* Why OR ?  Search: "Operational Research" (Br.) at .ac.uk, at .edu; "Operations Research" (Am.) at .ac.uk, at .edu

01' • (G) What is OR ? ⇒ Euro, Assoc. of European OR Soc.s (→ Op. Res. → What is OR ?); Wikipedia; APDIO → ..."O que é IO"; InfORMS

02' OR benefits from:  (i) several top 10 (a2000) algorithms of the 20.th century, namely Linear Programming and the Monte Carlo method; and (ii) the simultaneous computer-age revolution.  OR is typically interested in an optimum solution (least cost or wait, greatest profit).

03' • Prominent scientists in OR (in OR/MS 2002): George Dantzig (Linear Programming); Stanislaw Ulam (Monte Carlo); A. H. Land, A. G. Doig (branch-and-bound, Integer Progr.); Richard Bellman (Dynamic Progr.); J. C. Little (Queueing); T. M. Whitin (Inventory Management). • Scientific societies, periodicals.pdf   (.pdf if normal, .Pdf if scanned image)

* Linear Programming  Example [Resnick, exa. 10-1, p 279] fertilizer problem.Pdf (1 Mb), .xlsx or .xlsb, with graph, (Lindo) .ltx, % LP ("revised"), [p 280]%.pdf, % "standard, canonical" (§% via libr.) • Software for LP (CPLEX, Gurobi, etc.) • IBM CPLEX DropSolve

04' • [Sultan].Pdf (1 Mb, pp 2–18, Soln505–507, 26–29, 225–243, 394–403, Soln552–553, 476–481) diet, cars, transportation: Solver Sultan.xlsx, .xlsb; "Mathematica" soln. diet, cars, 1, 2.nb, transport., 3.nb

05' SAS • SAS/OR diet.xlsx, .ltx .lp • WinQSB.zip (search)

06'  • What is a simplex: [WolfrMW], [Dantzig].Pdf • Explaining the simplex: Zionts.pdf; H&L.pdf  "Wyndor" prb., .nb, Wyndor & Zionts.xls: feasible region and path of optimization

07' • Prepared data.pdf for (revised simplex %) several of the given LP problems.

08' • Artificial (H&L, Taha) variables.pdf; manually, ZiontsPlus.xlsx (.pdf) • Negative, free variables • Redundant.pdf  ? Impossible.pdf  ?

09' • Excel (and proper form): LP_ResnickManual.xlsx, LP_Bronson04_01to06.xlsx, LP_Bronson04_11to19.xlsx

10' • LP (Ziont's) typical "four types".Pdf : resource allocation.Pdf (28Mb, dog food), blending.pdf (candy shop, not linear?), cutting stock, flow.

11' • LP parallel resolution.pdf : algebraic, tabular, and matrix forms; or, more clearly, see (tableaux) Bronson prb4.3 (below).

13' • Revised simplex: % Zionts prb, inverse matrix updating (matrix Zionts.xls prb). • Excel limits: TP_big.xlsx

15' • [Craw] Q&A.pdf, machine shop.pdf, blending.pdf (p 4);  A. Alves.xls; [Ecker&Kup.] "scientific" Q&A.pdf, .xlsx (regression & Excel tricks),  1 .ltx,  2 .ltx

16' • Multiplicity: JLawr.ppsx • multi1.pdf • prb1.6.xls → with 3D graph.xlsx, .ltx (convex linear combination)

17' • Degeneracy and variants (unbounded, impossible): special.zip

18' • Cycling: Strayer.Pdf (2.6 Mb) (anti-cycling), Beale.xls, GassV.ltx (Gass&V.), Strayer.ltx • Efficiency.pdf (MCuturi: Klee-Minty)

19' • Duality [BronNaad].Pdf . Symmetric: Duality'16.zip (Excel+Lindo)

20' • [Bron.] prb5.2 LP_Bronson.05.02.pdf, LP_Bronson.05.02-QSB.pdf and soln. (tableaux) LP_Bronson.05.02.xlsx;  unsymmetric [Tavares].pdf (QSB)

21' • Exa.s [Desbazeille]: exa. 1.2.ltx, dual.ltx (exa. 1.8.xls, .ltx) • Jam prb. .xls, .xlsx with 0's, .ltx [Ramalhete, 2.16, prb. 14]

23' • Ramalhete sensit..xls • Arsham (search "315.101"): Game theory (→ =; ex1.ltx) • NEOS: Case Studies

* Transportation Problem  (Hitchcock) "OR notes": 1:intro, 2.TP.pdf (exa. 1, pp 9–10, 13–14) Degeneracy: Note 3, p 15.

