Production-Distribution Coordination of Industrial Gases Supply-chains
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1 Production-Distribution Coordination of Industrial Gases Supply-chains Pablo A. Marchetti, Ignacio E. Grossmann Department of Chemical Engineering Carnegie Mellon University Pittsburgh, PA Lauren Cook, Tong Li, Jean André Delaware Research and Technology Center American Air Liquide Inc. Newark, DE Center for Advanced Process Decision-making Enterprise-Wide Optimization (EWO) Meeting March 12-13, 2013
2 Background and Motivation 2
3 Background and Motivation Industrial Gases Supply-Chain Multiple Plants and Depots (located or not at plants) Multiple Products (LIN, LOX etc.) and Product Grades Over-the-fence, call-in and distributed customers (some shared customers) Storage facilities at production sites and customer locations 2
4 Background and Motivation Industrial Gases Supply-Chain Multiple Plants and Depots (located or not at plants) Multiple Products (LIN, LOX etc.) and Product Grades Over-the-fence, call-in and distributed customers (some shared customers) Storage facilities at production sites and customer locations C1 C3 C5 Plant 1 Plant 2 C2 C4 2
5 Background and Motivation Industrial Gases Supply-Chain Multiple Plants and Depots (located or not at plants) Multiple Products (LIN, LOX etc.) and Product Grades Over-the-fence, call-in and distributed customers (some shared customers) Storage facilities at production sites and customer locations C1 D1 C3 D2 C5 Plant 1 Plant 2 C2 C4 2
6 Background and Motivation Industrial Gases Supply-Chain Multiple Plants and Depots (located or not at plants) Multiple Products (LIN, LOX etc.) and Product Grades Over-the-fence, call-in and distributed customers (some shared customers) Storage facilities at production sites and customer locations C1 D1 C3 D2 C5 Plant 1 Plant 2 D3 C2 C4 2
7 Background and Motivation Industrial Gases Supply-Chain Multiple Plants and Depots (located or not at plants) Multiple Products (LIN, LOX etc.) and Product Grades Over-the-fence, call-in and distributed customers (some shared customers) Storage facilities at production sites and customer locations C1 D1 C3 D2 C5 Plant 1 Plant 2 D3 C2 C4 2
8 Background and Motivation Industrial Gases Supply-Chain Multiple Plants and Depots (located or not at plants) Multiple Products (LIN, LOX etc.) and Product Grades Over-the-fence, call-in and distributed customers (some shared customers) Storage facilities at production sites and customer locations C1 D1 C3 D2 C5 Plant 1 Plant 2 D3 C2 C4 Alternative Source 2
9 Background and Motivation Industrial Gases Supply-Chain Multiple Plants and Depots (located or not at plants) Multiple Products (LIN, LOX etc.) and Product Grades Over-the-fence, call-in and distributed customers (some shared customers) Storage facilities at production sites and customer locations C1 D1 C3 D2 C5 Plant 1 Plant 2 D3 C2 C4 Alternative Source Goal To quantify and access the savings associated with the Production-Distribution Coordination at Operational Level using an approximate model 2
10 Problem Statement and Main Assumptions 3
11 Problem Statement and Main Assumptions Given Plants, Products, Operating Modes and Production Limits Daily Electricity Prices (off-peak and peak) Customers and their demand/consumption profiles Max/Min inventory at production sites and customer locations Alternative sources and product availabilities Depots, Truck availabilities and capacities, Distances Fixed Planning Horizon (usually 1-2 weeks) 3
12 Problem Statement and Main Assumptions Given Plants, Products, Operating Modes and Production Limits Daily Electricity Prices (off-peak and peak) Customers and their demand/consumption profiles Max/Min inventory at production sites and customer locations Alternative sources and product availabilities Depots, Truck availabilities and capacities, Distances Fixed Planning Horizon (usually 1-2 weeks) Decisions in each time period t Modes and production rates at each plant Inventory level at customer location and plants How much product to be delivered to each customer through which route 3
