根据orders = [ 10, 1.6, 2.2, 480; % 订单1 20, 1.8, 2.4, 680; % 订单2 20, 1.7, 2.3, 550; % 订单3 15, 1.5, 2.0, 420 % 订单4 ]; % 原材料数据 raw_materials = [ 5.5,18; 6.8,22; 7,28; ]; s = 0.005; % 锯口宽度 tolerance = 0.01; % 尺寸容差 % 提取订单需求 n = orders(:, 1); % 订单量 w = orders(:, 2); % 宽度目标 h = orders(:, 3); % 高度目标 p = orders(:, 4); % 单价 % 原材料长度和成本 L = raw_materials(:, 1); C = raw_materials(:, 2); % 变量定义： % x(i,j,1): 从原材料j切割订单i的宽度 % x(i,j,2): 从原材料j切割订单i的高度 % y(j): 使用的原材料j的数量 %

以下是考虑原材料缺陷的优化切割方案MATLAB代码： ```matlab % 订单数据 orders = [ 10, 1.6, 2.2, 480; % 订单1 20, 1.8, 2.4, 680; % 订单2 20, 1.7, 2.3, 550; % 订单3 15, 1.5, 2.0, 420 % 订单4 ]; % 原材料数据（更新为表2数据） raw_materials = [ 5.5, 18, 1.0, 0.03, 2.5, 0.04; % 原材料1 6.2, 22, 0.5, 0.02, 1.8, 0.05; % 原材料2 7.8, 28, 3.0, 0.03, 0, 0 % 原材料3 ]; s = 0.005; % 锯口宽度 tolerance = 0.01; % 尺寸容差 % 提取订单需求 n = orders(:, 1); % 订单量 w = orders(:, 2); % 宽度目标 h = orders(:, 3); % 高度目标 p = orders(:, 4); % 单价 % 原材料长度、成本和缺陷信息 L = raw_materials(:, 1); C = raw_materials(:, 2); defects = raw_materials(:, 3:end); % 每行包含缺陷位置和长度 % 变量定义： % x(i,j,k): 从原材料j切割订单i的尺寸k (k=1宽度,k=2高度) % y(j): 使用的原材料j的数量 % z(i,j,k,m): 表示x(i,j,k)是否位于第m段无缺陷区域 num_orders = size(orders, 1); num_raw = size(raw_materials, 1); num_defects = 2; % 每个原材料最多2个缺陷 % 计算每根原材料的可用分段 available_segments = cell(num_raw, 1); for j = 1:num_raw defect_pos = defections(j, 1:2:end); defect_len = defections(j, 2:2:end); defect_pos = defect_pos(defect_pos > 0); defect_len = defect_len(1:length(defect_pos)); % 对缺陷位置排序 [defect_pos, idx] = sort(defect_pos); defect_len = defect_len(idx); % 计算可用分段 segments = []; start = 0; for d = 1:length(defect_pos) if defect_pos(d) > start segments = [segments; start, defect_pos(d)-start]; end start = defect_pos(d) + defect_len(d); end if start < L(j) segments = [segments; start, L(j)-start]; end available_segments{j} = segments; end % 变量总数：订单×原材料×2尺寸 + 原材料 + 订单×原材料×2尺寸×最大分段数 max_segments = max(cellfun(@(x) size(x,1), available_segments)); num_vars = num_orders*num_raw*2 + num_raw + num_orders*num_raw*2*max_segments; % 目标函数：最大化利润 = 总收益 - 总成本 f = zeros(num_vars, 1); f(num_orders*num_raw*2+1:num_orders*num_raw*2+num_raw) = C; % 原材料成本 f(1:num_orders*num_raw*2) = -repmat(p, num_raw*2, 1) / sum(n * 2); % 收益部分 % 约束条件 A = []; b = []; lb = zeros(num_vars, 1); ub = inf(num_vars, 1); intcon = 1:num_vars; % 需求约束：每个订单的宽度和高度需求 for i = 1:num_orders % 宽度需求：sum(x(i,j,1)) >= 2n(i) row = zeros(1, num_vars); for j = 1:num_raw idx = (i-1)*num_raw*2 + (j-1)*2 + 1; row(idx) = 1; end A = [A; -row]; b = [b; -2*n(i)]; % 高度需求：sum(x(i,j,2)) >= 2n(i) row = zeros(1, num_vars); for j = 1:num_raw idx = (i-1)*num_raw*2 + (j-1)*2 + 2; row(idx) = 1; end A = [A; -row]; b = [b; -2*n(i)]; end % 原材料长度约束（考虑缺陷） for j = 1:num_raw segments = available_segments{j}; num_segments = size(segments, 1); % 每个分段的约束 for m = 1:num_segments seg_start = segments(m, 1); seg_len = segments(m, 2); row = zeros(1, num_vars); for