24' • Stepping-stone solution TP_steppst.xlsx and Solver (StEdw.pps, 4 Mb).

25' • 3:TP-like.pdf: [H&L] production scheduling.Pdf (p 23; below, "N. Airplane"); transshipment (p 18); assignment (AP) (p 24)

26' • Prod. sched. [H&L] 'Northern Airplane' prb .xlsx, .ltx, .txt • Transsh. [Bron.] prb9.3.Pdf, 'transsh.→TP' routine.pdf (Peniche or exa. 2, p 21), soln..xls ([Tavares].Pdf 4 Mb)

27' • Facility location... (plant location, |at (J. Buescu) Ingenium.pdf|) • Shortest path (Java)

* Integer Programming MILP (branch & bound) [IP_Wolsey95].Pdf, basic exa. (11 pp, 3 Mb), Solver IP_Wolsey95.xlsx, IP_Wolsey95.lp, Wols95.ltx, Wols95ltx.zip & tree, Wols95.lpp • Gurobi MIP basics • MILP: nomenclatura portuguesa.pdf

28' [EiseltSandblom] B&B.Pdf p 211 (4 pp, 3 Mb), strategies: depth-first, breadth-first, best-bound-first+most fractional (6.2.2, p 217). Soln p 211 .xlsx, .ltx, tree.Pdf (p 211, not 122).

29' [Bron.] prb6.2.Pdf (1 Mb) and prb6.4 (←prb1.6), Bron62.ltx, Bron62ltx.zip (relax.).

30' Wiesemann IP_Wiesemann.pdf (380 kb), IP_Wiese.lp, IP_Wiese_ltx.zip (tree).

31' [Sultan] p395ff.Pdf, p400.xls (count iterations !), p400soln.zip • [EckerKup]prb..Pdf (node 7 wrong ? .xlsx), EckerKup.ltx, tree.Pdf

33' • Binary variables Knapsack problem: [Bron.] KnapsackPr4e5.pdf: KnapsPr4.ltx; KnapsPr5.ltx, 5.lpp, 5.pdf

34' • Chen et al.'s "Transformation using 0-1 var.s".pdf.

35' • Beasley 7 prbs.: (IP_Beasley_pdf.zip, solved or illustrative) prb1, blending IP_Beasley.pdf, limiting var.s and constr.s (with areas for IP or BIP use)

36' • Wikipedia: Travelling salesman problem (TSP) • 1992EJOR_Laporte.pdf, an overview • (CD) TSP_prototype.pdf

37' • %, as AP: [Bron.] prb9.6.Pdf (1 Mb) (prb9.6&18.xls, tree18.pdf ?)

38' • TSP as AP relaxation: (Parviainen, LUT.fi) #tsp5_2.pdf (=), LUTtspltx.zip, LUTtspap.xlsx (AP relaxation: 2 or more subproblems !) • TSP_Raffensperger.ppsx (sl. 1–7) • Covering (visiting) TSP_data.xlsx tray points (Carpaneto....)

* Simulation (Monte Carlo)  Exa.s: %; truck with sacks %; bag of oranges %; fishes on Venus %

39' • π [Boston]. Aeronautics... (Is Java safe ? No. See the [don't] "Download Applet".)

40' • Stanislaw Ulam: |MC in practice| (slides 19–22) • When not to use mc: two Gaussian bars.xlsx; if you insist... %

41' • Random number generation: mid-square.xls; NY Times, 'randu'.Pdf; |"linear congruential".xls| (μ, σ of uniform.pdf) • |Kruskal.pdf|: UMass-L(5), SFU(1) • Coin flipping H&L5: 21.1.sim.Pdf (3 Mb), .xls

42' • Simulation methods: inversion routine.pdf ; math tools.pdf • ◊|Excel frequency.xls|

43' • Exponential, Gauss, triangular variables.xlsx (2 exp.s.xlsx) (the lens…) • Box-Muller, .xlsx %

44' • Simulate some variables; Gaussian inversion.pdf • ||Truncated Gaussian.xlsx||

45' • RNG: [EckerKup468].Pdf (4 Mb); (RNG.pdf). Prb.s Sim 1–4.pdf. • Acceptance-rejection.pdf. Parabolic variable %.

