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A multicriteria approach to strategic planning: An application in inventory control
OMEGA, The Int. Jl of Mgmt Sci., Vol. 5, No. 1, 1977. Pergamon Press. Printed in Great Britain
A Multicriteria Approach to Strategic Planning: An Application in Inventory Control ROBERT C CARLSON Stanford University, California HANS H THERP McKinsey and Company, Copenhagen, Denmark (Received May 1976; in revised form August 1976)
A new planning method is proposed whereby a manager can observe the strategic consequences of his tactical decisions before those decisions are implemented. These consequences are presented as goal outcomes or values of criteria previously specified as being important by the decision maker. The methodology involves the embedding of relatively simple tactical optimization models within a larger and more complex descriptive model. The results obtained in applying this method to an electronics manufacturer are presented. Of particular interest is the comparison among three tactical inventory models.
1. I N T R O D U C T I O N I ~ v E N x o R y control is a total problem where management is interested in utilizing its resources in the best w a y - - t h i s is the strategic problem. But an inventory control system has m a n y subsystems, items to be controlled in the best w a y - - t h e s e are the tactical problems. Obviously, strategic and tactical problems are interdependent, and one should not be considered without concern for the other. This fact is often neglected in systems today because no relationship has been established between the tactical and the strategic decisions. Tactical decisions are made without considering the strategic consequences; but once the tactical decisions have been made, the strategic performance is implicitly determined. N u m e r o u s inventory control models exist which minimize the costs incurred for each item, considering only that item. Based on estimates of the cost coefficients involved, this gives a solution to the tactical problem of how to control each item. When such models are used in practice, the resulting strategic solutions are often far f r o m satisfactory [6]. The real problem is the selection of proper costs. The cost coefficients are estimates of marginal costs which are 57
Carlson, Therp--Multicriteria Approach to Strategic Planning difficult to obtain even from historical data. Estimates of future marginal costs will normally require some knowledge about the resulting outcome levels; but these are strategic consequences which are not considered in traditional inventory control methods.
2. ANALYZING STRATEGIC CONSEQUENCES The total costs of an inventory system arise because capital is tied up in inventory and facilities, because manpower is needed to obtain and maintain the inventory, and because a shortage situation may cause paper-work, lost sales, or delayed production. Commonly the performance of an inventory system is expressed by three outcomes--average inventory level, number of orders processed per year, and the level of backorders. These three outcomes can be considered goals of the inventory system, and their aggregate values are the strategic consequences of the inventory policy used. The tactical decision variables used in many inventory systems are an order point and an order quantity for each item. When the inventory level of an item is reviewed, a replenishment order is processed when the amount in stock and on order is less than the order point for that item. Many inventory control models suggest order points and order quantities which are optimal with respect to the criterion function of the model. Generally, however, the criterion function is a simplification of the true objectives of the inventory system. It includes estimates of cost coefficients; and the outcomes are expressed as a simplified function of the tactical decisions and the item parameters to facilitate finding 'optimal' decisions. This paper suggests the use of 'near optimal' tactical decisions derived from a traditional inventory model, but only after analyzing the implied strategic consequence. By changing the ratios between the cost co-efficients used in the inventory model, different tactical decisions will be 'optimal'. It is assumed that the cost ratios are common for all items. The strategic consequences are the aggregate values of the outcomes, and they are calculated for each set of tactical decisions. The calculation of the strategic consequences is the prediction of the strategic performance of the inventory system if a particular set of tactical decisions is used. The contribution from each item to the strategic consequences must be calculated more accurately than can be done using the approximate relationships used in the tactical inventory models. This is essential since a practical inventory system almost always is more complex than assumed in the inventory model, and the value of analyzing the strategic consequences depends on the accuracy with which they can be calculated. Often a simulation model is used [2, 3]. The inventory model enables us to calculate the strategic consequences corresponding to a set of cost ratios. Each set of strategic consequences is a 58
Omega, Vol. 5, No. 1 point in outcome space, and the points corresponding to different cost ratios constitute the 'efficient surface' [1,2] for that particular model. The efficient surface informs the decision maker about the alternatives which the considered inventory model allows. The strategic decision is made by selecting a point on the efficient surface [5]. Through the efficient surface, managers obtain insight into the trade-offs that exist between the inventory level, the number of orders processed, and the level of backorders. Through investigation and discussion of alternative combinations of these outcomes, the managers can weight the outcomes and agree upon a preferred point on the efficient surface. In this way managers are given the possibility of direct involvement in making strategic decisions and hence direct influence on strategic consequences. The information, experience, and intuition of the managers can be utilized in the strategic decision insteao of only in the evaluation of the past performance of the inventory system. After the selection of the preferred point on the efficient surface, the problem is to identify those tactical decisions which will lead to the particular combination of strategic outcomes defined by the point. Since each point on the efficient surface corresponds to a set of cost ratios, we can find the set of cost ratios which corresponds to the preferred point selected above. This set of cost ratios should then be used in the inventory model, and the optimal tactical decisions identified will correspond to the preferred point on the efficient surface. When these tactical decisions are used in the coming periods, the strategic decisions are implemented.
