Linear optimization problem
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SINOFERT HOLDINGS LIMITED: UREA DISTRIBUTION PLANNING
Submitted to: Prof. Surya Sarathi Majumdar
Submitted by:
Shaminder Saini (MBA Class of 2018)
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Case Summary
Sinofert Holdings Limited was the largest fertilizer enterprise in China.
Sinofert manufactured fertilizers and the product offerings included urea, diammonium phosphate (DAP) and monoammonium phosphate (MAP) potash.
The company sold the fertilizers in wholesale and retail markets and conducted R&D on new and improved fertilizers.
Sinofert also procured end products directly from suppliers for sale 40,000 customers that constituted small-sized wholesalers, retailers and farmers.
Urea was the biggest volume seller for the company that accounted for 40% of Sinofert’s distribution process.
Sinofert had its own production plants that equalled two million tons of capacity. Sinofert also outsourced four million tons of urea from 70 plants in China
through its partners.
Key Issues:
Throughout the country, keeping the supply and demand equilibrium for urea was becoming a challenge as transfer of urea from over-supplied province
to under-supplied province resulted in long transportation times and high freight costs.
Sinofert was facing challenges in meeting their financial expectations. They were:
High transportation costs
Supply demand imbalance
Intense Competition
Market volatility
Inappropriate production and inventory policies.
Due to the above reasons, Sinofert was unable to generate expected profits from urea.
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1. Scenario Analysis of 2009: I have used Exhibit 3 and made the calculations. The same can be referred to “2009_Scenario” sheet of the Excel File sent.
(Table A)
Average Manufacturing Price has been taken from Exhibit 2
Total Manufacturing Cost for each supplier= ManufQty* Average Manufacturing Price (For example, 950472*1700=1615802400)
Total Freight= 2406,73,019 (Calculated by Sum Product of Exhibit 3 and Exhibit 4 which are Table A and Table B in Excel)
Net Profit= Total Revenue – Total Manufacturing Cost – Total Freight= 58473,34,134 - 53599,15,660 - 2406,73,019 = 2467,45,455
According to the case, Sinofert had reported losses in the years 2007 and 2009. We have made the assumption that Sinofert had sold all its inventory in 2009, however we have got a Net Profit of RMB 2467,45,455. This implies that not all the inventory was sold by the company in 2009 and hence the supply chain can be optimized.
SP from
Exhibit 1
Revenue Sum of
shipments
Sum of
Manufacturing
Cost of all
suppliers
Suppliers/
Supplied province Sinofert Pingyuan Sinofert Changshan Shanxi Fengxi
Shandong
Lianmeng Shandong Ruixing Shandong Lunan Henan Xinlianxin
Henan
Pingdingshan Jiangsu Linggu Hebei Zhengyuan Hebei Jinghua Anhui Haoyuan
Neimeng
Erduosi
total quantity per
company
selling price
for each
company in
2010
total revenue in
2009
Heilongjiang 54171 0 13,533 14,610 30,000 30,000 13,920 0 0 13,920 0 0 50,456 2,20,610 1,917 4229,09,370
Jilin 44,143 2,92,479 6,189 3,780 20,000 10,000 16,080 0 0 14,640 4,860 0 14,280 4,26,451 1,864 7949,04,664
Liaoning 49,886 0 9,344 9,900 12,000 0 25,920 0 0 18,004 4,500 0 28,140 1,57,694 1,880 2964,64,720
Hebei 15,574 0 31,291 0 10,000 20,000 0 0 0 30,132 47,892 0 39,060 1,93,949 1,798 3487,20,302
Henan 18,926 0 67,792 0 10,000 10,000 24,360 50,000 0 0 0 0 18,032 1,99,110 1,787 3558,09,570
Shandong 4,98,726 0 5,000 1,03,860 20,000 10,000 0 0 0 0 5,754 0 47,880 6,91,220 1,812 12524,90,640