46' • Histograms: two styles.xls (search "two") • (Review: trucks, oranges) • Table legs.xls % • Can level.xlsx • Light bulbs.xls, Quality % • DiscreteVariables.xlsx • Random m..n.xls • Monte Carlo integration

47' • Cases: hopper (G, P) / cone bottom cylinder / tank wagons (W) / can filling • Tank wagons.xls ('discrete & continuous' variables).

48' • General: Ellipse, for Excel with macros: '.xlsm'. See also Computing/Misc./MS Office for macros (UDF) and sliders.

* Queueing  Wikip.; "Queueing Systems" (Springer journal) • QueuSys.pdf ¹ (A. A. Markov) • D. G. Kendall (notation)

49' • DePaul.ppsx (24 sl., 850 kB): DePaul5.xls sl. 15&17 • Simulate %. Simul8 • [Bron.] Q&A prb.s 23.Pdf (3 Mb), 23.xlsx

50' Queue vars. %; 24.Pdf • Find s; HL8.814.xlsx, .xlsm (opt. s.pdf) • (Search) xlsx xlsm xlsb.

51' • (Baker) Queu(e)ing_I.pdf, Queu(e)ing_II.pdf (cookbook.pdf) • QueueSysLimit.xls (s = 1, 2, 100) • Queues.pdf historic (≡ 'find s')

52' • Beasley: Queuing theory • (M. Hillier: General) M/G/1.xls • Quality Management:What about your customers ?.pdf

* Inventory management  (Am⊕Br Eng) Wiki. inventory management, ‘Economic Order Quantity’; Just-in-time, (ASQ) JIT.pdf (Just-in-case) • Theory.pdf (formulas), Kaufmann-stocks.xlsx • EOQ (economic order quantity): % (derivation); H&L analytical.xls or by Solver.xls • Order size % (with random demand) • Poisson last n.pdf.

* Revisions • Transportation problem.xlsx, with tolls, models.pdf • Simulation of distance.xlsx in a circle (COUNTIF) • "Julia".pdf.

53' • Beasley IP (Tutorials): "4 variants of product" manufacture, question, solution, answer.xlsx, =.ltx; ExamSimul2000.docx, better answer.xlsx  Project selection question, solution, answer.xlsx, =.ltx • Vandenberghe ilp.pdf (facility location, B&B), =.xlsx =.ltx (& see log)

54' • How to snatch into Excel • How to pilfer a 'ppsx' ? (save 'ppsx', start PP, open 'ppsx', etc.). See DePaul (above) and M/M/1, M/M/s (Kendall, Erlang). Mark Hillier.xlsx.

55' • LP w/ bin. var., fix cost.mp4 • IntegerProg.pptx (pptx or ppsx; 103 sl.: exa.s 45 bin 49 57 59 62 71 fixCh 87)

56' • Exam problems: cinetica.jpg, .xlsx; Plymax.jpg; exam1.pdf

• Boston Univ. • #Craw • IMSL lib.s • mc, Monte Carlo • MILP search (Mixed Integer Linear Programming) • NAG, Fortran library • NEOS (Network-Enabled Optimization Sys.) — ANL (Argonne Nat'l Lab.), MCS (Maths. & Computer Sci.), #OTC (Opt. Technology Center) • #QSB • TSP, travelling salesman problem • WolfrMW, Wolfram MathWorld (Mathematica)

• Dictionaries, etc....: optimum (n./adj.), greatest degree / best, most advantageous ← L., neut. s. of optimus (used as superl. of bonus, "good") ← ops, "power" (related to opt ← Fr. opter) • solution (soln.), an action or process of solving a problem; answer to a problem; specifically, a set of values of the variables that satisfies an equation • {un|a}symmetric(al) (sci.: -symmetric ?), symmetrical • to prune, to cut off parts (eg., tree branches) for better shape, more fruits (podar .pt .es, élaguer .fr, potare .it, stutzen .de) • to fathom, to measure by a sounding line (to evaluate)

• Bibliography  H&L [Hillier & Lieberman, 2005]; BronNaad [Bronson & Naadimuthu, 1997]; Chen et al. [Chen et al., 2010 (book !)]
EckerKup [Ecker & Kupferschmid, 1988]; Sultan [Sultan, 1993] • Mathematica, MathWorld, Integrator, Functions Site • NIST/SEMATECH e-Handbook of Statistical Methods • ASQ