13 Problem Statement and Main Assumptions Given Plants, Products, Operating Modes and Production Limits Daily Electricity Prices (off-peak and peak) Customers and their demand/consumption profiles Max/Min inventory at production sites and customer locations Alternative sources and product availabilities Depots, Truck availabilities and capacities, Distances Fixed Planning Horizon (usually 1-2 weeks) Decisions in each time period t Modes and production rates at each plant Inventory level at customer location and plants How much product to be delivered to each customer through which route Objective Function Minimize total production and distribution cost over planning horizon 3
14 Problem Statement and Main Assumptions Given Plants, Products, Operating Modes and Production Limits Daily Electricity Prices (off-peak and peak) Customers and their demand/consumption profiles Max/Min inventory at production sites and customer locations Alternative sources and product availabilities Depots, Truck availabilities and capacities, Distances Fixed Planning Horizon (usually 1-2 weeks) Decisions in each time period t Modes and production rates at each plant Inventory level at customer location and plants How much product to be delivered to each customer through which route Objective Function Minimize total production and distribution cost over planning horizon Main Assumptions Distribution Side Two time periods per day (peak and off-peak) are considered Trucks do not visit more than 4 customers in a single delivery 3
15 Mathematical Model (MILP) 4
16 Mathematical Model (MILP) Objective Minimize total Production and Distribution Costs 4
17 Mathematical Model (MILP) Objective Minimize total Production and Distribution Costs Constraints on Production Side 4
18 Mathematical Model (MILP) Objective Minimize total Production and Distribution Costs Constraints on Production Side 4
19 Mathematical Model (MILP) Objective Minimize total Production and Distribution Costs Constraints on Production Side Production Cost = Fixed Start-up cost + Variable production cost 4
20 Mathematical Model (MILP) Objective Minimize total Production and Distribution Costs Constraints on Production Side Production Cost = Fixed Start-up cost + Variable production cost Min/Max Production Capacity Constraints in each mode of operation Logic Constraints for switching between various modes of operation Max/Min Inventory limits at the production sites Plant Inventory Balance Constraints Demand satisfaction for pick-up customers 4
21 Mathematical Model (MILP) Objective Minimize total Production and Distribution Costs Constraints on Production Side Production Cost = Fixed Start-up cost + Variable production cost Min/Max Production Capacity Constraints in each mode of operation Logic Constraints for switching between various modes of operation Max/Min Inventory limits at the production sites Plant Inventory Balance Constraints Demand satisfaction for pick-up customers Ad Hoc Production Models To account for specific equipment configurations and production modes. 4
22 Mathematical Model (MILP) Objective Minimize total Production and Distribution Costs Constraints on Production Side Production Cost = Fixed Start-up cost + Variable production cost Min/Max Production Capacity Constraints in each mode of operation Logic Constraints for switching between various modes of operation Max/Min Inventory limits at the production sites Plant Inventory Balance Constraints Demand satisfaction for pick-up customers Ad Hoc Production Models To account for specific equipment configurations and production modes. Main binary variables mode selection B pmt 4
23 Mathematical Model (MILP) Constraints on Distribution Side 5
24 Mathematical Model (MILP) Constraints on Distribution Side 5
25 Mathematical Model (MILP) Constraints on Distribution Side Distribution Cost = Cost of deliveries by trucks + purchases from competitors 5
