Applied Mathematical Programming by Stephen P. Bradley

By Stephen P. Bradley

E-book via Bradley, Stephen P., Hax, Arnoldo C., Magnanti, Thomas L.

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50 when production is increased from one month to the next. 25 per unit. A smooth production rate is obviously desirable. Sales forecasts for the next twelve months are (in thousands): July 4 August 6 September 8 October 12 November 16 December 20 January 20 February 12 March 8 April 6 May 4 June 4 June’s production schedule already has been set at 4000 units, and the July 1 inventory level is projected to be 2000 units. Storage is available for only 10,000 units at any one time. Ignoring inventory costs, formulate a production schedule for the coming year that will minimize the cost of changing production rates while meeting all sales demands.

Further, the model can be stated with only nonnegative righthand-side values by multiplying by −1 any constraint with a negative righthand side. Then, to obtain a canonical form, we must make sure that, in each constraint, one basic variable can be isolated with a +1 coefficient. Some constraints already will have this form. 0, appears in no other equation in the model. It can function as an intial basic variable for this constraint. 5 does not serve this purpose, since its coefficient is −1. 3.

Usage per unit of trailer Resources Flat-bed Economy Luxury availabilities Metalworking days 1 2 2 1 24 Woodworking days Contribution ($ × 100) 1 6 2 14 4 13 60 Let the decision variables of the problem be: x1 = Number of flat-bed trailers produced per month, x2 = Number of economy trailers produced per month, x3 = Number of luxury trailers produced per month. Assuming that the costs for metalworking and woodworking capacity are fixed, the problem becomes: Maximize z = 6x1 + 14x2 + 13x3 , subject to: 1 2 x1 + 2x2 + x3 ≤ 24, x1 + 2x2 + 4x3 ≤ 60, x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.

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