Abstract
Predictions of future market demands for dairy products are important determinants in developing marketing strategies and farm-production planning decisions. For business operations in dairy industry, the accuracy of the forecast is of crucial importance because of the volatile demand pattern, influenced by an environment of rapid and dynamic response. The current study aims to compare the forecasting models like moving average, regression, multiple regression, and the Holt–Winters model based on accuracy measures, applied to demand forecasting of a time series formed by a group of perishable dairy products in milk processing industry. Further, the metric analysis of various error-measuring techniques is also applied to select the least error-producing model for such products as a performance measure. Findings of the study will help dairy industry to achieve high order fill rate, good inventory control as well as high profits. However, the selection of these models depends upon the knowledge, availability of data, and context of forecasting.
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Abbreviations
- F t :
-
Forecasted demand for the period ‘t’
- Y t :
-
Actual demand for the period ‘t’
- u i :
-
Level factor for the period ‘t’
- v i :
-
Trend factor for the period ‘t’
- S i :
-
Seasonal factor for the period ‘t’
- α :
-
Smoothing constant for demand or level
- β :
-
Smoothing constant for trend
- γ :
-
Smoothing constant for seasonality
- MAD:
-
Mean absolute deviation
- MSE:
-
Mean square error
- RMSE:
-
Root-mean-square error
- MAPE:
-
Mean absolute percentage error
- M.A.:
-
Moving average
- H-W:
-
Holt and Winters
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Acknowledgements
The authors would like to thank all the key resource persons from dairy industry. Further, the authors would like to express their sincere gratitude for the remarks and recommendations made by anonymous reviewers and editor which radically improved the quality of this work.
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6.1 Electronic supplementary material
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Appendix
Appendix
-
Forecasting Models and the Calculations for MAD, MSE, MAPE, and RMSE
-
1.
Moving Average (MA)
-
A.
MA5: Moving average of 5 months (MA5) has been considered here, as derived below:
The values in Table 6.11 have been calculated for ‘One period,’ and rest can be calculated by using formula for MAPE, MAD, MSE, and RMSE.
(a) Forecast Demand, i.e., C11 = AVERAGE(B6:B10)
(b) Error = B11 − C11
(c) abs error = ABS(D11)
(d) Square Error = E11 * E11
(e) % Error = E11/B11 * 100
(f) MAPE = AVERAGE(G11:G53)
(g) MAD = AVERAGE(E11:E53)
(h) MSE = AVERAGE(F11:F53)
(i) RMSE = SQRT(J11)
-
B.
MA6: Here, the moving average of 6 months has been derived, as explained below:
The values in Table 6.12 have been calculated for ‘One period,’ and rest can be calculated by using formula for MAPE, MAD, MSE, and RMSE.
(a) Forecast Demand, i.e., C66 = AVERAGE(B60:B65)
(b) Error = B66 − C66
(c) abs error = ABS(D66)
(d) Square Error = E66 * E66
(e) % Error = E66/B66 * 100
(f) MAPE = AVERAGE(G66:G107)
(g) MAD = AVERAGE(E66:E107)
(h) MSE = AVERAGE(F66:F107)
(i) RMSE = SQRT(J66)
-
C.
MA7: Here, the moving average of 7 months has been derived, as explained below:
The values in Table 6.13 have been calculated for ‘One period,’ and rest can be calculated by using formula for MAPE, MAD, MSE, and RMSE.
(a) Forecast Demand, i.e., C121 = AVERAGE(B114:B120)
(b) Error = B121 − C121
(c) abs error = ABS(D121)
(d) Square Error = E121 * E121
(e) % Error = E121/B121 * 100
(f) MAPE = AVERAGE(G121:G161)
(g) MAD = AVERAGE(E121:E161)
(h) MSE = AVERAGE(F121:F161)
(i) RMSE = SQRT(J121)
-
D.
MA8: Here, the moving average of 8 months has been derived, as explained below:
The values in Table 6.14 have been calculated for ‘One period,’ and rest can be calculated by using formula for MAPE, MAD, MSE, and RMSE.
(a) Forecast Demand, i.e., C176 = AVERAGE(B168:B175)
(b) Error = B176 − C176
(c) abs error = ABS(D176)
(d) Square Error = E176 * E176
(e) % Error = E176/B176 * 100
(f) MAPE = AVERAGE(G176:G215)
(g) MAD = AVERAGE(E176:E215)
(h) MSE = AVERAGE(F176:F215)
(i) RMSE = SQRT(J176)
-
E.
MA9: Here, the moving average of 9 months has been derived, as explained below:
The values in Table 6.15 have been calculated for one period, and rest can be calculated by using formula for MAPE, MAD, MSE, and RMSE.
(a) Forecast Demand, i.e., C230 = AVERAGE(B221:B229)
(b) Error = B230 − C230
(c) abs error = ABS(D230)
(d) Square Error = E230 * E230
(e) % Error = E230/B230 * 100
(f) MAPE = AVERAGE(G230:G268)
(g) MAD = AVERAGE(E230:E268)
(h) MSE = AVERAGE(F230:F268)
(i) RMSE = SQRT(J230)
-
2.