3. A R E A L - W O R L D I N V E N T O R Y APPLICATION
CONTROL
Our method for strategic decision making was applied to a real-world inventory system consisting of approx 7000 parts that are used in the production of measuring instruments. Production of the instruments was in batches, called runs, according to a production schedule. The sales rate for each instrument fluctuated, and for all practical purposes we could assume these sales rates to be independent. Because the production schedule was changed every month to reflect realized sales and forecast changes, the usage of parts deviated from the planned level. These deviations were of course not strictly independent; but the practical situation was such that many changes in the production schedule occurred every month, and furthermore most parts went into several instruments. We therefore made the assumption that the usage rates of the parts were normally distributed and independent. The parts were purchased on an order point/order quantity basis, and we could use the framework of the strategic planning method to evaluate alternative 59
Carlson, Therp--Multicriteria Approach to Strategic Planning purchasing rules for the inventory system. The inventory performance was measured in terms of the following three goals: average total inventory; number of replenishment orders per year; number of backorders at any point in time. An inventory analysis was undertaken to find the impact of the purchasing rules used on the performance of the inventory system. The following two studies were performed: (1) comparison between the theoretical performance of the current purchasing rules and purchasing rules derived from two different inventory models; (2) analysis of the impact of forecast errors on the performance of the inventory system. Since the calculation of the tactical decisions for a part involves an optimization algorithm, the computations can be considerable. We therefore performed the consequence calculations for a sample of the parts and extrapolated the results to obtain estimates of the strategic consequences for the total inventory. The inventory considered here consists of 7300 parts classified as A, B, C and D parts, shown in Table 1. TABLE 1. A, B, C, D CLASSIFICATIONOF PARTS
Class
~of $ usage
Yoof inventory $
Number of parts
A B C D
77 17 5 1
61 23 12 4
720 1130 1530 3920
Sample size 100 100 100 100
First we calculated the three consequences for the 100 A parts. Each of these three consequences was then multiplied by the ratio between the total forecast for all A parts and the forecast for the 100 parts in the sample. In this way we estimated strategic consequences for the inventory of all A parts. We repeated these calculations for the other three classes and added the consequences for all four classes. In addition to reducing the computations involved, sampling greatly reduces the amount of part data required by the method. For the 400 parts in the samples, the current list prices and leadtimes were retrieved from a data file. The number of monthly pulls and the size of each pull were obtained from a file containing past transactions for the 400 parts covering a 6-month period. The forecast of the usage for each part was based on the part explosion of scheduled production for the 6-month period. This forecast was revised every month, but for simplicity, a single 6-month forecast was used. From the data on monthly pulls, we estimated the average pull size, the mean actual usage, and the standard deviation of the usage rate for each part. The existing purchasing rules specified 60
Omega, Vol. 5, No. 1 a set of tactical decisions for all parts. Different order points and order quantities were used depending on the classification of a part, the usage rate, and the leadtime (Table 2). These tactical decisions were not based on any inventory model, but on intuitive rules adjusted over the years using feedback from actual inventory performance. The theoretical performance of these rules was then calculated for these order points and order quantities for the samples of A, B, C and D parts. The performance of the total inventory was estimated using the sampling procedure previously described. The reorder quantities (EOQ's) were computed through the use of the conventional square root EOQ formula. TABLE 2. CURRENT PURCHASING RULES
The order point (OP) for each part is determined by OP = (safety stock + leadtime) x (weekly usage) where safety stock (in weeks of coverage) is determined by Leadtime Safety stock 0-8 weeks 2 weeks 8-14 weeks 3 weeks 14-20 weeks 4 weeks above 20 weeks 5 weeks The order quantity is determined by Class Order quantity A 6 weeks usage B 8 weeks usage C 20 weeks usage D 32 weeks usage The safety stock was taken as [7], P × cri, where P is a constant determined by a policy decision and cri the standard deviation of demand during the leadtime. Using this safety stock calculation for all parts theoretically implies the same chance of stockouts for all parts during each order cycle. In our case we assumed that ch was the square root of the mean demand during the leadtime [4]. Under the assumptions of normally distributed, independent usage rates, our inventory model optimizes the combination of the three consequences used in evaluating the inventory performance. We then used some approximations [3, 4] for the case of continuous review and independent, normally distributed usage rate.