26 Mathematical Model (MILP) Constraints on Distribution Side Distribution Cost = Cost of deliveries by trucks + purchases from competitors Max/Min Inventory limits at the customer locations Customer Inventory Balance Constraints Truck Capacity constraints Material balance constraints for product pick-up and delivery points Max product purchase limit from competitor sources 5
27 Mathematical Model (MILP) Constraints on Distribution Side Distribution Cost = Cost of deliveries by trucks + purchases from competitors Max/Min Inventory limits at the customer locations Customer Inventory Balance Constraints Truck Capacity constraints Material balance constraints for product pick-up and delivery points Max product purchase limit from competitor sources Route = Depot + Plant + Customers 5
28 Mathematical Model (MILP) Constraints on Distribution Side Distribution Cost = Cost of deliveries by trucks + purchases from competitors Max/Min Inventory limits at the customer locations Customer Inventory Balance Constraints Truck Capacity constraints Material balance constraints for product pick-up and delivery points Max product purchase limit from competitor sources Route = Depot + Plant + Customers truck k D1 P1 C1 C2 Cn 5
29 Mathematical Model (MILP) Constraints on Distribution Side Distribution Cost = Cost of deliveries by trucks + purchases from competitors Max/Min Inventory limits at the customer locations Customer Inventory Balance Constraints Truck Capacity constraints Material balance constraints for product pick-up and delivery points Max product purchase limit from competitor sources Route = Depot + Plant + Customers truck k Customer Set D1 P1 C1 C2 Cn 5
30 Mathematical Model (MILP) Constraints on Distribution Side Distribution Cost = Cost of deliveries by trucks + purchases from competitors Max/Min Inventory limits at the customer locations Customer Inventory Balance Constraints Truck Capacity constraints Material balance constraints for product pick-up and delivery points Max product purchase limit from competitor sources Main binary variables truck-customers association y kst Route = Depot + Plant + Customers Customer Set truck k D1 P1 C1 C2 Cn truck-source association Y kpt 5
31 Mathematical Model (MILP) Constraints on Distribution Side Distribution Cost = Cost of deliveries by trucks + purchases from competitors Max/Min Inventory limits at the customer locations Customer Inventory Balance Constraints Truck Capacity constraints Material balance constraints for product pick-up and delivery points Max product purchase limit from competitor sources Main binary variables truck-customers association y kst truck-source association Y kpt Route = Depot + Plant + Customers truck k Customer Set D1 P1 C1 C2 Cn Route Generation Algorithm Parameters: maximum distance, number of customers visited, etc Main ordering criteria: traveling distance 5
32 Supply-chain Example Definition of Customer Sets: Depots Plants Customers D1 truck k P1 C 1 C 2 D2 P2 C 3 6
33 Supply-chain Example Definition of Customer Sets: Depots Plants Customers D1 truck k P1 C 1 C 2 D2 P2 C 3 7
34 Supply-chain Example Definition of Customer Sets: Depots Plants Customers D1 truck k P1 C 1 C 2 D2 P2 C 3 7
35 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k D1 P1 C 1 C 2 D2 P2 C 3 7
36 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k s 1 D1 P1 C 1 C 2 D2 P2 C 3 7
37 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k s 1 D1 P1 s 2 C 1 C 2 D2 P2 C 3 7
38 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k s 1 D1 P1 s 2 C 1 s 3 C 2 D2 P2 C 3 7
39 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k s 1 D1 P1 s 2 C 1 s 3 C 2 D2 P2 s 4 C 3 7
40 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k s 1 D1 P1 s 2 C 1 s 3 C 2 D2 P2 s 4 C 3 s 5 7
41 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k s 1 D1 P1 s 2 C 1 s 3 C 2 D2 P2 s 4 C 3 s 5 7
42 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k s 1 D1 P1 s 2 C 1 s 3 C 2 D2 P2 s 4 C 3 s 5 7
43 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k s 1 D1 P1 s 2 C 1 s 3 C 2 D2 P2 s 4 C 3 s 5 7
44 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k s 1 D1 P1 s 2 C 1 s 3 C 2 D2 P2 s 4 C 3 s 5 7
45 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k s 1 D1 P1 s 2 C 1 s 3 C 2 D2 P2 s 4 C 3 s 5 7
