XYZ is a glass bottle manufacturer which has four plants (P1, P2, P3, and P4) and five customers at cities 1, 2,3,4 and 5. The production capacities at plants are given in Table 1. Based on past data, average demand at each city for the following months is estimated as in Table 2 Currently, the products are shipped from the plants to the customer locations by train. Due to increasing shipping costs, the company is considering using ships and this alter native will require some investment. The shipping costs (per 1000 units) are given in Table 3 for the current shipping strategy (by rail) and for the new one (excluding the investment costs). Table 1 Table 2 Table 3 It is assumed that if invested, a ship will be on service for 10 years and once a shipping plan is obtained, it will not change in the lifetime of the ships. The ship type invested depends on the amount transported. Hence the investment cost is assumed to be proportional to the shipment amount on that route. The required investment on ships for one thousand units to be transported by ship is given in Table 4. for each route. After some economics analysis (taking the time value of the money into consideration) it is decided that monthly equivalent cost of an investment will be one-twentieth(1/20) of it. 1. (45 pts) What is the optimal shipping strategy for each of the following cases? What is the total cost for each of them? a. If the company does not want to invest in ships. b. If ships are used only (except the routes that transportation by ships is not feasible. For such routes, you can do transportation by rail.] c. If the shipping choice on each route are independent. d. Which plan has the minimum cost? "Formulate and solve the problems on Python using PuLp package. Submit your Python model (.ipynb or .py file). Define the decision variables explicitly. In the report, provide shipment amounts and the objective value. 2. (55 pts) Assume that you decided not to invest in ships in question 1 . Answer the following questions accordingly and treat each case independently. If you use the same decision variables, repeat solve0 for your relevant model again, so that you don't continue with overwritten solutions. a. The production team realized that they made a mistake in the estimation of second plant's capacity. The true capacity is 230 instead of 220 . Estimate the new total cost without solving an LP. Then, check your result by resolving the problem. b. The sales team realized that they made a mistake in the estimation of second customer's demand. The true estimate is 195 instead of 200 . Estimate the new total cost without solving an LP. c. Assume that the true capacity of the second plant is 400 instead of 220 . Try to guess the new total cost without solving an LP. Now, solve the new LP and comment why it is not possible to calculate the total cost without resolving the problem. d. The top management asks you to change the plan such that there must be some flow on route P3-C1 due to some prearrangements. What is the minimum decrease in the shipping cost on P3-C1 route that will yield a new plan as the top management wants? *Clearly explain your reasoning for each part. Use interpretations of your model outputs. (No submission of code files for this question.) You need to submit your report(.pdf) and your source code (.ipynb or -py file). Note that this is an individual work assignment. You are expected to formulate the problems and solve them by Python-PuLp. The main body of the report should include your formulation (with the definition of parameters and decision variables) and answers to Questions 1-2 together with discussions and comments. You can put output images to your report, if your report(.pdf) reaches the size limit, you can use online size reducers before uploading. Also, your source code should include comments if necessary. If you work in Colab, you can download your ipynb or .py files from the menu bar by FilesDownload. Solutions without Python codes will not be taken into consideration