4. RESULTS OF ANALYSIS Figure 1 shows the possible combinations of the strategic consequences for P = 2 and P -----3.7 respectively. Figure 2 shows the results for the corresponding 61
Carlson, Therp--Multicriteria Approach to Strategic Planning
800 ~coo INVENTORY (in $10 '6 )
9oo AVERAGE NUMBER OF BACKORDERS
IIO 0 ~ k l ~ 1 13
P200 0
3
1.5
0 ~ 1400 1500
1400
1700 P=3.7 1800
P
2ooo
4000
I0,000
:
2.0
16,000
NUMBER OF ORDERS
FIo. 1. Efficient surface for EOQ model (using actual forecast).
41I
- ....
ACTUAL FORECAST PERFECT FORECAST
INVENTORY ( in $10 6)
~, \~, k
2-
0
2000
\
N \
AVERAGE NUMBER OF BACKORDERS 500
,~ ~
~&o
6o'oo
NUMBER OF ORDERS
F[o. 2. Efficient surface for stochastic model
62
Omega, Vol. 5, No. 1 stochastic inventory model. It is obvious that the three inventory control techniques perform very differently. As we would expect, the stochastic inventory model can always find solutions that dominate those of the EOQ model, and the EOQ model in turn can produce solutions that dominate the consequences of the current buying rules. A closer comparison is made in Table 3. We then investigated the impact of a general forecast error on the goals of the inventory system. If the aggregated forecast is too high, the actual inventory level will be higher than expected; and if the forecast is too low, the number of backorders will be higher than expected. We calculated the inventory performance under two conditions: the first as in the foregoing analysis (order points and order quantities based on the forecast, while the inventory performance on the actual average usage rate of each part), the second relies on a perfect forecast (i.e. the forecast and actual demand coincide). The difference in the three strategic consequences between these two calculations can be attributed to the forecast errors. TABLE 3. COMPARISONOF THE THREEINVENTORYTECHNIQUES
For number of orders per year = 15,000 and expected number of backorders = 1600 Technique Current EOQ (P = 4) Stochastic
Inventory $1,730,000 $1,370,000 $1,150,000
For inventory level = $1,730,000 and expected number of backorders = 1100 Number of Technique orders per year EOQ 7000 Stochastic 5100
For inventory level = $1,730,000 and number of orders per year = 7000 Expected number Technique of backorders EOQ 1100 Stochastic 800
In the example used, the forecast on the aggregate was 33 ~o too high. The results for the two models are shown in Table 4. OM~A5/1--~
63
Carlson, Therp--Multicriteria Approach to Strategic Planning TABLE4. EFFECTOF FORECASTERRORS
Forecast
Inventory
Number of orders
Expected number of backorders
Model 1 : Current purchasing rules
Actual Perfect
$1,730,500 $931,700
15,500 17,800
1630 1425
Model 2: Stochastic inventory model
Actual Perfect
$1,730,000 $1,080,000
5100 5100
1100 1100
A warning A number of factors exist in practice which have not been included in this analysis. They all have an impact on the performance and the calculations of the performance. It is important to note that these factors not only affect the absolute accuracy of the consequence calculation, but have less influence on the relative performance of the three techniques compared. Some of the factors are listed here. 1. Overriding of purchasing rules based on detailed knowledge about the production schedule often occurs. 2. The use of split shipments was not considered. 3. No consideration was given to quantity discounts in the models. 4. Minimum shipments are required by some vendors. 5. The revision of forecast every month was not included. 6. Six month usage data may not be enough to estimate the standard deviation reliably. 7. The usage rate may not be normally distributed and independent.