46 Supply-chain Example Definition of Customer Sets: Depots Plants Customer sets Customers truck k s 1 D1 P1 s 2 C 1 s 3 C 2 D2 P2 s 4 C 3 s 5 7
47 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 P1 C 1 s 2 s 3 C 2 D2 P2 s 4 C 3 s 5 8
48 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 P1 C 1 s 2 s 3 C 2 D2 P2 s 4 C 3 s 5 8
49 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 P1 C 1 s 2 s 3 C 2 D2 P2 s 4 C 3 s 5 8
50 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 P1 C 1 s 2 s 3 C 2 truck k D2 P2 s 4 C 3 s 5 8
51 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 truck D p, i, t P1 s 2 C 1 s 3 C 2 truck k D2 P2 s 4 C 3 s 5 8
52 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 truck D p, i, t P1 E kpt s 2 C 1 s 3 C 2 truck k D2 P2 s 4 C 3 s 5 8
53 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets D1 P1 s 2 k 1 s 3 s 4 D2 P2 s 5 9
54 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets D1 P1 truck D p, i, t Ekpt s 2 k 1 s 3 s 4 D2 P2 s 5 9
55 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets D1 truck D p, i, t P1 E kpt s 2 k 1 s 3 k 2 s 4 D2 P2 s 5 9
56 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets D1 truck D p, i, t P1 E kpt s 2 k 1 s 3 k 2 s 4 D2 P2 s 5 9
57 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets D1 truck D p, i, t P1 E kpt s 2 k 1 s 3 k 2 k 3 s 4 D2 P2 s 5 9
58 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets D1 truck D p, i, t P1 E kpt s 2 k 1 s 3 k 2 k 3 s 4 D2 P2 s 5 9
59 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 truck D p, i, t P1 E kpt s 2 C 1 s 3 C 2 truck k D2 P2 s 4 C 3 s 5 10
60 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 truck D p, i, t P1 E kpt s 2 C 1 s 3 C 2 truck k D2 P2 e kst s 4 C 3 s 5 10
61 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 truck D p, i, t P1 E kpt s 2 C 1 s 3 C 2 truck k D2 P2 e kst s 4 C 3 s 5 d sct 10
62 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 truck D p, i, t P1 E kpt s 2 C 1 s 3 C 2 truck k D2 P2 e kst s 4 C 3 s 5 d sct D c, t 10
63 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 truck D p, i, t P1 E kpt s 2 C 1 s 3 C 2 truck k D2 P2 e kst s 4 C 3 s 5 d sct D c, t Material flow (model s perspective) 10
64 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 truck D p, i, t P1 E kpt s 2 C 1 s 3 C 2 truck k D2 P2 e kst s 4 C 3 s 5 d sct D c, t Material flow (model s perspective) Plant - Truck 10
65 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 truck D p, i, t P1 E kpt s 2 C 1 s 3 C 2 truck k D2 P2 e kst s 4 C 3 s 5 d sct D c, t Material flow (model s perspective) Plant - Truck Truck - Customer Set 10
66 Supply-chain Example Meaning of continuous variables to transfer products from plants to customers: Depots Plants Customer sets Customers s 1 D1 truck D p, i, t P1 E kpt s 2 C 1 s 3 C 2 truck k D2 P2 e kst s 4 C 3 s 5 d sct D c, t Material flow (model s perspective) Plant - Truck Truck - Customer Set Customer Set - Customer 10
67 Industrial Size Test Case 11
68 Industrial Size Test Case 4 Plants / Depots 2 products (LIN, LOX) 2-4 production modes for each plant 2 alternative sources 258 customers 14 time periods (peak and off-peak) 37 trucks (25 for LIN, 12 for LOX) Min/max inventory, distances, electricity prices, truck deliveries, etc. 11
69 Industrial Size Test Case 4 Plants / Depots 2 products (LIN, LOX) 2-4 production modes for each plant 2 alternative sources 258 customers 14 time periods (peak and off-peak) 37 trucks (25 for LIN, 12 for LOX) 4 depots 6 sources Min/max inventory, distances, electricity prices, truck deliveries, etc. 11
70 Industrial Size Test Case 4 Plants / Depots 2 products (LIN, LOX) 2-4 production modes for each plant 2 alternative sources 258 customers 14 time periods (peak and off-peak) 37 trucks (25 for LIN, 12 for LOX) 4 depots 6 sources 521 customer sets Min/max inventory, distances, electricity prices, truck deliveries, etc. 11
