I need help with Linear Optimization for a logistics problem

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Supply-Chain-Analytics-Case-Study-Template.xlsx
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Model Attempt

S1 - Store 1
Problem Data C D N T Variable
"From" DistributionDenters X + SUPPLY Travel Times (in Min) Cambridge, OH Dover, OH Newark, OH Toronto, OH
Cambridge, OH Dover, OH Newark, OH Toronto, OH Cambridge, OH 0 45 62 90
S2 - Store 2 Maximum Supply: 45 15 15 15 Bellaire, OH 56 88 105 52
ShippingDosts Decision Variables (48 in total) xIJ = # of units shipped from DistritubionDenter I to Store J Cadiz, OH 56 47 105 38
"To" Stores Minimum Demand LogisticDost per minute per unit: $0.85 I =D (Cambridge), D (Dover), N (Newark), T (Toronto) Calcutta, OH 108 86 154 27
1 Bellaire, OH (S1) 5 $47.60 $74.80 $89.25 $44.20 XC1 = # of units shipped from Cambridge, OH to Bellaire, OH (S1) J = 1(S1), 2(S2), 3(S3), 4(S4), 5(S5), 6(S6), 7(S7), 8(S8), 9(S9), 10(S10), 11(S11), 12(S12) Coshocton, OH 47 46 44 104
S3 - Store 3 2 Cadiz, OH (S2) 5 $47.60 $39.95 $89.25 $32.30 XC2 = # of units shipped from Cambridge, OH to Cadiz, OH (S2) Dover, OH 45 0 81 81
3 Calcutta, OH (S3) 9 $91.80 $73.10 $130.90 $22.95 XC3 = # of units shipped from Cambridge, OH to Calcutta, OH (S3) Objective Function is to minimize cost: East Palestine, OH 129 90 165 48
4 Coshocton, OH (S4) 4 $39.95 $39.10 $37.40 $88.40 XC4 = # of units shipped from Cambridge, OH to Coshocton, OH (S4) Lisbon, OH 106 68 142 38
5 East Palestine, OH (S5) 10 $109.65 $76.50 $140.25 $40.80 XC5 = # of units shipped from Cambridge, OH to East Palestine, OH (S5) Min: 47.6XC1 +47.6XC2 +91.8XC3 +39.95XC4 +109.65XC5 +90.1XC6 +101.15XC7 +79.9XC8 +56.95XC9 +36.55XC10 +71.4XC11 +28.05XC12 +74.8XD1 +39.95XD2 +73.1XD3 +39.1XD4 +76.5XD5 +57.8XD6 +92.65XD7 +106.25XD8 +85.85XD9 +17XD10 +63.75XD11 +56.95XD12 +89.25XN1 +89.25XN2 +130.9XN3 +37.4XN4 +140.25XN5 +120.7XN6 +61.2XN7 +120.7XN8 +22.95XN9 +68XN10 +113.9XN11 +31.45XN12 +44.2XT1 +32.3XT2 +22.95XT3 +88.4XT4 +40.8XT5 +32.3XT6 +147.05XT7 +76.5XT8 +127.5XT9 +55.25XT10 +17.85XT11 +95.2XT12 Mt. Gilead, OH 119 109 72 173
S4 - Store 4 6 Lisbon, OH (S6) 8 $90.10 $57.80 $120.70 $32.30 XC6 = # of units shipped from Cambridge, OH to Lisbon, OH (S6) New Martinsville, WV 94 125 142 90
7 Mt. Gilead, OH (S7) 9 $101.15 $92.65 $61.20 $147.05 XC7 = # of units shipped from Cambridge, OH to Mt. Gilead, OH (S7) Newark, OH 62 81 0 140
8 New Martinsville, WV (S8) 3 $79.90 $106.25 $120.70 $76.50 XC8 = # of units shipped from Cambridge, OH to New Martinsville, WV (S8) Pataskala, OH 67 101 27 150
9 Pataskala, OH (S9) 10 $56.95 $85.85 $22.95 $127.50 XC9 = # of units shipped from Cambridge, OH to Pataskala, OH (S9) Toronto, OH 90 81 140 0
S5 - Store 5 10 Uhrichsville, OH (S10) 5 $36.55 $17.00 $68.00 $55.25 XC10 = # of units shipped from Cambridge, OH to Uhrichsville, OH (S10) Uhrichsville, OH 43 20 80 65
11 Weirton, WV (S11) 7 $71.40 $63.75 $113.90 $17.85 XC11 = # of units shipped from Cambridge, OH to Weirton, WV (S11) Subject To: XC1 + XC2 + XC3 + XC4 + XC5 + XC6 + XC7 + XC8 + XC9 + XC10 + XC11 + XC12 ≤ 45 Weirton, WV 84 75 134 21
12 Zanesville, OH (S12) 6 $28.05 $56.95 $31.45 $95.20 XC12 = # of units shipped from Cambridge, OH to Zanesville, OH (S12) XD1 + XD2 + XD3 + XD4 + XD5 + XD6 + XD7 + XD8 + XD9 + XD10 + XD11 + XD12 ≤ 15 Zanesville, OH 33 67 37 112
Total 81 XN1 + XN2 + XN3 + XN4 + XN5 + XN6 + XN7 + XN8 + XN9 + XN10 + XN11 + XN12 ≤ 15
S6 - Store 6 XD1 = # of units shipped from Dover, OH to Bellaire, OH (S1) XT1 + XT2 + XT3 + XT4 + XT5 + XT6 + XT7 + XT8 + XT9 + XT10 + XT11 + XT12 ≤ 15 What do I know?
