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zbRzb8cV2|VzE;YU75Y$ZDmrr5rr1kMg_VxLvadHvb+Om$iZj9^pMNtj7S@?EVeg_y zv-||*w5*rr89T}rjdHyQ=8h~L__^>|`{*EAhldh!6BbQ_LG$84<~}%idBS5CuI@+? tcwH-W>NkdoB`~klqewOpP1*CmZ>ayg9?o!{H2@K|ATBE_ 0) { + row[idx_prod(i, t)] <- prod_time[m, i] + } + } + add.constraint(lp_model, row, "<=", n_machines[m] * time_per_machine) + } + } + + # 2. Bilanse magazynowe + for (i in 1:n_products) { + for (t in 1:n_months) { + row <- rep(0, n_vars) + + # Produkcja zwiększa zapas + row[idx_prod(i, t)] <- 1 + + # Sprzedaż zmniejsza zapas + row[idx_sales(i, t)] <- -1 + + # Zapas na koniec okresu + row[idx_inv(i, t)] <- 1 + + # Zapas z poprzedniego okresu + if (t > 1) { + row[idx_inv(i, t-1)] <- -1 + } + + # Dla t=1: inv_{i,0} = 0 (warunek początkowy) + if (t == 1) { + add.constraint(lp_model, row, "=", 0) + } else { + add.constraint(lp_model, row, "=", 0) + } + } + } + + # 3. Ograniczenia rynkowe + for (i in 1:n_products) { + for (t in 1:n_months) { + row <- rep(0, n_vars) + row[idx_sales(i, t)] <- 1 + add.constraint(lp_model, row, "<=", market_limits[t, i]) + } + } + + # 4. Ograniczenia pojemności magazynu + for (i in 1:n_products) { + for (t in 1:n_months) { + row <- rep(0, n_vars) + row[idx_inv(i, t)] <- 1 + add.constraint(lp_model, row, "<=", 200) + } + } + + # 5. Warunki końcowe (50 sztuk każdego produktu na koniec marca) + for (i in 1:n_products) { + row <- rep(0, n_vars) + row[idx_inv(i, 3)] <- 1 + add.constraint(lp_model, row, "=", 50) + } + + # 6. Ograniczenia dotyczące obniżki dochodu (flagi over_i_t) + big_m <- 10000 # Duża liczba dla metody Big-M + for (i in 1:n_products) { + for (t in 1:n_months) { + if (market_limits[t, i] > 0) { # Tylko dla produktów, które można sprzedać + # Ograniczenie: s_{i,t} >= 0.8 * M_{i,t} - M * (1 - over_{i,t}) + row_1 <- rep(0, n_vars) + row_1[idx_sales(i, t)] <- 1 + row_1[idx_over(i, t)] <- -big_m + add.constraint(lp_model, row_1, ">=", 0.8 * market_limits[t, i] - big_m) + + # Ograniczenie: s_{i,t} <= 0.8 * M_{i,t} + M * over_{i,t} + row_2 <- rep(0, n_vars) + row_2[idx_sales(i, t)] <- 1 + row_2[idx_over(i, t)] <- -big_m + add.constraint(lp_model, row_2, "<=", 0.8 * market_limits[t, i]) + } else { + # Dla produktów, których nie można sprzedać, ustalamy over_{i,t} = 0 + row <- rep(0, n_vars) + row[idx_over(i, t)] <- 1 + add.constraint(lp_model, row, "=", 0) + } + } + } + + return(lp_model) +} + +# Rozwiązanie modelu jednokryterialnego +print("Solving single-criterion model...") +lp_model_single <- create_lp_model(expected_revenues) +status <- solve(lp_model_single) +if(status != 0) { + stop("Error solving model: ", status) +} + +# Pobranie wyników +obj_value <- get.objective(lp_model_single) +solution <- get.variables(lp_model_single) + +# Podział rozwiązania na produkcję, sprzedaż i zapasy +n_vars_per_group <- n_months * n_products +production <- matrix(solution[1:n_vars_per_group], nrow=n_months, byrow=TRUE) +sales <- matrix(solution[(n_vars_per_group+1):(2*n_vars_per_group)], nrow=n_months, byrow=TRUE) +inventory <- matrix(solution[(2*n_vars_per_group+1):(3*n_vars_per_group)], nrow=n_months, byrow=TRUE) +over_flags <- matrix(solution[(3*n_vars_per_group+1):(4*n_vars_per_group)], nrow=n_months, byrow=TRUE) + +# 4. Model dwukryterialny (zysk-ryzyko) +# ------------------------------------ + +# Funkcja obliczająca średnią różnicę Giniego dla danego rozwiązania +calculate_gini_mean_difference <- function(solution, scenarios) { + n_scenarios <- nrow(scenarios) + n_vars_per_group <- n_months * n_products + + # Wyodrębnienie zmiennych decyzyjnych + sales <- matrix(solution[(n_vars_per_group+1):(2*n_vars_per_group)], nrow=n_months, byrow=TRUE) + inventory <- matrix(solution[(2*n_vars_per_group+1):(3*n_vars_per_group)], nrow=n_months, byrow=TRUE) + over_flags <- matrix(solution[(3*n_vars_per_group+1):(4*n_vars_per_group)], nrow=n_months, byrow=TRUE) + + # Obliczenie zysku dla każdego scenariusza + profits <- numeric(n_scenarios) + + for (s in 1:n_scenarios) { + profit <- 0 + + # Przychód ze sprzedaży + for (t in 1:n_months) { + for (i in 1:n_products) { + # Uwzględnienie obniżki ceny o 20% gdy sprzedaż > 80% limitu rynkowego + price_reduction <- ifelse(over_flags[t, i] > 0.5, 0.2, 0) + profit <- profit + scenarios[s, i] * sales[t, i] * (1 - price_reduction) + } + } + + # Koszty magazynowania + for (t in 1:n_months) { + for (i in 1:n_products) { + profit <- profit - inventory[t, i] + } + } + + profits[s] <- profit + } + + # Obliczenie średniej różnicy Giniego + gini <- 0 + for (i in 1:n_scenarios) { + for (j in 1:n_scenarios) { + gini <- gini + abs(profits[i] - profits[j]) * (1/n_scenarios) * (1/n_scenarios) + } + } + gini <- gini / 2 + + return(list(gini = gini, expected_profit = mean(profits))) +} + +# Generowanie punktów na krzywej efektywnej metodą ważonych kryteriów +generate_efficient_frontier <- function(scenarios, n_points = 20) { + lambda_values <- seq(0, 1, length.out = n_points) + results <- data.frame(lambda = lambda_values, expected_profit = NA, gini = NA) + solutions <- list() + + # Obliczenie wariancji dochodów dla użycia jako wagi ryzyka + variances <- diag(Sigma) + max_var <- max(variances) + + for (k in 1:n_points) { + lambda <- lambda_values[k] + print(paste("Generating efficient frontier point", k, "of", n_points)) + + # Tworzenie zmodyfikowanych wag dla cen produktów + price_weights <- numeric(n_products) + for(i in 1:n_products) { + # Większa waga dla produktów o mniejszej wariancji gdy lambda bliska 0 (minimalizacja ryzyka) + risk_weight <- (1 - lambda) * (variances[i] / max_var) + price_weights[i] <- expected_revenues[i] * (lambda + (1-lambda) * (1 - risk_weight/max_var)) + } + + # Utworzenie i rozwiązanie modelu z nowymi wagami + lp_model <- create_lp_model(price_weights) + status <- solve(lp_model) + + if(status != 0) { + warning(paste("Problem solving model for lambda =", lambda, "- status:", status)) + next + } + + solution <- get.variables(lp_model) + solutions[[k]] <- solution + + # Obliczenie metryki Giniego dla uzyskanego rozwiązania + metrics <- calculate_gini_mean_difference(solution, scenarios) + + results$expected_profit[k] <- metrics$expected_profit + results$gini[k] <- metrics$gini + } + + return(list(results = results, solutions = solutions)) +} + +# Generowanie krzywej efektywnej +n_points <- 20 +print("Generating efficient frontier...") +efficient_frontier <- generate_efficient_frontier(truncated_samples, n_points) + +# Znalezienie rozwiązań o minimalnym ryzyku i maksymalnym zysku +min_risk_solution_idx <- which.min(efficient_frontier$results$gini) +max_profit_solution_idx <- which.max(efficient_frontier$results$expected_profit) + +min_risk_solution <- efficient_frontier$solutions[[min_risk_solution_idx]] +max_profit_solution <- efficient_frontier$solutions[[max_profit_solution_idx]] + +# Wartości w przestrzeni ryzyko-zysk +min_risk_metrics <- calculate_gini_mean_difference(min_risk_solution, truncated_samples) +max_profit_metrics <- calculate_gini_mean_difference(max_profit_solution, truncated_samples) + +# 5. Analiza dominacji stochastycznej +# --------------------------------- + +# Wybieramy 3 rozwiązania efektywne do analizy +solution_indices <- c(min_risk_solution_idx, + round(n_points/2), + max_profit_solution_idx) + +selected_solutions <- efficient_frontier$solutions[solution_indices] + +# Funkcja obliczająca empiryczne dystrybuanty zysków dla