Jiangsu 76,900 0 19,920 44,280 10,000 0 27,000 0 2,48,024 0 4,848 0 0 4,30,972 1,866 8041,93,752
Anhui 84,857 0 21,351 36,360 5,000 5,000 0 0 0 0 4,500 31,410 21,000 2,09,478 1,842 3858,58,476
Hubei 6,886 0 51,656 0 30,000 0 600 20,000 0 2,192 0 0 0 1,11,334 1,837 2045,20,558
Hunan 17,634 0 51,440 8,100 20,000 0 7,000 0 0 10,560 0 0 0 1,14,734 1,901 2181,09,334
Jiangxi 17,426 0 12,960 5,040 10,000 0 29,260 0 0 14,160 0 0 0 88,846 1,915 1701,40,090
Fujian 33,600 0 726 7,020 0 40,000 0 0 0 0 0 42,750 31,080 1,55,176 1,960 3041,44,960
Guangdong 22,229 0 4,152 6,498 0 0 14,652 0 0 15,200 0 8,700 52,983 1,24,414 1,930 2401,19,020
Guangxi 9,514 0 0 5,220 0 0 2,400 0 0 0 0 0 8,400 25,534 1,917 489,48,678
Manuf Qty 9,50,472 2,92,479 2,95,354 2,44,668 1,77,000 1,25,000 1,61,192 70,000 2,48,024 1,18,808 72,354 82,860 3,11,311 31,49,522 58473,34,134
Average
Manufacturing
Price (RMB)
1700 1750 1650 1720 1700 1700 1700 1700 1750 1700 1700 1750 1650
total
manufactoring
cost
total
manufacturing
cost for each
supplier
1615802400 5118,38,250 4873,34,100 4208,28,960 3009,00,000 2125,00,000 2740,26,400 1190,00,000 4340,42,000 2019,73,600 1230,01,800 1450,05,000 5136,63,150 53599,15,660
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2. Optimizing the Supply Chain ( Refer Sheet ‘Optimized & Profit’)
Transportation Model- Maximization In Exhibit 4, Average Freight cost from factory to each provincial market is given. Therefore, to calculate the profit we require average selling cost and average manufacturing cost, which are available from Exhibit 1 and Exhibit2. Profit for supplier Sinofert Pingyuan and Heilongjiang is calculated as below
Profit Coefficient= Average selling price of Heilongjiang – Average manufacturing price of Sinofert Pingyua – Average freight cost from Exhibit 4
(Table C)
(Table D)
Suppliers/
Supplied province Sinofert Pingyuan
Sinofert
Changshan
Shanxi
Fengxi
Shandong
Lianmeng
Shandong
Ruixing
Shandong
Lunan
Henan
Xinlianxin
Henan
Pingdingshan
Jiangsu
Linggu
Hebei
Zhengyuan
Hebei
Jinghua Anhui Haoyuan Neimeng Erduosi
Heilongjiang 98 97 138 61 72 98 32 74 3 97 109 16 112
Jilin 63 74 104 25 36 62 -3 41 -33 63 74 -19 77
Liaoning 99 70 139 62 73 98 32 75 4 98 111 18 112
Hebei 53 -52 103 14 25 51 -7 40 -44 58 66 -21 73
Henan 4 -93 98 -18 10 38 3 65 -44 17 18 -9 78
Shandong 54 -48 112 39 51 76 -7 48 -15 50 66 4 73
Jiangsu 99 -34 160 74 101 135 49 112 72 92 109 70 132
Anhui 73 -48 139 49 77 111 28 101 49 67 84 56 111
Hubei 41 -63 131 19 47 77 28 98 10 51 55 26 102
Hunan 79 -9 165 59 87 120 60 127 66 87 94 71 141
Jiangxi 101 5 177 80 108 143 62 145 99 101 115 94 155
Fujian 131 40 208 111 136 174 89 176 144 132 146 125 186
Guangdong 66 10 154 46 69 104 68 111 63 72 81 55 129
Guangxi 61 7 158 40 49 84 65 124 40 69 75 35 123
Suppliers/
Supplied
province
Sinofert
Pingyuan
Sinofert
Changshan
Shanxi
Fengxi
Shandong
Lianmeng
Shandong
Ruixing
Shandong
Lunan
Henan
Xinlianxin
Henan
Pingdingshan
Jiangsu
Linggu
Hebei
Zhengyuan
Hebei
Jinghua
Anhui
Haoyuan
Neimeng
Erduosi
Total
Demand Demand
Heilongjiang 0 2,20,000
Jilin 0 4,00,000
Liaoning 0 1,80,000
Hebei 0 2,00,000
Henan 0 2,10,000
Shandong 0 5,00,000
Jiangsu 0 4,50,000
Anhui 0 2,30,000
Hubei 0 2,00,000
Hunan 0 2,00,000
Jiangxi 0 2,70,000
Fujian 0 1,80,000
Guangdong 0 2,30,000
Guangxi 0 1,00,000
Total Supply 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Supply 9,80,000 3,00,000 3,00,000 3,50,000 3,00,000 1,20,000 3,00,000 1,00,000 4,50,000 1,20,000 1,20,000 1,00,000 3,50,000
Sum (Demand Side)
Sum (Supply Side)
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Objective:
Profit needs to be maximized