Optimized Model XD2 = # of units shipped from Dover, OH to Cadiz, OH (S2) There is a total minimum supply of 81 pallets per day that need to be delivered
XD3 = # of units shipped from Dover, OH to Calcutta, OH (S3) XC1 + XD1 + XN1 + XT1=5 Bellaire, OH (S1) SUPPLY Each truck can deliver a maximum of 26 pallets
maximize: 45C+15D+15N+15T=Z XD4 = # of units shipped from Dover, OH to Coshocton, OH (S4) XC2 + XD2 XN2 XT2=5 Cadiz, OH (S2) Each truck only has 11 hours to deliver everything
S7 - Store 7 objective function XD5 = # of units shipped from Dover, OH to East Palestine, OH (S5) XC3 + XD3 XN3 XT3=9 Calcutta, OH (S3) 11 hours *60 mins = 660 mins
XD6 = # of units shipped from Dover, OH to Lisbon, OH (S6) XC4 + XD4 XN4 XT4=4 Coshocton, OH (S4) 660 mins * $0.85 = $561.00
C D N T Z XD7 = # of units shipped from Dover, OH to Mt. Gilead, OH (S7) XC5 + XD5 XN5 XT5=10 East Palestine, OH (S5) 3 truck * 660 mins = 1980 mins
0 0 0 0 0.00 XD8 = # of units shipped from Dover, OH to New Martinsville, WV (S8) XC6 + XD6 = XN6 = XT6=8 Lisbon, OH (S6) # of units shipped from maximum budget of 3 trucks = $1683.00
S8 - Store 8 45 15 15 15 XD9 = # of units shipped from Dover, OH to Pataskala, OH (S9) XC7 + XD7 = XN7 = XT7=9 Mt. Gilead, OH (S7) # of units shipped from Total travel time for all 5 routs is 1254 minutes or 20.9 hours per day which is $1065.90
XD10 = # of units shipped from Dover, OH to Uhrichsville, OH (S10) XC8 + XD8 = XN8 = XT8=3 New Martinsville, WV (S8) # of units shipped from
Constraints XD11 = # of units shipped from Dover, OH to Weirton, WV (S11) XC9 + XD9 = XN9 = XT9=10 Pataskala, OH (S9) # of units shipped from
C D N T LHS Inequality RHS XD12 = # of units shipped from Dover, OH to Zanesville, OH (S12) XC10 + XD10 = XN10 = XT10=5 Uhrichsville, OH (S10) # of units shipped from
S9 - Store 9 47.6 74.8 89.25 44.2 0 <= 5 XC11 + XD11 = XN11 = XT11=7 Weirton, WV (S11) # of units shipped from
47.6 39.95 89.25 32.3 0 <= 5 XN1 = # of units shipped from Newark, OH to Bellaire, OH (S1) XC12 + XD12 = XN12 = XT12=6 Zanesville, OH (S12) # of units shipped from
91.8 73.1 130.9 22.95 0 <= 9 XN2 = # of units shipped from Newark, OH to Cadiz, OH (S2)
39.95 39.1 37.4 88.4 0 <= 4 XN3 = # of units shipped from Newark, OH to Calcutta, OH (S3) XIJ ≥ 0
S10 - Store 10 109.65 76.5 140.25 40.8 0 <= 10 XN4 = # of units shipped from Newark, OH to Coshocton, OH (S4)
90.1 57.8 120.7 32.3 0 <= 8 XN5 = # of units shipped from Newark, OH to East Palestine, OH (S5)
101.15 92.65 61.2 147.05 0 <= 9 XN6 = # of units shipped from Newark, OH to Lisbon, OH (S6)
79.9 106.25 120.7 76.5 0 <= 3 XN7 = # of units shipped from Newark, OH to Mt. Gilead, OH (S7)
S11 - Store 11 56.95 85.85 22.95 127.5 0 <= 10 XN8 = # of units shipped from Newark, OH to New Martinsville, WV (S8)