danych rozwiązań +calculate_profit_distributions <- function(solutions, scenarios) { + n_solutions <- length(solutions) + n_scenarios <- nrow(scenarios) + + profit_distributions <- list() + + for (s in 1:n_solutions) { + solution <- solutions[[s]] + n_vars_per_group <- n_months * n_products + + # Wyodrębnienie zmiennych decyzyjnych + sales <- matrix(solution[(n_vars_per_group+1):(2*n_vars_per_group)], nrow=n_months, byrow=TRUE) + inventory <- matrix(solution[(2*n_vars_per_group+1):(3*n_vars_per_group)], nrow=n_months, byrow=TRUE) + over_flags <- matrix(solution[(3*n_vars_per_group+1):(4*n_vars_per_group)], nrow=n_months, byrow=TRUE) + + # Obliczenie zysku dla każdego scenariusza + profits <- numeric(n_scenarios) + + for (sc in 1:n_scenarios) { + profit <- 0 + + # Przychód ze sprzedaży + for (t in 1:n_months) { + for (i in 1:n_products) { + # Uwzględnienie obniżki ceny o 20% gdy sprzedaż > 80% limitu rynkowego + price_reduction <- ifelse(over_flags[t, i] > 0.5, 0.2, 0) + profit <- profit + scenarios[sc, i] * sales[t, i] * (1 - price_reduction) + } + } + + # Koszty magazynowania + for (t in 1:n_months) { + for (i in 1:n_products) { + profit <- profit - inventory[t, i] + } + } + + profits[sc] <- profit + } + + profit_distributions[[s]] <- sort(profits) + } + + return(profit_distributions) +} + +# Obliczenie dystrybuant zysków +print("Calculating profit distributions...") +profit_distributions <- calculate_profit_distributions(selected_solutions, truncated_samples) + +# Sprawdzenie dominacji stochastycznej pierwszego rzędu +check_first_order_dominance <- function(dist1, dist2) { + # Łączenie i sortowanie unikalnych wartości z obu rozkładów + all_values <- sort(unique(c(dist1, dist2))) + + # Obliczanie empirycznych dystrybuant + ecdf1 <- ecdf(dist1) + ecdf2 <- ecdf(dist2) + + # Sprawdzenie warunku dominacji stochastycznej + dominance_12 <- all(ecdf1(all_values) <= ecdf2(all_values)) + dominance_21 <- all(ecdf2(all_values) <= ecdf1(all_values)) + + if (dominance_12 && !dominance_21) { + return("1 dominuje 2") + } else if (!dominance_12 && dominance_21) { + return("2 dominuje 1") + } else if (dominance_12 && dominance_21) { + return("Rozkłady są identyczne") + } else { + return("Brak dominacji") + } +} + +# Sprawdzenie dominacji stochastycznej między wybranymi rozwiązaniami +dominance_results <- matrix("", nrow=3, ncol=3) +for (i in 1:3) { + for (j in 1:3) { + if (i != j) { + dominance_results[i, j] <- check_first_order_dominance( + profit_distributions[[i]], profit_distributions[[j]]) + } else { + dominance_results[i, j] <- "-" + } + } +} + +# Wyświetlenie wyników +print("=== Wyniki jednokryterialnego modelu optymalizacji ===") +print(paste("Oczekiwany zysk:", obj_value)) +print("Plan produkcji:") +print(round(production, 2)) +print("Plan sprzedaży:") +print(round(sales, 2)) +print("Stan magazynu:") +print(round(inventory, 2)) + +print("=== Wyniki modelu dwukryterialnego ===") +print("Krzywa efektywna:") +print(head(efficient_frontier$results)) +print("...") + +print("Rozwiązanie o minimalnym ryzyku:") +print(paste("Zysk:", round(min_risk_metrics$expected_profit, 2))) +print(paste("Ryzyko (Gini):", round(min_risk_metrics$gini, 2))) + +print("Rozwiązanie o maksymalnym zysku:") +print(paste("Zysk:", round(max_profit_metrics$expected_profit, 2))) +print(paste("Ryzyko (Gini):", round(max_profit_metrics$gini, 2))) + +print("=== Analiza dominacji stochastycznej ===") +print(dominance_results) + +# Wizualizacja wyników +ggplot(efficient_frontier$results, aes(x=gini, y=expected_profit)) + + geom_point() + + geom_line() + + geom_point(data=efficient_frontier$results[c(min_risk_solution_idx, 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