5. CONCLUSIONS The proposed method of calculating the efficient surface for an inventory system is a tool which enables managers to deal with the strategic decisions for inventory systems. The efficient surface tells the managers about alternative combinations of the three outcomes--average inventory level, number of orders per year, and the level of backorders. They can relate these outcomes to the overall objectives and operating restrictions of the company. The method will not calculate one magic optimal solution, but it will leave the final strategic decision to the managers and thus make it possible to include their experience and intuition. The method will prove particularly useful in adjusting to changes in the environment which affect the inventory system such as the supply of 64
Omega, Vol. 5, No. 1 capital, leadtimes, and cost changes. The method can be used with any existing or future tactical inventory models, and strategic consequences other than those considered here can be included.
REFERENCES 1. BAUM S and CARLSONRC (1974) Multi-goal optimization in managerial science. Omega 2(5), 607-623. 2. FEENEYGJ (1955) A basis for strategic decisions on inventory control operations. Mgmt Sci. 2(1), 69-82. 3. GUNGE T and THERP H H (1972) Ressourceallokering i Lagerstyring. Thesis from the Institute of Mathematical Statistics and Operations Research at the Technical University of Denmark. 4. HADLEYG and W n m N TM (1963) Analysis of Inventory Systems. Prentice-Hall, Englewood Cliffs. 5. HANSSMANNF (1962) Operations Research in Production and Inventory Control. Wiley, New York. 6. HARTYJD, PLOSSLG W and WIGHT OW (1963) Management of lot-size inventories. American Production and Inventory Control Society, Special Report. 7. WIGHT OW (1974) Production and Inventory Management in the Computer Age. Cahners Publishing Company.
Professor RC Carlson, Department of Industrial Engineering, Stanford University, School of Engineering, Stanford, California 94305, USA.
ADDRESS FOR CORRESPONDENCE:
65
A Multicriteria Approach to Strategic Planning: An Application in Inventory Control ROBERT C CARLSON Stanford University, California HANS H THERP McKinsey and Company, Copenhagen, Denmark (Received May 1976; in revised form August 1976)
A new planning method is proposed whereby a manager can observe the strategic consequences of his tactical decisions before those decisions are implemented. These consequences are presented as goal outcomes or values of criteria previously specified as being important by the decision maker. The methodology involves the embedding of relatively simple tactical optimization models within a larger and more complex descriptive model. The results obtained in applying this method to an electronics manufacturer are presented. Of particular interest is the comparison among three tactical inventory models.
1. I N T R O D U C T I O N I ~ v E N x o R y control is a total problem where management is interested in utilizing its resources in the best w a y - - t h i s is the strategic problem. But an inventory control system has m a n y subsystems, items to be controlled in the best w a y - - t h e s e are the tactical problems. Obviously, strategic and tactical problems are interdependent, and one should not be considered without concern for the other. This fact is often neglected in systems today because no relationship has been established between the tactical and the strategic decisions. Tactical decisions are made without considering the strategic consequences; but once the tactical decisions have been made, the strategic performance is implicitly determined. N u m e r o u s inventory control models exist which minimize the costs incurred for each item, considering only that item. Based on estimates of the cost coefficients involved, this gives a solution to the tactical problem of how to control each item. When such models are used in practice, the resulting strategic solutions are often far f r o m satisfactory [6]. The real problem is the selection of proper costs. The cost coefficients are estimates of marginal costs which are 57
Carlson, Therp--Multicriteria Approach to Strategic Planning difficult to obtain even from historical data. Estimates of future marginal costs will normally require some knowledge about the resulting outcome levels; but these are strategic consequences which are not considered in traditional inventory control methods.
