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# (Solved): Formulate An ILP Model For This Problem. III. (25 Pts.) A Factory Works A 24 Hour Day, 7 Day Week In...

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Formulate an ILP model for this problem. III. (25 pts.) A factory works a 24 hour day, 7 day week in producing four products. Since only one product can be produced at a time the factory operates a system where, throughout one day, the same product is produced (and then the next day either the same product is produced or the factory produces a different product). The rate of production is: Product 3 No. of Units Produced Per Hour 100 250 190 Worked 150 The only complication in changing from producing product I one day to producing product 2 the next day is that five working hours are lost due to the necessity of cleaning certain oil tanks. To assist in planning the production for the next week the following data is available: Product Current Stock (Units) 5000 7000 9000 8000 1500 4000 2000 3000 1700 500 2000 2000 Daily 1900 1000 3000 2000 Demand 1000 2000 1000 (units) 2000 500 2000 1000 500 - 1000 2000 500 500 2000 500 500 alw 3000 on Day 0. The factory is not allowed to be idle (i.e. one of the four Product 3 was produced on Day 0. The factory is not allowed to be We must be produced each day). Back orders are allowed except Day 7. At the end of Day 7. there must be (for each product) at least 1750 units in stock actack is PhP1.50 per unit for products 1 and 2 but PhP2.50 per unit for the stock held at the end of each day). The company incurs a If the cost of holding stock is PhP1.50 per u products 3 and 4 (based on the stock held penalty of PhP5.00 per back ordered unit. Formulate the problem of planning the prod program. You may opt to use general notari problem to simplify your model. Do not Janning the production for the next week as an integer linear general notations to represent the numerical values given in the model. Do not forget to define your notations. 412018-2019

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Solution Formulating Variables We need to make the decision related to the type of product that is produced on each dayTherefore let: xit= 1 where i is 1,2,3,4 where t is 1,2,3,4,5,6,7 Now lets defi