March 16, 2016A&MIS 5251 Session 28 A&MIS 525 May 8, 2002 William F. Bentz

March 16, 2016A&MIS 5252 Agenda Today  Formulation of linear programming problems  Go over Bakker Industries

March 16, 2016A&MIS 5253 Product mix decisions The objective is to schedule production in a manner that effectively utilizes resources to maximize income from operations. To the extent that fixed costs are unaffected by changes in the product mix, the maximization of contribution margin effectively maximizes income from operations.

March 16, 2016A&MIS 5254 Product mix decisions  A linear program formulation for planning production can be very helpful--if not necessary--in a multiple- constraint environment.  By-products of a linear programming formulation include information about constrained resources the value of relaxing these constraints.

March 16, 2016A&MIS 5255 Objective functions  Maximize function (i.e., contribution margin)  Minimize function (i.e., cost)  Come as close as possible to …(i.e., meeting some goal)

March 16, 2016A&MIS 5256 Bakker Industries GrossContribution ProductMargin Margin 611$81$96 613$42$52 615$42$74

March 16, 2016A&MIS 5257 Bakker Industries  Max 96X 1 + $52X 2 + $74X 3

March 16, 2016A&MIS 5258 General  Resource constrains are linear inequalities that are used to model the utilization and the availability of resources.

March 16, 2016A&MIS 5259 Bakker Industries Direct labor resource constraints: 2X 1 + 1X 2 + 2X 3  3,700 3X 1 + 2X 2 + 2X 3  4,500 3X 1 + 0X 2 + 2X 3  2,750 1X 1 + 2X 2 + 1X 3  2,600

March 16, 2016A&MIS Bakker Industries Machine-hour resource constraints: 2X 1 + 1X 2 + 2X 3  3,000 1X 1 + 1X 2 + 2X 3  3,100 2X 1 + 0X 2 + 1X 3  2,700 2X 1 + 2X 2 + 1X 3  3,300

March 16, 2016A&MIS Bakker Industries Marketing constraints: X 1  500 X 2  400 X 3  1,000

March 16, 2016A&MIS Bakker Industries Non-negativity constraints: X 1  0 X 2  0 X 3  0

March 16, 2016A&MIS Bakker Industries Direct labor demand: 2(500) + 1(400) + 2(1,000) = 3,400 3(500) + 2(400) + 2(1,000) = 4,300 3(500) + 0(400) + 2(1,000) = 3,500 1(500) + 2(400) + 1(1,000) = 2,300

March 16, 2016A&MIS Bakker Industries Machine hour demand: 2(500) + 1(400) + 2(1,000) = 3,400 1(500) + 1(400) + 2(1,000) = 2,900 2(500) + 0(400) + 1(1,000) = 2,000 2(500) + 2(400) + 1(1,000) = 2,800

March 16, 2016A&MIS Bakker Industries Possible tactics to increase production include:  Decrease the time required to complete machine maintenance in Department 1  Reduce the machine time per unit of one of the products in Department 1  Enhance the capacity of the machines used in Department 1

March 16, 2016A&MIS Bakker Industries  Improve labor efficiency, particularly in Department 3  Move more skilled workers to Department 3  Improve processes in Department 3 to reduce the labor content in one or more products.  Increase the effective availability of labor in Department 3

March 16, 2016A&MIS Bakker Industries  Next look at the Excel workbook for this problem to see the optimal solution calculation. The file is “Bakker.xls” and the solution steps are under “tools>scenarios”.