Towards a Useful Whey Economic Model What we know so far

Transcription

1 Towards a Useful Whey Economic Model What we know so far R. García-Flores, O. Vieira de Souza Filho and P. Juliano CSIRO COMPUTATIONAL INFORMATICS

2 Contents Extracting value from the whey supply chain First steps toward a useful model Modelling production Existing models: Network design and technology selection (CSIRO) Production logistics (CEPEAD-UFMG) How do we get there? Towards a Useful Economic Model: Slide 2 of 42

3 Contents Extracting value from the whey supply chain First steps toward a useful model Modelling production Existing models: Network design and technology selection (CSIRO) Production logistics (CEPEAD-UFMG) How do we get there? DATA GATHERING Towards a Useful Economic Model: Slide 3 of 42

4 Modelling the Supply Chain Towards a Useful Economic Model: Slide 4 of 42

5 Optimisation of Product Mix OPM (Optimal Product Mix) is a decision support tool for the Murray- Goulburn Co-operative. Find the best combination of products and transportation schedule to maximise revenue and minimise waste. Provided as an Excel interface to a linear programming solver. Built in collaboration with the company s managers. Input data: Milk composition, processing stages, plant and equipment availabilities and capacities and composition requirements. Towards a Useful Economic Model: Slide 5 of 42

6 Developing a useful a model a All models are wrong, but some models are useful What aspects of the problem should the model consider? Towards a Useful Economic Model: Slide 6 of 42

7 Discussion Highlights Data to collect from questionnaires and expert knowledge: Geographical Production Minimum capacities and economies of scale Investment costs and estimates Market information (prices and demands) A list of plausible scenarios relevant to all four countries. Aspects to cover: transportation, facility location and technology selection. Drinks and biomass production are a priority in all countries involved. Towards a Useful Economic Model: Slide 7 of 42

8 Modelling Production Cheesemaker cluster data: Number of sites per cluster Cheesemaker location and size Whey volumes produced per year Type of whey (sweet, acid) Whey quality (if available) Cheese making Cheese whey Sweet 6<pH<7 Acid ph<5 (a) Direct disposal (b) Animal feed (storage refr) (c) Preprocessing Pasteurization + Storage (refrigeration) + Concentration? Cost requirements (a): Environmental costs for whey disposal Transportation costs Liquid whey Whey concentrate Market price inputs (b): Market price of animal products from whey (d) Preprocessing Storage (refrigeration) Transportation cost, Optimum transportation routes Transportation cost, Optimum transportation routes Cost inputs(b): Animal feed preservation cost Costs of animal products from whey Transportation costs Liquid whey Whey concentrate Market price inputs (c): Whey based ingredients Whey soups, Bars WPC, WPI Biogas Bioethanol Food grade lactose Ricotta cheese manuf costs Location and scale of processing site according to cheesemaker cluster region Biogas, Bioethanol Animal products Direct use Protein separation (ultrafiltration/ diafiltration) Cost inputs (c): Whey storage costs Pasteurisation costs Refrigeration costs Distribution infrastructure costs Fuel costs per country Transportation costs for Liquid whey Whey concentrate Cost of building processing site Concentration costs Drying costs Whey soups costs Whey bar costs WPC, WPI production costs Ricotta cheese manuf. costs Biogas, Bioethanol production costs Lactose Drying Concentration Ricotta cheese Whey Protein Lactose Minerals Whey based ingredients / other whey products WPC, WPI Biogas, Bioethanol Crystallization Food grade lactose Towards a Useful Economic Model: Slide 8 of 42

9 Network Design and Technology Selection Model CSIRO Towards a Useful Economic Model: Slide 9 of 42

10 Case Study Figure 1: Hypothetical dairy farms and connecting road network. Towards a Useful Economic Model: Slide 10 of 42

11 Model Assumptions A cluster of equivalent small cheese producers produce different amounts of whey. Towards a Useful Economic Model: Slide 11 of 42

12 Model Assumptions A cluster of equivalent small cheese producers produce different amounts of whey. The whey produced is transported to a processing facility whose location must be determined from the cheese producers in the cluster. Towards a Useful Economic Model: Slide 12 of 42

13 Model Assumptions A cluster of equivalent small cheese producers produce different amounts of whey. The whey produced is transported to a processing facility whose location must be determined from the cheese producers in the cluster. The selected facility dries up the whey in one stage. Towards a Useful Economic Model: Slide 13 of 42