i = 1:num_orders idx_w = (i-1)*num_raw*2 + (j-1)*2 + 1; idx_h = (i-1)*num_raw*2 + (j-1)*2 + 2; % 对应z变量的索引 z_idx_w = num_orders*num_raw*2 + num_raw + (i-1)*num_raw*2*max_segments + (j-1)*2*max_segments + (m-1)*2 + 1; z_idx_h = z_idx_w + 1; row(idx_w) = w(i) + s; row(idx_h) = h(i) + s; row(z_idx_w) = -seg_len; row(z_idx_h) = -seg_len; end A = [A; row]; b = [b; 0]; end end % 约束：x(i,j,k)必须分配到某个分段 for i = 1:num_orders for j = 1:num_raw segments = available_segments{j}; num_segments = size(segments, 1); for k = 1:2 % 宽度和高度 idx_x = (i-1)*num_raw*2 + (j-1)*2 + k; row = zeros(1, num_vars); row(idx_x) = 1; for m = 1:num_segments z_idx = num_orders*num_raw*2 + num_raw + (i-1)*num_raw*2*max_segments + (j-1)*2*max_segments + (m-1)*2 + k; row(z_idx) = -1; end A = [A; -row]; b = [b; 0]; end end end % 求解 options = optimoptions('intlinprog', 'Display', 'iter'); [x, fval, exitflag] = intlinprog(f, intcon, A, b,[],[], lb, ub, options); % 解析结果 if exitflag > 0 disp('Optimal solution found with defects considered.'); y = x(num_orders*num_raw*2+1:num_orders*num_raw*2+num_raw); total_cost = sum(y .* C); total_revenue = sum(n .* p); profit = total_revenue - total_cost; disp(['Total Profit: ', num2str(profit)]); % 计算切割损失率和利用率 total_raw = sum(y .* L); total_used = 0; for j = 1:num_raw segments = available_segments{j}; num_segments = size(segments, 1); for i = 1:num_orders idx_w = (i-1)*num_raw*2 + (j-1)*2 + 1; idx_h = (i-1)*num_raw*2 + (j-1)*2 + 2; x_w = x(idx_w); x_h = x(idx_h); % 计算实际使用的材料（考虑锯口） total_used = total_used + x_w * (w(i) + s) + x_h * (h(i) + s); end end % 计算缺陷区域的总损失 defect_loss = 0; for j = 1:num_raw segments = available_segments{j}; defect_pos = defections(j, 1:2:end); defect_len = defections(j, 2:2:end); defect_loss = defect_loss + y(j) * sum(defect_len(defect_len > 0)); end total_loss = (total_raw - total_used) + defect_loss; loss_rate = total_loss / total_raw * 100; utilization = 100 - loss_rate; disp(['Total Cutting Loss: ', num2str(total_loss), ' meters']); disp(['Cutting Loss Rate: ', num2str(loss_rate), '%']); disp(['Utilization Rate: ', num2str(utilization), '%']); % 显示切割方案细节 disp('Cutting plan details:'); for j = 1:num_raw if y(j) > 0 disp(['Raw material ', num2str(j), ' (L=', num2str(L(j)), 'm): ', num2str(y(j)), ' pieces']); for i = 1:num_orders idx_w = (i-1)*num_raw*2 + (j-1)*2 + 1; idx_h = (i-1)*num_raw*2 + (j-1)*2 + 2; if x(idx_w) > 0 || x(idx_h) > 0 disp([' Order ', num2str(i), ': width cuts=', num2str(x(idx_w)), ', height cuts=', num2str(x(idx_h))]); end end end end else disp('No feasible solution found with defects considered.'); end ``` 代码主要改进： 1. 重新定义了原材料数据，包含缺陷位置和长度信息 2. 为每根原材料计算可用分段（避开缺陷区域） 3. 引入新变量z(i,j,k,m)表示切割分配到的具体分段 4. 添加约束确保切割只在可用分段进行 5. 计算结果时考虑缺陷区域的固有损失 6. 输出更详细的切割方案信息 模型现在能够： - 避开所有已知缺陷区域进行切割 - 准确计算包含缺陷损失的利用率 - 提供详细的切割分配方案 注意：实际运行时可能需要根据具体MATLAB版本调整优化选项，对于大规模问题可能需要更高效的建模方式。 [2025-05-10 15:47:18 | AI问答 | 2480点数解答]