When the TARRES company began to have financial performance problems due to the impact of the pandemic generated by Covid - 19, they noticed the opportunity to add economic value through a better design of the logistics network, since they carried out mathematical simulations where they concluded that a change In this network, it would be more efficient and would add value in reducing transportation costs, as well as improving the level of service. This company is dedicated to the production and sale of fertilizers and has three production plants and twenty wineries, from which they serve the demand of their customers.

The current logistics network can be seen in the following diagram¹:

Figure 1: Current distribution network

Given the interest of the Board of Directors of the company in evaluating the change in the design of the network, you are hired as consultants to develop an optimization model with linear programming that includes the use of two centers of distribution (CEDIs), where the plants deliver to any of these CEDIs (they can deliver to one or both of them in specific) and from these, the demand of all the wineries is met (the wineries can receive product from one or both CEDIs). The new network is shown in Figure 2.

Figure 2: New distribution network

The company has high expectations of this optimization model and are waiting for the results to be able to answer the questions that are posed later.

The TARRES supply chain manager comments that this type of model is known in the literature as a transshipment model² and that they are a complex version of the transport model, since they are made up of two flow stages instead of one. In Figure 1 the system consists of two levels (plants and warehouses) and all the flow happens in one stage, from the plants to the warehouses. On the other hand, in transshipment models there are three levels, namely: plants, distribution centers and warehouses; in these systems, the flow regularly happens in two stages³.

In the case of TARRES, the following information is provided:

• The CEDIs do not have their own demand, they are centers of added value for the distributionorn efficient.

• CEDIs do not have lstorage and processing capacity limit.

• The company's demand is what is generated in the warehouses and the capacity is what is in the plants.

• The unit of measure, for both demand and capacity, is pounds of fertilizer.

• The unit costs of distributionorn are taken per pound.

• Plant 1's capacity is 7,200 pounds.

• Plant 2 capacity is 8,250 pounds.

• The capacity of Plant 3 is 7,500 pounds.

• The costs of distributing from plant 1 to CEDIs 1 and 2 are respectively: $ 1.36 and $1.28.

• The costs of distributing from plant 2 to CEDIs 1 and 2 are respectively: $ 1.28 and $ 1.35.

• The costs of distributing from plant 3 to CEDIs 1 and 2 are respectively: $ 1.68 and $ 1.55.

Additionally, Table 1 shows the costs from each CEDI to each winery and the respective demand for each winery.

Table 1: Costs and demands in the CEDI - Warehouses stage

	Origin
Destiny	CEDI 1	CEDI 2	Demand
W1	0.6	0.8	1250
W2	0.36	0.56	1000
W3	0.32	0.42	1600
W4	0.44	0.4	1750
W5	0.72	0.55	1500
W6	0.08	0.04	615
W7	0.05	0.09	1169
W8	0.07	0.08	1355
W9	0.08	0.07	1334
W10	0.05	0.04	751
W11	0.04	0.06	1166
W12	0.06	0.08	1358
W13	0.05	0.09	1415
W14	0.09	0.03	733
W15	0.03	0.07	908
W16	0.03	0.06	1447
W17	0.09	0.05	791
W18	0.06	0.06	608
W19	0.03	0.07	781
W20	0.07	0.08	1419

As the Board of Directors of the company is so interested in the results of this model, you are hired, but are instructed to deliver the model and the analysis of the results a week later. In addition, they are instructed that the model must be made and delivered in MS Excel using the Solver add-in, this so that the company's analysts can use and modify it in the future. Please step by step.

¹C: Capacity. P: Plant. W: Cellar. D: Demand.

²The CEDIs are known as transshipment points due to the fact that the products arrive at these facilities and then must be dispatched to their destinations.

³For the development of these models, two-stage transport models or programming models can be used.orn that work with balance equations to apply the law of conservation.orn of flows in networks. This law states that the total amount that leaves a node must be equal to the amount that enters.

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