Competitive purchasing policies under price volatility.

ABSTRACT

Consider the repeated purchase of a commodity whose price fluctuates over time. There are several purchase (replenishment) policies we may adopt, such as buying as much as storage space would allow, or buying more when price is low. Among different purchasing policies, some

INTRODUCTION

There has been an increasing realization that purchasing is a strategic function for firms (Rajagopal, 1993). Although cost of input material is not the only criteria in purchasing, it is an important one, and a simple arithmetic exercise illustrates the impact 0f cost reduction on competitiveness--consider a firm with revenue of $100, 80 percent of which is its cost (which is $80). A 10 percent increase in sales leads to a revenue of $110 at a cost of $88, an improvement of profits from $20 to $22. Instead, a 10 percent reduction in cost (so cost goes from $80 to $72) leads to an improvement of profits from $20 to $28, a 40 percent increase.

The operational issues in purchasing have long been considered in inventory management literature. The basic economic order quantity model (Harris, 1915) is an attempt to minimize overall costs taking into account the cost of ordering (replenishment) and the cost of holding stock. This model assumes a uniform rate of usage of the material over time. When the usage is not uniform but probabilistic (random), other models such as the reorder point method (stock level is continually monitored, and when it reaches a certain level--called reorder point--an order for replenishment is made), the fixed order interval method (orders are placed at regular intervals in time), or the (s,S) policy (when the stock falls below 's' units, a replenishment order is placed to bring the stock level up to 'S' units) are used (Silver, Pyke, and Peterson, 1998).

In all of the above models, the purchase price of material does not figure prominently (it does affect the holding cost, and hence has an impact), except for models that take into account quantity discounts. Generally the price of the material is considered to be known and fixed, and whatever the purchase policy, the same cost is incurred (at least in the long term). However, in the case of large fluctuations in the price of the input material, the price itself is an important factor that must directly affect the purchasing policy. In this paper we will present two such purchasing policies, and investigate their optimality.

ALTERNATIVE PURCHASING POLICIES

For a commodity that is used continually, one can adopt several different purchasing policies. In describing them, it would be helpful to have a concrete situation in mind. Thus, let us think of the case of purchasing gasoline for a car, and one may substitute any other commodity instead of gasoline without any loss in the argument. We will assume that the gasoline consumption each day is a random amount, and that the price of gasoline also fluctuates on a daily basis.

One may fill up the gas tank of the car any time by going to the gas station. One possible approach is to head to the gas station at the end of day if the fuel drops below a quarter tank (this is similar to a reorder point). At the gas station, a common policy is to fill up the tank--the volume of the tank translates to the available warehouse capacity for a given commodity. We will call this approach Purchase Policy 1 (or just Policy 1), and this clearly is not affected by the price.

A different policy (Policy 2) would be to visit the gas station as before (which is at the end of day if the fuel drops below a quarter tank), but purchase an amount of gasoline that can be obtained for a certain amount of money (for example, we may always buy $20 worth of gasoline, and depending on the price of gasoline, the amount purchased may be different each time). From a practical point of view, we should also restrict the amount purchased to be no more than what the tank can hold. In a sense, this follows the 'dollar cost averaging' method of financial investments (for a discussion on dollar cost averaging, see Leggio (2003).

A third policy (Policy 3) would be to visit the gas station on days (at the end of day for consistency) when the price falls below a certain amount (such as $1.25) and fill the tank. Again from a practical point of view, we need to add the condition that if the amount of fuel falls below a certain amount (say a quarter tank), then gasoline will be purchased, regardless of price, to fill the tank (else we may get into a situation of running out of gasoline while we wait for lower prices).

PERFORMANCE OF THE THREE POLICIES--RESULTS FROM SIMULATION

Since we assume that daily usage and price of gasoline are random, it is difficult to see clearly which is the best policy. To help us resolve this, we can use simulation and see which policy results in lower purchasing cost in the long run.