14 Model Assumptions A cluster of equivalent small cheese producers produce different amounts of whey. The whey produced is transported to a processing facility whose location must be determined from the cheese producers in the cluster. The selected facility dries up the whey in one stage. Each of the candidate whey processing facilities may use one of two types of drier, or technologies, named D1 and D2. Towards a Useful Economic Model: Slide 14 of 42

15 Model Assumptions A cluster of equivalent small cheese producers produce different amounts of whey. The whey produced is transported to a processing facility whose location must be determined from the cheese producers in the cluster. The selected facility dries up the whey in one stage. Each of the candidate whey processing facilities may use one of two types of drier, or technologies, named D1 and D2. The driers differ in their efficiency and in their operating costs. These may correspond to spray drying or roller drying techniques (Jelen, 2009). Towards a Useful Economic Model: Slide 15 of 42

16 Decision Variables Network flow: k Commodity, whey produced by a cheese maker. x ij Indicate if link between nodes i and j are open. y k ij Fraction of commodity supply k that flows on link (i, j). z i Indicates if an whey processing facility is located at node i. wi k Fraction of commodity supply k served by node i. Technology selection: δ ie Take the value one if site i selects technology e. π ie Replaces the product z i δ ie. Towards a Useful Economic Model: Slide 16 of 42

17 Objective Function The following model builds upon Melkote and Daskin (2001). Maximise the profit of the cluster of cheese makers, expressed as the income from the whey protein sales, minus the cost of setting up the whey processing facility, minus the variable transportation costs, minus fixed transportation costs, (pqφη e g ie ) π ie e E i N (i,j) L k N,k i T C ij y k ij (i,j) L c ij x ij. Towards a Useful Economic Model: Slide 17 of 42

18 Mathematical Model Subject to: Nodes selected as facilities fulfill the total processing demand; there are no outbound links transporting whey from the sites chosen as facilities. z i + j N x ij = 1 i N, (1) Processing demand of all other nodes that are not facilities is supplied by the facilities. z k + wi k = 1 k N, (2) i N,i k Towards a Useful Economic Model: Slide 18 of 42

19 Mathematical Model Flow conservation: x ki + yji k = yij k + wi k j N :j k j N i, k N, i k, (k, i) L, (3) yji k = yij k + wi k j N j N i, k N, i k, (k, i) / L, (4) Flow is only permitted in the links that are part of the transportation design, y k ij x ij (i, j) L, k N, i k, (5) Towards a Useful Economic Model: Slide 19 of 42

20 Mathematical Model Whey produced by an individual cheese maker is processed by a node only if this node is selected as a facility, w k i z i i, k N, i k. (6) Links are open or closed, regardless of their direction, x ij + x ji 1 (i, j) L. (7) Only one combination of site and technology is chosen, δ ie = 1. (8) i N e E Towards a Useful Economic Model: Slide 20 of 42

21 Mathematical Model The total amount of protein is Qφη 1 z i δ i1 + Qφη 2 z i δ i2, (9) And variables π ie are used to replace the products z i δ ie. With these, we can write the budget constraint as g ie π ie + c ij x ij B (10) i N e E (i,j) L Towards a Useful Economic Model: Slide 21 of 42

22 Case Study Figure 2: Optimal transportation network showing removed links. Towards a Useful Economic Model: Slide 22 of 42

23 Case Study Figure 3: Optimal transportation network. Facility is Wyuna, technology is D1. Towards a Useful Economic Model: Slide 23 of 42

24 Logistics and Production Model CEPEAD-UFMG Towards a Useful Economic Model: Slide 24 of 42

25 Brazilian Whey Producers Towards a Useful Economic Model: Slide 25 of 42

26 Model Assumptions The model aims at determining the viability of whey processing supply chains taking into account transportation logistics. Towards a Useful Economic Model: Slide 26 of 42

27 Model Assumptions The model aims at determining the viability of whey processing supply chains taking into account transportation logistics. Determine (by comparing scenarios) the optimal site to place a number of processing facilities. Towards a Useful Economic Model: Slide 27 of 42

