أرجو من عنده كيفية حل مسائل Operation Reserch مع شرح كيفية الحل ولكم الشكر
Example 2.3.4 (Single-period Production Model)
In preparation for the winter season, a clothing company is manufacturing parks and goose overcoats, insulated pants, and gloves. All products are manufactured in four different departments: cutting, insulating, sewing and packaging. The company has received firm orders for its products. The contract stipulates a penalty for undelivered items. The following table provides the pertinent data of the solution.
Department Parka Goose Pants Glover Capacity
Cutting .30 .30 .25 .15 1000
Insulating .25 .35 .30 .10 1000
Sewing .45 .50 .40 .22 1000
Packaging .15 .15 .1 .05 1000
Demand 800 750 600 500
Unit profit $30 $40 $20 $10
Unit penalty $15 $20 $10 $8
Devise an optimal production plan for the company.
Example 2.3.7 (Crude Oil Refining and Gasoline Blending)
Shale Oil, located on the island of Aruba, has capacity of 1,500,000 bbl of crude oil per day. The final products from the refinery include three types of unleaded gasoline with different octane numbers (ON): regular with ON=87, premium with ON=89, and super with ON=92. The refining process encompasses three stages: (1) a distillation tower that produces feedstock (ON=82) at the rate of .2 bbl per bbl of crude oil, (2) a cracker unit that produces gasoline stock (ON=98) by using a portion of the feedstock produced from the distillation tower at the rate of .5bbl per bbl of feedstock, and (3) a blender unit that blends the gasoline stock from the cracker unit and the feedstock from the distillation tower. The company estimates the net profit per barrel of the three types of gasoline to be $6.70, $7.20, and $8.10 respectively. The input capacity of the cracker unit is 200,000 barrels of a feedstock a day. The demand limits for regular, premium, and super gasoline are 50,000, 30,000 and 40,000 barrels per day. Develop a model for determining the optimum production schedule for the refinery.
Example 2.3.8 (Bus Scheduling)
Progress City is studying the feasibility of introducing a mass-transit bus system that will alleviate the smog problem by reducing in-city driving. The study seeks the minimum number of buses that can handle the transportation needs. After gathering necessary information, the city engineer noticed that the minimum number of buses needed fluctuated with the time of the day and that the required number of buses could be approximated by constant values over successive 4-hour intervals. Figure below summarizes the engineer’s findings. To carry out the required daily maintenance, each bus can operate 8 successive hours a day only.