For the purpose of running the simulation, we will have to choose values for several parameters, and they are described here. Let the usage of gasoline each day be independent and normally distributed with a mean of 2 gallons and a standard deviation of 0.2 gallons. Let the price of gasoline each day be independent and uniformly distributed in the range $1 to $2 (this exaggerates the reality somewhat, but lets us see the consequences clearly). Let the capacity of the gas tank in the car be 20 gallons.

On any day, the amount of gasoline in the car at the end of the day is equal to the amount of gasoline at the beginning of day less the amount that is used that day. In Policy I, if the amount of gasoline at the end of day is less than 5 gallons, then enough gasoline will be purchased to fill the tank. In Policy 2, if the amount of gasoline at the end of day is less than 5 gallons, then $20 worth of gasoline will be purchased (but if that makes the tank overflow, we will stop at filling the tank). In Policy 3, any day the price of gasoline is below $1.25, the tank will be filled (or if the amount of gasoline is less than 5 gallons, then the tank will be filled regardless of the price of gasoline).

The three policies can be easily modeled in a spreadsheet (Microsoft Excel was used in this study). Each policy was followed for a thousand days (starting with a full tank of gasoline), and the results obtained were repeated a hundred times (simulation was done using a Microsoft Excel macro described in Simon (1998); instead, one could use add-ins like @Risk published by Palisade Corporation (Winston, 1996)). The average of those results are shown in Table 1.

The differences were statistically extremely significant that there is no doubt that cost savings can be achieved using Policies 2 and 3. Intuitively it is easy to see why Policy 3 works well--it is taking advantage of the low prices. Policy 2 also does well compared to Policy 1 since buying gasoline for a fixed dollar amount tends toward buying more gasoline when price is low, and less when price is high. Obviously we pay a penalty for these cost savings--we need to visit the gas station more often!

OPTIMIZING THE PARAMETER IN POLICY 2

In Policy 2, we assumed that when we bought gasoline, we bought $20 worth of it each time (unless that exceeded the tank capacity, in which case we stopped at a tank full). To investigate how the total fuel cost would behave if this dollar amount is changed, a simulation was run on Microsoft Excel with various values for this dollar amount, and the results are shown in Table 2 and Figure 1.

[FIGURE 1 OMITTED]

This behavior is interesting. When the dollar amount of purchase is rather large, most of the time we would end up filling the tank, and cost savings would be small (total cost would be high). As we decrease this dollar amount, we will see increasing cost savings. This is borne out by the results of simulation. But then when the dollar amount is reduced below $16, we do not see any further cost reductions, while the number of replenishments continues to increase. This suggests that there is an optimal dollar amount of purchase for someone following this purchase policy.

OPTIMIZING THE PARAMETER IN POLICY 3

In Policy 3, we assumed that we purchased gasoline any day the price of gasoline was below $1.25. To investigate how the total cost would behave if this threshold price value is changed, a simulation was run on Microsoft Excel with various values for this threshold price, and the results are shown in Table 3 and Figure 2.

[FIGURE 2 OMITTED]

Again the total cost behavior is interesting. When the threshold price for purchase is very low, it is rarely reached, and no large cost savings is seen; if the threshold is large, then fuel is purchased even when the price is high, and again, no large cost savings is seen. There is an optimal threshold price--in this case, around $1.35--where the cost savings are the highest.

LIMITATIONS AND EXTENSIONS

As noted earlier, several parameter values were assumed (the daily amount of gasoline used was assumed to be normally distributed with a mean of 2 gallons and a standard deviation of 0.2 gallon; the gas tank was assumed to have a capacity of 20 gallons, with replenishment required at a quarter tank or 5 gallons; daily price of gasoline was assumed to be independent and uniformly distributed between $1 and $2; etc). Different assumptions will lead to different results, but we believe that the overall pattern will persist.

In particular, the assumption that the daily price exhibits such variation may not be realistic, and there will be serial correlation between the price values. These changes will most likely reduce the amount of cost savings, particularly in Policy 3. However this study is intended to show the possible differences among the three purchasing policies, and these simple assumptions allow us to see the differences clearly. When more realistic parameter values are available, those can be used to find the optimal purchasing policy.