71 Industrial Size Test Case 4 Plants / Depots 2 products (LIN, LOX) 2-4 production modes for each plant 2 alternative sources 258 customers 14 time periods (peak and off-peak) 37 trucks (25 for LIN, 12 for LOX) 4 depots 6 sources 521 customer sets 15,504 possible routes Min/max inventory, distances, electricity prices, truck deliveries, etc. 11
72 Industrial Size Test Case 4 Plants / Depots 2 products (LIN, LOX) 2-4 production modes for each plant 2 alternative sources 258 customers 14 time periods (peak and off-peak) 37 trucks (25 for LIN, 12 for LOX) 4 depots 6 sources 521 customer sets 15,504 possible routes Min/max inventory, distances, electricity prices, truck deliveries, etc. Model Size CPU results Binary variables 18,378 Continuous variables 26,241 Constraints 27,101 Time 79 s Nodes 1,632 Relative gap 0.1% Models implemented with GAMS CPU results obtained with solver CPLEX
73 Industrial Size Test Case 4 Plants / Depots 2 products (LIN, LOX) 2-4 production modes for each plant 2 alternative sources 258 customers 14 time periods (peak and off-peak) 37 trucks (25 for LIN, 12 for LOX) 4 depots 6 sources 521 customer sets 15,504 possible routes Min/max inventory, distances, electricity prices, truck deliveries, etc. Model Size CPU results Binary variables 18,378 Continuous variables 26,241 Constraints 27,101 Time 79 s Nodes 1,632 Relative gap 0.1% Models implemented with GAMS CPU results obtained with solver CPLEX 12.3 Good solutions found in few CPU sec.!!! 11
74 Industrial Size Test Case Results are compared with historical data by fixing volume sourced from each plant. 12
75 Industrial Size Test Case Results are compared with historical data by fixing volume sourced from each plant. 12
76 Industrial Size Test Case Results are compared with historical data by fixing volume sourced from each plant. Historical Model: Volume sourced is fixed to historical data. Production and distribution subproblems do not need to be solved simultaneously. Production subproblems can be solved for each plant. 12
77 Industrial Size Test Case Results Comparison of volume sourced: optimal model solution vs historical data. 13
78 Industrial Size Test Case Results Comparison of volume sourced: optimal model solution vs historical data. Optimal solution shifts production and distribution from plant P 1 to plant P 4, mainly due to lower electricity costs at P 4 13
79 Industrial Size Test Case Results 14
80 Industrial Size Test Case Results Production cost % for each plant 14
81 Industrial Size Test Case Results Production cost % for each plant Percentage of Total Historical Cost 14
82 Industrial Size Test Case Results Production cost % for each plant Percentage of Total Historical Cost Savings = [Amount saved] [Historical model total] = 9% per week 14
83 Conclusions and Future Work Conclusions Proposed Simultaneous Production-Distribution MILP Model for optimal operational planning of industrial gases supply-chain Multiple products, plants and depots Route generation algorithm Ad hoc production models Selection of routes is a critical aspect to reduce the total cost of production and distribution. Good quality solutions for industrial size examples obtained in short CPU times. Significant potential savings due to better coordination of production and distribution. 15
84 Conclusions and Future Work Conclusions Proposed Simultaneous Production-Distribution MILP Model for optimal operational planning of industrial gases supply-chain Multiple products, plants and depots Route generation algorithm Ad hoc production models Selection of routes is a critical aspect to reduce the total cost of production and distribution. Good quality solutions for industrial size examples obtained in short CPU times. Significant potential savings due to better coordination of production and distribution. Future work Handling uncertainty through stochastic version of the model. 15
85 Production-Distribution Coordination of Industrial Gases Supply-chains Pablo A. Marchetti, Ignacio E. Grossmann Department of Chemical Engineering Carnegie Mellon University Lauren Cook, Tong Li, Jean André Delaware Research and Technology Center American Air Liquide Inc. Thanks for your attention... Questions?
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