472.21 5 & 6 Fall 2011

MS 472.21 5 & 6 Fall 2011

Working on together: more product mix Quick-Screen diet Breathtakers transportation Zephyr Television investment Kathleen Allen Assignment: probs 2: ch 4 prob 2: 1st paragraph options Excel sheet prob 3 all Excel sheet ½ page memo prob 5 all ½ page memo Applications

Quick Screen ch 4 pg 111 • product mix • elaboration of St. Adolphe • ox-carts & churches • more • products • constraints

Breathtakers ch 4 pg 116 • each food • has a cost • most foods • have a benefit • have a harm • goal • achieve minimum benefit • don’t exceed maximum harm • at minimum cost constraints objective function

Zephyr Television ch 4 pg 129 • supply • a warehouse • demand • stores • goal • satisfy demand • at minimum transportation cost

Kathleen Allen ch 4 pg 119 • Investment • building a portfolio • various options • returns • risk • dealt with only through diversification • goal • maximize return

More uses ch 4 • blend example • Petroleum Co. • multiperiod scheduling • PM Computer • DEA • Delancy

Petroleum Co. ch 4 9th ed: pg 132 • blending • multiple finished products • from multiple components • consider both revenue & expense

PM Computer ch 4 9th ed: pg 135 • multiperiod scheduling • first peek into scheduling • remarkably like a blending problem • inputs • constrained • with an expense • outputs • constrained • with a revenue

DEA • “Data Envelopment Analysis” formulation not intuitive an intriguing idea no probabilities!

DEA any process with multiple inputs & multiple outputs • How good are you at…? could be for-profit service providers efficiency usually non-profit any service measurable quality hospitals schools day-care

DEA jargon alert! • How good are you at…? “benchmarking” DMU decision-making unit weighted sum outputs weighted sum inputs PPS production possibility set

DEA • compares a number of service units • of same type • can vary in size • based on • their inputs (resources) • their outputs • result indicates • if a unit is less efficient than others

DEA • basic math idea: • most efficiency can be is 1 (100%)

DEA

DEA example ch 4 pg 140 • Delancey elementary school • inputs • teacher/student • supplementary $/student • parent education level • outputs • reading • math • history ratios average scores on standardized tests

DEA target

Delancey ch 4 pg 140 • DEA • “Data Envelopment Analysis” lets save this for next week

Integer Programming • ch 5 • has lots of practical uses • in some ways is simplest of all • adds decision-making wrinkles

Integer Applications investments Nancy Smith capital budgeting University Bookstore at Tech facility location Frijo-Lane American Parcel Service Terraco sports drafts Tennessee Pterodactyls

0-1 Integer Model • at least some values are constrained to either 0 or 1 • e.g.: • If you have to pick either x1, x2 or x3, • then constraints are: x1 + x2 + x3 = 1 xi >= 0 and integer

0-1 Integer Model > Example • Community capital building decision • page 182 • start with standard situation • have $120,000 to spend • need to choose among 4 options • swimming pool • tennis centre • athletic field • gymnasium

0-1 Example • Community capital building decision • goal • Maximize usage

0-1 Example • Community capital building decision • constraints • $120,000 to spend • 12 acres available • land used for x1 (swimming pool) is same as x2 (tennis centre)

0-1 Variations • conditional constraint • Can only build x2 if x1 gets built x2 <= x1 • corequisite constraint • If you build x2, you must also build x1 x2 = x1 • multiple-choice constraint • Must build either x1 or x2 x1 + x2 = 1 x1 + x2 <= 1

investments Nancy Smith capital budgeting University Bookstore at Tech facility location Frijo-Lane American Parcel Service Terraco sports drafts Tennessee Pterodactyls Integer Applications

472.21 5 & 6 Fall 2011