We also ignored the order (replenishment) cost and holding cost of the material (gasoline). These (in particular the order cost) could be incorporated into a larger model, and we can study the behavior of the total cost. In such a model, one would have to be careful to study the interactions between the causal variables. One could also investigate more complex policies--for example, we could create an extension of Policy 3 as follows: if the amount of gasoline at the end of day falls below a quarter tank and the price of gasoline is above the threshold price, then we will buy a certain dollar amount worth of gasoline (instead of filling up the tank). Another parameter that could be investigated is the reorder point--here we assumed that replenishment is required at a quarter tank, and changing this value will affect the total cost.

IMPLICATIONS AND CONCLUSION

We have clearly shown that when the price of a commodity fluctuates, different purchasing policies will lead to different total cost of purchase in the long term. It would benefit a firm to try to seek an optimal purchasing policy, since cost reduction is a strategic tool for competitiveness. In this paper we have shown how we can analyze some of the different policies using simulation done on a spreadsheet, and we were also able to gain some insights into the behavior of the total cost with respect to some of the parameters used in the purchase policies.

REFERENCES

Harris, F. W. (1915). Operations and costs. Chicago: A. W. Shaw.

Leggio, K. B., and Lien, D. (2003). Comparing alternative investment strategies using risk-adjusted performance measures. Journal of Financial Planning, 16 (I), pp. 82-86.

Rajagopal, S., and Bernard, K. (1993). Cost containment strategies: Challenges for strategic purchasing in the 1990s. International Journal of Purchasing and Materials Management, 29 (1), p. 17.

Silver, E., Pyke, D., and Peterson, R. (1998). Decision systems for inventory management and production planning and control. 3rd ed. New York: Wiley.

Simon, J. T. (1998, March). Easy simulation on spreadsheets without add-ins. Decision Line, pp. 6-8.

Winston, W. L. (1996). Simulation modeling using @ risk. Belmont: Wadsworth Publishing Company.

John T. Simon has a doctorate in Industrial Engineering and Management Sciences from Northwestern University, Evanston, Illinois. His research interests are in the area of operations management, and he has published articles in journals such as International Journal of Production Research, Journal of Global Competitiveness, and American Business Review. He is currently an assistant professor of management at the State University of New York College at Geneseo.

TABLE 1

Comparison of the Three Purchasing Policies

           Total fuel cost for 1000    Number of replenishments
           days (averaged over         in 1000 days (averaged
           100 simulations)            over 100 simulations)

Policy 1   $2,984                      124
Policy 2   $2,891                      149
Policy 3   $2,468                      278

TABLE 2

Behavior of Total Cost under Policy 2 When the Dollar Amount
of Purchase Is Varied

     Dollar Amount of      Total fuel cost   Number of replenishments
Purchase under Policy        for 1000 days     in 1000 days (averaged
                    2   (averaged over 500      over 500 simulations)
                              simulations)

                 $10               $2,869                       287
                  11                2,868                       261
                  12                2,869                       239
                  13                2,869                       221
                  14                2,869                       205
                  15                2,871                       191
                  16                2,870                       179
                  17                2,875                       170
                  18                2,883                       161
                  19                2,888                       154
                  20                2,897                       149
                  21                2,908                       144
                  22                2,921                       140
                  23                2,927                       136
                  24                2,942                       134
                  25                2,954                       131

TABLE 3

Behavior of Total Cost under Policy 3 When the Threshold Price
for Purchase Is Varied

Threshold Price for   Total fuel cost for     Number of
Purchase              1000 days (averaged     replenishments in
                      over 100 simulations)   100 days (averaged
                                              over 100 simulations)

             $1.05                 $2,833                    148
              1.10                  2,700                    176
              1.15                  2,598                    206
              1.20                  2,520                    239
              1.25                  2,468                    277
              1.30                  2,441                    317
              1.35                  2,436                    359
              1.40                  2,448                    405
              1.45                  2,475                    452
              1.50                  2,513                    502
              1.55                  2,555                    550
              1.60                  2,600                    599
              1.65                  2,649                    648
              1.70                  2,698                    698
              1.75                  2,748                    748
              1.80                  2,799                    798