Exam 6: Integer Linear Programming

A company produces three products which must be painted,assembled,and inspected.The machinery must be cleaned and adjusted before each batch is produced.They want to maximize their profits for the amount of operating time they have.The unit profit and setup cost per batch are: Product Profit per unit Setup cost per batch 1 9 500 2 10 600 3 12 650 The operation time per unit and total operating hours available are: Operating Time per Unit Operation Product 1 Product 2 Product 3 Operating Hours Available Paint 1 2 2 400 Assemble 2 3 2 600 Inspection 2 4 3 540 Based on this ILP formulation of the problem and the optimal solution X₁,X₂,X₃)= 270,0,0),what values should appear in the shaded cells in the following Excel spreadsheet? X_i = amount of product i produced Y_i = 1 if product i produced,0 otherwise MAX: ^{9 X}₁ ^{+ 10 X}₂ ^{+ 12 X}₃ ^{? 500 Y}₁ ^{? 600 Y}₂ ^{? 650 Y}₃ Subject to: ^{1 X}₁ ^{+ 2 X}₂ ^{+ 2 X}₃ ^{? 400} 2 X₁ + 3 X₂ + 2 X₃ ? 600 2 X₁ + 4 X₂ + 3 X₃ ? 540 X₁ ? M₁ Y₁ OR 270 Y₁ X₂ ? M₂ Y₂ OR 135 Y₂ X₃ ? M₃ Y₃ OR 180 Y₃ Y_i = 0,1 X_i ? 0 and integer

The feasible region for the pure ILP problem

A company is developing its weekly production plan.The company produces two products,A and B,which are processed in two departments.Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80.Each unit of A generates a profit of $17 while a unit of B earns a profit of $21.The company can sell all the units it produces.The data for the problem are summarized below. Hours required by Operation A B Hours Cutting 3 4 48 Welding 2 1 36 What is the appropriate formula to use in cell E8 of the following Excel implementation of the ILP model for this problem?

How is the integer tolerance factor set in the Analytic Solver Platform ASP)?

If a company selects either of Project 1 or Project 2 or both),then either Project 3 or Project 4 or both)must also be selected.Which of the following constraints enforce this condition?

The feasible region for the pure ILP problem

Project 6.2 ? Dayton Electronics Manufacturing Inc.DEMI) The Dayton Electronic Manufacturing,Inc DEMI)company manufactures two styles of remote keyless entry systems the X30 and the X40)that various auto dealers supply to customers when a new or used)automobile is purchased.DEMI currently operates four production facilities located in Springfield OH,Hartford,New Orleans,and Orlando.The manufactured items are shipped from the plants to regional distribution centers located in Trenton,Chicago and Seattle.It is from these regional locations that the product is distributed nationwide. As more automobile manufactures include keyless entry as a standard option,and DEMI finds itself locked out of the manufacturer market,demand for DEMI's products have decreased.As a result,management is contemplating closing one or more of its production facilities.Distribution facilities are not currently being considered for closing. Each production facility carries a fixed operating cost and a variable cost associated with building each of the products.Data has been compiled on production costs,resource availability,and resource usage at each of the production plants.That information is summarized in the table below. Plant Fixed Cost Per Month \ 1000 ) Production Cost per 100 ) X 30-40 Production Time /100 ) 30-40 Available Hours per Month Springfield 53 11001300 66 720 Hartford 38 11001250 78 780 New Orleans 25 10001000 55 530 Orlando 28 12001500 59 680 The entry systems are sold nationwide at the same prices: $24 for the X30 and $30 for the X40. Current monthly demand projections at each distribution center for both products are given in the following table. Demand Trenton Chicago Seattle X30 2200 3100 4000 X40 4500 5800 6000 The transportation costs between each plant and each distribution center,which are the same for either product,are shown in the following table: $\text {Cost per 100}$ $\quad$$\quad$$\text {To}$ From Trenton Chicago Seattle Springfield \ 200 \ 270 \ 450 Hartford \ 100 \ 200 \ 700 New Orleans \ 250 \ 240 \ 300 Orlando \ 180 \ 220 \ 350 • Determine which of the plants to close and which to keep open. • Determine the number of X30 and X40 to be produced at each plant. • Determine a shipping pattern from the plants to the distribution centers. • Maximize the net total monthly profit.If any plants were closed,what was the impact of the closing on profits? • Do not exceed the production capacities at any plant. Formulate DEMI's problem as a fixed charge,integer program.Implement your model in Excel and solve the model to answer DEMI's questions.

A company wants to select 1 project from a set of 4 possible projects.Which of the following constraints ensures that only 1 will be selected?