Holt and Winters
-
A.
Monthly Demand
The values in Table 6.16 have been calculated for ‘One period,’ and rest can be calculated by using formula for MAPE, MAD, MSE, and RMSE.
(a) Forecast Demand
-
For first period
Level Factor (u), D15 = C15/F15
Trend Factor (v), E15 = 0
Seasonal Factor (s), F4 = C4/AVERAGE(C$4:C$15)
-
For the other periods using the following formula
(u), D16 = M$14 * C16/F4 + (1 − M$14) * (D15 + E15)
(v), E16 = O$14 * (D16 − D15) + (1 − O$14) * E15
(s), F16 = Q$14*C16/D16 + (1 − Q$14) * F4
So, the Forecast, G16 = (D15 + E15) * F4
(b) Error = C16 − G16
(c) abs error = ABS(H16)
(d) Square Error = I16 * I16
(e) % Error = I16/C16 * 100
(f) MAPE = AVERAGE(K16:K51)
(g) MAD = AVERAGE(I16:I51)
(h) MSE = AVERAGE(J16:J51)
(i) RMSE = SQRT(M4)
-
B.
Daily Demand
The values in Table 6.17 have been calculated for ‘One period,’ and rest can be calculated by using formula for MAPE, MAD, MSE, and RMSE.
(a) Forecast Demand
-
For first period
Level Factor (u), D9 = C9/F9
Trend Factor (v), E9 = 0
Seasonal Factor (s), F3 = C3/AVERAGE(C$3:C$9)
-
For the other periods using the following formula
(u), D10 = M$16 * C10/F3 + (1 − M$16) * (D9 + E9)
(v), E10 = O$16 * (D10 − D9) + (1 − O$16) * E9
(s), F10 = Q$16*C10/D10 + (1 − Q$16) * F3
So, the Forecast, G10 = (D9 + E9) * F3
(b) Error = C10 − G10
(c) abs error = ABS(H10)
(d) Square Error = I10 * I10
(e) % Error = I10/C10 * 100
(f) MAPE = AVERAGE(K10:K1463)
(g) MAD = AVERAGE(I10:I1463)
(h) MSE = AVERAGE(J10:J1463)
(i) RMSE = SQRT(M3)
-
3.
Regression Analysis
The values in Table 6.18 have been calculated for ‘One period,’ and rest can be calculated by using formula for MAPE, MAD, MSE, and RMSE.
(a) Forecast Demand, F3 = M$20 + D3 * M$21
(b) Error = C3 − F3
(c) abs error = ABS(G3)
(d) Square Error = H3 * H3
(e) % Error = H3/C3 * 100
(f) MAPE = AVERAGE(J3:J50)
(g) MAD = AVERAGE(H3:H50)
(h) MSE = AVERAGE(I3:I50)
(i) RMSE = SQRT(S4)
-
4.
Multiple Regression
-
A.
Monthly Demand
The values in Tables 6.19 and 6.20 have been calculated for ‘One period,’ and rest can be calculated by using formula for MAPE, MAD, MSE, and RMSE.
(a) Forecast Demand, P57
P57 = C$126 + C$127 * D57 + C$128 * E57 + C$129*F57 + C$130 * G57 + C$131 * H57 + C$132 * I57 + C$133 * J57 + C$134 * K57 + C$135 * L57 + C$136 * M57 + C$137 * N57 + C$138 * O57
(b) Error = C57 − P57
(c) abs error = ABS(Q57)
(d) Square Error = R57 * R57
(e) % Error = R57/C57 * 100
(f) MAPE = AVERAGE(S57:S104)
(g) MAD = AVERAGE(R57:R104)
(h) MSE = AVERAGE(T57:T104)
(i) RMSE = SQRT(W57)
-
B.
Daily Demand
The values in Tables 6.21 and 6.22 have been calculated for ‘One period,’ and rest can be calculated by using formula for MAPE, MAD, MSE, and RMSE.
(a) Forecast Demand, J4
J4 = Q$22 + C4 * Q$23 + D4 * Q$24 + E4 * Q$25 + F4 * Q$26 + G4 * Q$27 + H4 * Q$28 + I4 * Q$29
(b) Error = B4 − J4
(c) abs error = ABS(K4)
(d) Square Error = L4 * L4
(e) % Error = L4/B4 * 100
(f) MAPE = AVERAGE(N4:N1464)
(g) MAD = AVERAGE(L4:L1464)
(h) MSE = AVERAGE(M4:M1464)
(i) RMSE = SQRT(R4)
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Mor, R.S., Jaiswal, S.K., Singh, S., Bhardwaj, A. (2019). Demand Forecasting of the Short-Lifecycle Dairy Products. In: Chahal, H., Jyoti, J., Wirtz, J. (eds) Understanding the Role of Business Analytics. Springer, Singapore. https://doi.org/10.1007/978-981-13-1334-9_6
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