36.55 17 68 55.25 0 <= 5 XN9 = # of units shipped from Newark, OH to Pataskala, OH (S9)
71.4 63.75 113.9 17.85 0 <= 7 XN10 = # of units shipped from Newark, OH to Uhrichsville, OH (S10)
28.05 56.95 31.45 95.2 0 <= 6 XN11 = # of units shipped from Newark, OH to Weirton, WV (S11)
S12 - Store 12 XN12 = # of units shipped from Newark, OH to Zanesville, OH (S12)
XT1 = # of units shipped from Toronto, OH to Bellaire, OH (S1)
XT2 = # of units shipped from Toronto, OH to Cadiz, OH (S2)
XT3 = # of units shipped from Toronto, OH to Calcutta, OH (S3)
XT4 = # of units shipped from Toronto, OH to Coshocton, OH (S4)
XT5 = # of units shipped from Toronto, OH to East Palestine, OH (S5)
XT6 = # of units shipped from Toronto, OH to Lisbon, OH (S6)
XT7 = # of units shipped from Toronto, OH to Mt. Gilead, OH (S7)
XT8 = # of units shipped from Toronto, OH to New Martinsville, WV (S8)
XT9 = # of units shipped from Toronto, OH to Pataskala, OH (S9)
XT10 = # of units shipped from Toronto, OH to Uhrichsville, OH (S10)
XT11 = # of units shipped from Toronto, OH to Weirton, WV (S11)
XT12 = # of units shipped from Toronto, OH to Zanesville, OH (S12)

Template

Problem Data L1 L2 L3 L4
"From" Distribution Centers Travel Times (in Min) Cambridge, OH Dover, OH Newark, OH Toronto, OH
Cambridge, OH Dover, OH Newark, OH Toronto, OH Cambridge, OH 0 45 62 90
Maximum Supply: 45 15 15 15 Bellaire, OH 56 88 105 52
Shipping Costs Cadiz, OH 56 47 105 38
"To" Stores Minimum Demand Logistic Cost per minute per unit: $0.85 Calcutta, OH 108 86 154 27
A Bellaire, OH 5 $47.60 $74.80 $89.25 $44.20 Coshocton, OH 47 46 44 104
B Cadiz, OH 5 $47.60 $39.95 $89.25 $32.30 Dover, OH 45 0 81 81
C Calcutta, OH 9 $91.80 $73.10 $130.90 $22.95 East Palestine, OH 129 90 165 48
D Coshocton, OH 4 $39.95 $39.10 $37.40 $88.40 Lisbon, OH 106 68 142 38
E East Palestine, OH 10 $109.65 $76.50 $140.25 $40.80 Mt. Gilead, OH 119 109 72 173
F Lisbon, OH 8 $90.10 $57.80 $120.70 $32.30 New Martinsville, WV 94 125 142 90
G Mt. Gilead, OH 9 $101.15 $92.65 $61.20 $147.05 Newark, OH 62 81 0 140
H New Martinsville, WV 3 $79.90 $106.25 $120.70 $76.50 Pataskala, OH 67 101 27 150
I Pataskala, OH 10 $56.95 $85.85 $22.95 $127.50 Toronto, OH 90 81 140 0
J Uhrichsville, OH 5 $36.55 $17.00 $68.00 $55.25 Uhrichsville, OH 43 20 80 65
K Weirton, WV 7 $71.40 $63.75 $113.90 $17.85 Weirton, WV 84 75 134 21
L Zanesville, OH 6 $28.05 $56.95 $31.45 $95.20 Zanesville, OH 33 67 37 112
Total 81
What do I know?
Optimized Model There is a total minimum supply of 81 pallets per day that need to be delivered
Each truck can deliver a maximum of 26 pallets
Each truck only has 11 hours to deliver everything
11 hours *60 mins = 660 mins
660 mins * $0.85 = $561.00
3 truck * 660 mins = 1980 mins
maximum budget of 3 trucks = $1683.00
Total travel time for all 5 routs is 1254 minutes or 20.9 hours per day which is $1065.90