28 Model Assumptions The model aims at determining the viability of whey processing supply chains taking into account transportation logistics. Determine (by comparing scenarios) the optimal site to place a number of processing facilities. Data on collection frequency, volumes and commercial links between producers and buyers obtained from questionnaires. Towards a Useful Economic Model: Slide 28 of 42

29 Model Assumptions The model aims at determining the viability of whey processing supply chains taking into account transportation logistics. Determine (by comparing scenarios) the optimal site to place a number of processing facilities. Data on collection frequency, volumes and commercial links between producers and buyers obtained from questionnaires. Processing options include waste, refrigeration, concentration and drying. Towards a Useful Economic Model: Slide 29 of 42

30 Model Assumptions The model aims at determining the viability of whey processing supply chains taking into account transportation logistics. Determine (by comparing scenarios) the optimal site to place a number of processing facilities. Data on collection frequency, volumes and commercial links between producers and buyers obtained from questionnaires. Processing options include waste, refrigeration, concentration and drying. This model already assumes minimum processing thresholds, investments and value per litre of whey for each processing option. Towards a Useful Economic Model: Slide 30 of 42

31 Model Assumptions The model aims at determining the viability of whey processing supply chains taking into account transportation logistics. Determine (by comparing scenarios) the optimal site to place a number of processing facilities. Data on collection frequency, volumes and commercial links between producers and buyers obtained from questionnaires. Processing options include waste, refrigeration, concentration and drying. This model already assumes minimum processing thresholds, investments and value per litre of whey for each processing option. The optimiser does not determine the site of concentrators or dryers. Towards a Useful Economic Model: Slide 31 of 42

32 Logistics Model Refrigeration Waste Cheese Production Concentration Drying Towards a Useful Economic Model: Slide 32 of 42

33 Decision Variables and Objective Function X ij Amount of whey sent from i to a concentration unit j. P C jk Amount of whey sent from j to a drying unit k. S k Whey demand in a drying unit k. Minimise the costs of whey transportation, from producers to concentrators to dryers, C ij X ij + i j j D jk P C jk. k Towards a Useful Economic Model: Slide 33 of 42

34 Mathematical Model Minimum demands for concentration units, X ij (11) i Minimum demands for drying units, S k > (12) The amount of whey transported from municipality i cannot exceed the production in i, X ij = P r i. (13) j Towards a Useful Economic Model: Slide 34 of 42

35 Mathematical Model The concentrated whey protein is one third of the mass of liquid whey, X ij = 3 P C jk. (14) i j j k The dry whey protein is a fraction of the mass of concentrate whey, P C jk = S k (15) j k k Towards a Useful Economic Model: Slide 35 of 42

36 Optimal Locations of Concentration Units Towards a Useful Economic Model: Slide 36 of 42

37 Optimal Locations of Drying Units Towards a Useful Economic Model: Slide 37 of 42

38 Next Steps Optimal selection of routes, processes and facilities is not easy, even for small supply networks. Towards a Useful Economic Model: Slide 38 of 42

39 Next Steps Optimal selection of routes, processes and facilities is not easy, even for small supply networks. Next: Compile a list of plausible scenarios, investments and processes. Collect the necessary data to model these scenarios, investments and processes. Determine actual volume, quality and type of whey. State relevant questions and use the model to answer them. What if...? Towards a Useful Economic Model: Slide 39 of 42

40 Next Steps Optimal selection of routes, processes and facilities is not easy, even for small supply networks. Next: Compile a list of plausible scenarios, investments and processes. Collect the necessary data to model these scenarios, investments and processes. Determine actual volume, quality and type of whey. State relevant questions and use the model to answer them. What if...? Stakeholders involvement is paramount to achieve the aim of the model. Towards a Useful Economic Model: Slide 40 of 42

41 References P Jelen. Dried Whey, Whey Proteins, Lactose and Lactose Derivative Products, volume Dairy Powders and Concentrated Products (ed A. Y. Tamime), chapter 7, pages Wiley-Blackwell, Oxford, UK, S Melkote and MS Daskin. An integrated model of facility location and transportation network design. Transportation Design Part A, 35: , Towards a Useful Economic Model: Slide 41 of 42

42 CSIRO Computational Informatics Rodolfo García-Flores t e Rodolfo.Garcia-Flores@csiro.au w CSIRO Computational Informatics web CSIRO COMPUTATIONAL INFORMATICS