Constraints:
Sum of demand= Sum of Sales
Supply to Jiangsu from Jiangsu Linggu >= 200000
Supply to Jilin from Sinofert Changshan >= 250000
Sum of supply of Sinofert Pingyuan =980000
Sum of Supply of Sinofert Changshan =300000
Sum of Supply of Sinofert Pingyuan and Sinofert Changshan <=2000000
Sum of supply ( Except Sinofert Pingyuan and Sinofert Changshan) <= Contract Quantity
After satisfying all the constraints and using Solver, we get the below result:
After using optimization, New Profit= 323610000 whereas Profit in 2009 was 246745455. Hence, the profit has been optimized by 323610000-246745455=76864545 Optimized values for each province are as follows:
Suppliers/
Supplied province Sinofert Pingyuan
Sinofert
Changshan
Shanxi
Fengxi
Shandong
Lianmeng
Shandong
Ruixing
Shandong
Lunan
Henan
Xinlianxin
Henan
Pingdingshan
Jiangsu
Linggu
Hebei
Zhengyuan
Hebei
Jinghua Anhui Haoyuan Neimeng Erduosi Total Demand Demand
Heilongjiang 220000 0 0 0 0 0 0 0 0 0 0 0 0 220000 2,20,000
Jilin 100000 300000 0 0 0 0 0 0 0 0 0 0 0 400000 4,00,000
Liaoning 180000 0 0 0 0 0 0 0 0 0 0 0 0 180000 1,80,000
Hebei 0 0 0 0 0 0 0 0 0 120000 80000 0 0 200000 2,00,000
Henan 0 0 0 0 0 0 0 0 0 0 0 0 210000 210000 2,10,000
Shandong 360000 0 0 100000 0 0 0 0 0 0 40000 0 0 500000 5,00,000
Jiangsu 120000 0 0 0 70000 60000 0 0 200000 0 0 0 0 450000 4,50,000
Anhui 0 0 0 0 230000 0 0 0 0 0 0 0 0 230000 2,30,000
Hubei 0 0 100000 0 0 0 0 100000 0 0 0 0 0 200000 2,00,000
Hunan 0 0 100000 0 0 0 0 0 0 0 0 0 100000 200000 2,00,000
Jiangxi 0 0 0 0 0 60000 0 0 70000 0 0 100000 40000 270000 2,70,000
Fujian 0 0 0 0 0 0 0 0 180000 0 0 0 0 180000 1,80,000
Guangdong 0 0 0 0 0 0 230000 0 0 0 0 0 0 230000 2,30,000
Guangxi 0 0 100000 0 0 0 0 0 0 0 0 0 0 100000 1,00,000
Total Supply 980000 300000 300000 100000 300000 120000 230000 100000 450000 120000 120000 100000 350000 1280000
Supply 9,80,000 3,00,000 3,00,000 3,50,000 3,00,000 1,20,000 3,00,000 1,00,000 4,50,000 1,20,000 1,20,000 1,00,000 3,50,000
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Province Optimized Demand Supplier Optimized Supply
Heilongjiang 220000 Sinofert Pingyuan 980000
Jilin 400000 Sinofert Changshan 300000
Liaoning 180000 Shanxi Fengxi 300000
Hebei 200000 Shandong Lianmeng 100000
Henan 210000 Shandong Ruixing 300000
Shandong 500000 Shandong Lunan 120000
Jiangsu 450000 Henan Xinlianxin 230000
Anhui 230000 Henan Pingdingshan 100000
Hubei 200000 Jiangsu Linggu 450000
Hunan 200000 Hebei Zhengyuan 120000
Jiangxi 270000 Hebei Jinghua 120000
Fujian 180000 Anhui Haoyuan 100000
Guangdong 230000 Neimeng Erduosi 350000
Guangxi 100000
3. Demand Forecast: (Refer sheet ‘Demand Forecast’)- Using the demand of 2009 and 2010 we can forecast the demand using the moving average method.
Forecast
Province 2009 2010 2011
Heilongjiang 220610 220000 220305
Jilin 426451 400000 413226
Liaoning 157694 180000 168847
Hebei 193949 200000 196975
Henan 199110 210000 204555
Shandong 691220 500000 595610
Jiangsu 430972 450000 440486
Anhui 209478 230000 219739
Hubei 111334 200000 155667
Hunan 114734 200000 157367
Jiangxi 88846 270000 179423
Fujian 155176 180000 167588
Guangdong 124414 230000 177207
Guangxi 25534 100000 62767
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Conclusion:
We found out that using the optimized supply and demand Sinofert can optimize their profit by 76864545.
Sinofert can do planning more effectively if they take in consideration the forecast results of 2011.
The outsourcing partners can use their 4 Million tons capacity in an efficient way if they know the forecasted demand.
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