CRPJ Inc. ("CRPJ") manufactures at its plant in Longueuil, the product P from a variety of components from suppliers one located in the Montreal metropolitan area, the others in Ontario, British Columbia and the United States United. The factory capacity is 200 P units per week. The factory manager wants to plan production for the next six weeks. The table below describes the demand forecast for this period. The first line gives the number of units that CRPJ has committed to deliver to regular customers. They absorb a significant part of the factory's production and ensure its financial stability. Therefore, CRPJ management agrees to respond to their orders, even if sometimes it incurs a shortfall. The second line indicates the maximum quantity of unit that CRPJ could sell in addition to orders from regular customers. Demand (in units) of product P Weeks 1 2 3 4 5 6 Orders 154 209 108 117 132 145 Additional demand 70 7 0 60 60 75 75 Total 224 279 168 177 207 2 20 Deliveries are made at the end of each week. Units that are not delivered in a given week are stored at the factory. The factory can keep a maximum of 50 units, the storage cost being estimated at $ 3 per unit per week. On Monday of week 1, the factory will have 20 units of product P in stock. One of the suppliers attracted to the Longueuil plant has just suffered an equipment failure and its production capacity will be reduced considerably for a few weeks. Part X, which this supplier is the only one to manufacture in North America, constitutes a key component of product P. Therefore, the director called the supplier and, after lively negotiations, accompanied by a reminder of the long and fruitful collaboration between the two companies, it was agreed that the supplier would respect the following delivery schedule, if CRPJ deems it appropriate. | Weeks Orders Component X delivery schedule 2 240 240 280 420 240 Deliveries from this supplier are made on Monday morning. The quantities indicated in the table constitute maximums. The order received in a given week cannot exceed the number of units mentioned in the table. On the other hand, the director of CRPJ could not necessarily demand this maximum, which incidentally, benefit the supplier, who could thus satisfy other customers. A P unit requires two pieces of X. The Longueuil plant can store up to 200 X pieces, at a cost of $ 1 per unit per week. Finally, on Monday of week 1, the factory will have 30 X pieces in stock. The factory capacity will drop by 20% in weeks 1 and 2, due to public holidays. a) Complete the network for this problem. Be sure to include all the details. b) Explain what the different types of flow represent. c) CRPJ makes a profit of $ 50 per unit of P sold at the "posted price". It also offers regular customers a reduction of $ 17 per unit on this posted price. Indicate how to modify the network of the question to translate this reduction in price (plot only one series for the additional part - do not trace the entire network)