2. ANALYZING STRATEGIC CONSEQUENCES The total costs of an inventory system arise because capital is tied up in inventory and facilities, because manpower is needed to obtain and maintain the inventory, and because a shortage situation may cause paper-work, lost sales, or delayed production. Commonly the performance of an inventory system is expressed by three outcomes--average inventory level, number of orders processed per year, and the level of backorders. These three outcomes can be considered goals of the inventory system, and their aggregate values are the strategic consequences of the inventory policy used. The tactical decision variables used in many inventory systems are an order point and an order quantity for each item. When the inventory level of an item is reviewed, a replenishment order is processed when the amount in stock and on order is less than the order point for that item. Many inventory control models suggest order points and order quantities which are optimal with respect to the criterion function of the model. Generally, however, the criterion function is a simplification of the true objectives of the inventory system. It includes estimates of cost coefficients; and the outcomes are expressed as a simplified function of the tactical decisions and the item parameters to facilitate finding 'optimal' decisions. This paper suggests the use of 'near optimal' tactical decisions derived from a traditional inventory model, but only after analyzing the implied strategic consequence. By changing the ratios between the cost co-efficients used in the inventory model, different tactical decisions will be 'optimal'. It is assumed that the cost ratios are common for all items. The strategic consequences are the aggregate values of the outcomes, and they are calculated for each set of tactical decisions. The calculation of the strategic consequences is the prediction of the strategic performance of the inventory system if a particular set of tactical decisions is used. The contribution from each item to the strategic consequences must be calculated more accurately than can be done using the approximate relationships used in the tactical inventory models. This is essential since a practical inventory system almost always is more complex than assumed in the inventory model, and the value of analyzing the strategic consequences depends on the accuracy with which they can be calculated. Often a simulation model is used [2, 3]. The inventory model enables us to calculate the strategic consequences corresponding to a set of cost ratios. Each set of strategic consequences is a 58
Omega, Vol. 5, No. 1 point in outcome space, and the points corresponding to different cost ratios constitute the 'efficient surface' [1,2] for that particular model. The efficient surface informs the decision maker about the alternatives which the considered inventory model allows. The strategic decision is made by selecting a point on the efficient surface [5]. Through the efficient surface, managers obtain insight into the trade-offs that exist between the inventory level, the number of orders processed, and the level of backorders. Through investigation and discussion of alternative combinations of these outcomes, the managers can weight the outcomes and agree upon a preferred point on the efficient surface. In this way managers are given the possibility of direct involvement in making strategic decisions and hence direct influence on strategic consequences. The information, experience, and intuition of the managers can be utilized in the strategic decision insteao of only in the evaluation of the past performance of the inventory system. After the selection of the preferred point on the efficient surface, the problem is to identify those tactical decisions which will lead to the particular combination of strategic outcomes defined by the point. Since each point on the efficient surface corresponds to a set of cost ratios, we can find the set of cost ratios which corresponds to the preferred point selected above. This set of cost ratios should then be used in the inventory model, and the optimal tactical decisions identified will correspond to the preferred point on the efficient surface. When these tactical decisions are used in the coming periods, the strategic decisions are implemented.
3. A R E A L - W O R L D I N V E N T O R Y APPLICATION
CONTROL
Our method for strategic decision making was applied to a real-world inventory system consisting of approx 7000 parts that are used in the production of measuring instruments. Production of the instruments was in batches, called runs, according to a production schedule. The sales rate for each instrument fluctuated, and for all practical purposes we could assume these sales rates to be independent. Because the production schedule was changed every month to reflect realized sales and forecast changes, the usage of parts deviated from the planned level. These deviations were of course not strictly independent; but the practical situation was such that many changes in the production schedule occurred every month, and furthermore most parts went into several instruments. We therefore made the assumption that the usage rates of the parts were normally distributed and independent. The parts were purchased on an order point/order quantity basis, and we could use the framework of the strategic planning method to evaluate alternative 59
