers on the Modesto plant whichproduces barium and strontium chemicals. The processes of interest combine eitherbarite ore or celestite with coke and some other materials to produce barium or strontiumcarbonate, respectively. Both of these products are produced on the same equipment.However, production planning and inventory control procedures are difficult to imple-ment because the markets fiuctuate considerably and the cost of a production changeoveris significant.

An examination of the usage rates for materials used in the carbonate productionprocesses indicates that classical "ABC analysis" is again applicable; about 80% of thetotal dollar value of raw materials purchases is provided by about 20% of the rawmaterials. Since the raw materials otherthan coke, barite, and celestite materials are usedcontinuously, ordered infrequently, and tie up a negligible amount of working capital,there is no need to incorporate them into a detailed analysis.

Upon investigation it is found that both processes use coke at nearly the same rateand are normally run at 95% capacity. However, usages do fluctuate somewhat overshort periods for reasons similar to those presented in the EOQ/SS section. For thesereasons, we employed the EOQ/SS approach for coke and based the usage factor on themaximum of the two budgeted rates. The lead time pattern has substantial variationwhich led to the setting of the safety stock and the reorder point. In our discussions withplant personnel we emphasized the need for regular review of both the demand and leadtime parameters.

This simple procedure had a major impact because of another facet of the problemwhich we now briefly describe. In-plant storage space for coke was restricted, necessitat-ing the usage of incoming rail cars as inventory storage bins. Although this practice was

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convenient and avoided a substantial capital outlay, the associated demurrage costs weresubstantial. Thus the principal impact of our inventory control efforts for coke wasreduction of its monthly demurrage bill by about 40%.

On the other hand, a time phased approach was used for barite and celestite becauseof the discontinuity of their respective runs. Past history demonstrates that although thedaily usage of these ores is fairly uniform during their respective runs, the length of theirproduction runs are subject to marketing pressures, as previously suggested. It is thennecessary to build some safety stock into the general MRP framework. Discussions withthe materials manager led us to postulate that a week's worth of material was necessaryfor each process as safety stock.

It should be noted that the time phasing of orders was complicated by severalexternal factors. For instance, celestite is not produced domestically and our sole NorthAmerican supplier faces several critical problems associated with rail car procurementand the stability of his labor force. These factors explain the large fiuctuations in thehistorical lead time pattems that were observed. At the request of plant manufacturingpersonnel, an "ideal ordering schedule" was prepared under the following set ofassumptions:

(1) shipment of one rail car per day continuously over specified time periods;(2) a safety stock of seven days raw materials usage was to be held at the plant;(3) time phasing based on maximum historical lead time and recent input/ouput

factors.The theoretical expected inventory levels resulting from this policy are related to

those depicted in the solid curve in Figure 1.

FIGURE 1. Sample expected inventory position for celestite

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However, subsequent discussions with the purchasing agent and the plant manufac-turing manager indicated that assumption (1) was not totally acceptable because thepresent purchase supply contract required ordering of carloads in approximately equalmonthly quantities regardless of our production schedule. This led to subsequent negoti-ation with the supplier and his eventual acceptance of a shipping policy which placesmonthly minimums and maximums on the number of rail cars available for shipment.

The final theoretical expected inventory levels are related to those given in thedashed curve of Figure 1. It is interesting to note that additional expected inventoryreductions were gained because the maximum number of monthly carload shipments wasgreater than our previous assumption of one shipment per day. This schedule as adjustedduring 1977 provided a working capital reduction of $36,000, or about 12% over 1976inventory levels. The true savings from the control system were actually larger, sincesubstantially more strontium carbonate production occurred in 1977 than in 1976, andthese and other deviations from schedule necessitated an increase in safety stock.

ConclusionThe selection of raw materials inventory management techniques is as much an art

as it is a science. It is often necessary to consider many seemingly external factors toarrive at an acceptable solution. The EOQ/SS and MRP approaches have spheres ofapplicability as previously discussed. In moderately complex systems a hybrid approachis often ample. Care should be taken in large MRP implementations not to "over model"the potential process structures and to allow for the impact of uncertainty. It is especiallyifnportant in the application of across-the-board systems (whether EOQ/SS or MRP) tobe aware of special cases as illustrated in the previous section. There is no substitute foran in-depth understanding of the "whole problem" for key manufacturing processes.

REFERENCES[ 1] Blackburn, Joseph D. and Kunreuther, Howard, "Planning Horizons for the Dynamic Lot Size Model

with Backlogging," Management Science, Vol. 21, No. 3 (November 1974), pp. 251—255.[2] Liberatore, Matthew J., " A Stochastic Lead Time Inventory Model," unpublished doctoral dissertation,

University of Pennsylvania, Philadelphia, Pa., 1976.[3] Orlicky, Joseph, Materials Requirements Planning. New York: McGraw Hill, 1975.[4] Wagner, Harvey M. and Whitin, T. M., "Dynamic Version of the Economic Lot Size Model,"

Management Science, Vol. 5, No. 1 (October 1958), pp. 89—96.[5] Whybark, D. Clay and Williams, J. Gregg, "Material Requirements Planning under Uncertainty,"

Decision Sciences, Vol. 7, No. 4 (October 1976), pp. 595—606.

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