Hello, i want to ask you Inventory cost =3.6(B1+B2)/2+3.75(B2+B3)/2+3.98(B3+B4)/2+4.28(B4+B5)/2+4.2(B5+B6)/2+3.9(B6+B7)/2, So, how to compute 3.6, 3.75, 3.98, 4.28, 4.2? And why 3.6X(B1+B2) and divide by 2? Also, i want to ask the objective function for this problem why is minimize, not maximize? Thank you for your help!
The Upton Corporation manufactures heavy-duty air compressors for the home and light industrial markets. Upton is presently trying to plan its production and inventory levels for the next six months. Because of seasonal fluctuations in utility and raw material costs, the per unit cost of producing air compressors varies from month to month - as does the demand for air compressors. Production capacity also varies from month to month due to differences in the number of working days, vacations, and scheduled maintenance and training. The following table summarizes the monthly production costs, demands, and production capacity that Upton's management expects to face over the next six months. Given the size of Upton's warehouse, a maximum of 6,000 units can be held in inventory at the end of any month. The owner of the company likes to keep at least 1,500 units in inventory as safety stock to meet unexpected demand contingencies. To maintain a stable workforce, the company wants to produce no less than one half of its maximum production capacity each month. Upton's controller estimates that the cost of carrying a unit in any given month is approximately equal to 1.5% of the unit production cost in the same month. Upton estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month. 1 2 3 4 5 6 Unit Production Cost $240 $250 $265 $285 | $280 | $260 Units Demanded 1000 4000 4500 3500 6000 4000 5500 4500 3500 4000 4000 3500 Maximum Production Write the mathematical formulation using the decision variables. I'm just confused on how to put this question into mathematical terms before I can keep going with the problem. I know that the decision variables are how much needs to be produced each month by Upton but I'm not sure how to express that The basic decision Upton's management team faces is how many units to manufacture in each of the next six months. We will represent these decision variables as follows: P1 = number of units to produce in month 1 P2 = number of units to produce in month 2 P3 = number of units to produce in month 3 P4 = number of units to produce in month 4 Ps = number of units to produce in month 5 Po=number of units to produce in month 6 The objective in this problem is to minimize the total production and inventory costs. The total production cost is computed easily as: Production Cost = 240P1 + 250P2 +265P3 +285P4 + 280P5 +260P Let Bi represent the beginning inventory for month i, the total inventory cost is given by: Inventory Cost = 3.6(B1 + B2)/2 +3.75(B2 + B3)/2 +3.98(B3 + B^)/2 + 4.28(B4 + B5)/2 +4.20(B5+ B6)/2+3.9(B6+B7)/2 Thus, the objective function for this problem is given as: MIN: 240P1 + 250P2 +265P3 +285P4 + 280P5 +260P +3.6(B1 + B2)/2 +3.75(B2+ B3)/2 +3.98(B3 + B4)/2 + 4.28(B4 + B5)/2 +4.20(B5 + B6)/2+3.9(B6+B7)/2 total cost Constraints 2,000