Carlson, Therp--Multicriteria Approach to Strategic Planning purchasing rules for the inventory system. The inventory performance was measured in terms of the following three goals: average total inventory; number of replenishment orders per year; number of backorders at any point in time. An inventory analysis was undertaken to find the impact of the purchasing rules used on the performance of the inventory system. The following two studies were performed: (1) comparison between the theoretical performance of the current purchasing rules and purchasing rules derived from two different inventory models; (2) analysis of the impact of forecast errors on the performance of the inventory system. Since the calculation of the tactical decisions for a part involves an optimization algorithm, the computations can be considerable. We therefore performed the consequence calculations for a sample of the parts and extrapolated the results to obtain estimates of the strategic consequences for the total inventory. The inventory considered here consists of 7300 parts classified as A, B, C and D parts, shown in Table 1. TABLE 1. A, B, C, D CLASSIFICATIONOF PARTS
Class
~of $ usage
Yoof inventory $
Number of parts
A B C D
77 17 5 1
61 23 12 4
720 1130 1530 3920
Sample size 100 100 100 100
First we calculated the three consequences for the 100 A parts. Each of these three consequences was then multiplied by the ratio between the total forecast for all A parts and the forecast for the 100 parts in the sample. In this way we estimated strategic consequences for the inventory of all A parts. We repeated these calculations for the other three classes and added the consequences for all four classes. In addition to reducing the computations involved, sampling greatly reduces the amount of part data required by the method. For the 400 parts in the samples, the current list prices and leadtimes were retrieved from a data file. The number of monthly pulls and the size of each pull were obtained from a file containing past transactions for the 400 parts covering a 6-month period. The forecast of the usage for each part was based on the part explosion of scheduled production for the 6-month period. This forecast was revised every month, but for simplicity, a single 6-month forecast was used. From the data on monthly pulls, we estimated the average pull size, the mean actual usage, and the standard deviation of the usage rate for each part. The existing purchasing rules specified 60
Omega, Vol. 5, No. 1 a set of tactical decisions for all parts. Different order points and order quantities were used depending on the classification of a part, the usage rate, and the leadtime (Table 2). These tactical decisions were not based on any inventory model, but on intuitive rules adjusted over the years using feedback from actual inventory performance. The theoretical performance of these rules was then calculated for these order points and order quantities for the samples of A, B, C and D parts. The performance of the total inventory was estimated using the sampling procedure previously described. The reorder quantities (EOQ's) were computed through the use of the conventional square root EOQ formula. TABLE 2. CURRENT PURCHASING RULES
The order point (OP) for each part is determined by OP = (safety stock + leadtime) x (weekly usage) where safety stock (in weeks of coverage) is determined by Leadtime Safety stock 0-8 weeks 2 weeks 8-14 weeks 3 weeks 14-20 weeks 4 weeks above 20 weeks 5 weeks The order quantity is determined by Class Order quantity A 6 weeks usage B 8 weeks usage C 20 weeks usage D 32 weeks usage The safety stock was taken as [7], P × cri, where P is a constant determined by a policy decision and cri the standard deviation of demand during the leadtime. Using this safety stock calculation for all parts theoretically implies the same chance of stockouts for all parts during each order cycle. In our case we assumed that ch was the square root of the mean demand during the leadtime [4]. Under the assumptions of normally distributed, independent usage rates, our inventory model optimizes the combination of the three consequences used in evaluating the inventory performance. We then used some approximations [3, 4] for the case of continuous review and independent, normally distributed usage rate.
4. RESULTS OF ANALYSIS Figure 1 shows the possible combinations of the strategic consequences for P = 2 and P -----3.7 respectively. Figure 2 shows the results for the corresponding 61
Carlson, Therp--Multicriteria Approach to Strategic Planning
800 ~coo INVENTORY (in $10 '6 )
9oo AVERAGE NUMBER OF BACKORDERS
IIO 0 ~ k l ~ 1 13
P200 0
3
1.5
0 ~ 1400 1500
1400
1700 P=3.7 1800
P
2ooo
4000
I0,000
:
2.0
16,000
NUMBER OF ORDERS
FIo. 1. Efficient surface for EOQ model (using actual forecast).
41I
- ....
ACTUAL FORECAST PERFECT FORECAST
INVENTORY ( in $10 6)
~, \~, k
2-
0
2000
\
N \
AVERAGE NUMBER OF BACKORDERS 500
,~ ~
~&o
6o'oo
NUMBER OF ORDERS
F[o. 2. Efficient surface for stochastic model
62
Omega, Vol. 5, No. 1 stochastic inventory model. It is obvious that the three inventory control techniques perform very differently. As we would expect, the stochastic inventory model can always find solutions that dominate those of the EOQ model, and the EOQ model in turn can produce solutions that dominate the consequences of the current buying rules. A closer comparison is made in Table 3. We then investigated the impact of a general forecast error on the goals of the inventory system. If the aggregated forecast is too high, the actual inventory level will be higher than expected; and if the forecast is too low, the number of backorders will be higher than expected. We calculated the inventory performance under two conditions: the first as in the foregoing analysis (order points and order quantities based on the forecast, while the inventory performance on the actual average usage rate of each part), the second relies on a perfect forecast (i.e. the forecast and actual demand coincide). The difference in the three strategic consequences between these two calculations can be attributed to the forecast errors. TABLE 3. COMPARISONOF THE THREEINVENTORYTECHNIQUES
For number of orders per year = 15,000 and expected number of backorders = 1600 Technique Current EOQ (P = 4) Stochastic
Inventory $1,730,000 $1,370,000 $1,150,000
For inventory level = $1,730,000 and expected number of backorders = 1100 Number of Technique orders per year EOQ 7000 Stochastic 5100
For inventory level = $1,730,000 and number of orders per year = 7000 Expected number Technique of backorders EOQ 1100 Stochastic 800
In the example used, the forecast on the aggregate was 33 ~o too high. The results for the two models are shown in Table 4. OM~A5/1--~
63
Carlson, Therp--Multicriteria Approach to Strategic Planning TABLE4. EFFECTOF FORECASTERRORS
Forecast
Inventory
Number of orders
Expected number of backorders
Model 1 : Current purchasing rules
Actual Perfect
$1,730,500 $931,700
15,500 17,800
1630 1425
Model 2: Stochastic inventory model
Actual Perfect
$1,730,000 $1,080,000
5100 5100
1100 1100
A warning A number of factors exist in practice which have not been included in this analysis. They all have an impact on the performance and the calculations of the performance. It is important to note that these factors not only affect the absolute accuracy of the consequence calculation, but have less influence on the relative performance of the three techniques compared. Some of the factors are listed here. 1. Overriding of purchasing rules based on detailed knowledge about the production schedule often occurs. 2. The use of split shipments was not considered. 3. No consideration was given to quantity discounts in the models. 4. Minimum shipments are required by some vendors. 5. The revision of forecast every month was not included. 6. Six month usage data may not be enough to estimate the standard deviation reliably. 7. The usage rate may not be normally distributed and independent.
5. CONCLUSIONS The proposed method of calculating the efficient surface for an inventory system is a tool which enables managers to deal with the strategic decisions for inventory systems. The efficient surface tells the managers about alternative combinations of the three outcomes--average inventory level, number of orders per year, and the level of backorders. They can relate these outcomes to the overall objectives and operating restrictions of the company. The method will not calculate one magic optimal solution, but it will leave the final strategic decision to the managers and thus make it possible to include their experience and intuition. The method will prove particularly useful in adjusting to changes in the environment which affect the inventory system such as the supply of 64
Omega, Vol. 5, No. 1 capital, leadtimes, and cost changes. The method can be used with any existing or future tactical inventory models, and strategic consequences other than those considered here can be included.
REFERENCES 1. BAUM S and CARLSONRC (1974) Multi-goal optimization in managerial science. Omega 2(5), 607-623. 2. FEENEYGJ (1955) A basis for strategic decisions on inventory control operations. Mgmt Sci. 2(1), 69-82. 3. GUNGE T and THERP H H (1972) Ressourceallokering i Lagerstyring. Thesis from the Institute of Mathematical Statistics and Operations Research at the Technical University of Denmark. 4. HADLEYG and W n m N TM (1963) Analysis of Inventory Systems. Prentice-Hall, Englewood Cliffs. 5. HANSSMANNF (1962) Operations Research in Production and Inventory Control. Wiley, New York. 6. HARTYJD, PLOSSLG W and WIGHT OW (1963) Management of lot-size inventories. American Production and Inventory Control Society, Special Report. 7. WIGHT OW (1974) Production and Inventory Management in the Computer Age. Cahners Publishing Company.
Professor RC Carlson, Department of Industrial Engineering, Stanford University, School of Engineering, Stanford, California 94305, USA.
ADDRESS FOR CORRESPONDENCE:
65