线性规划求解商超补货和定价策略

clc close all % 预测的销售总量 sales_forecast = [530.03,4254.42,2928.54,589.71,2182.43,718.12; % 品类1~6在第1天的预测销售总量 729.89,4624.61,3711.17,545.16,2364.67,833.21; % 品类1~6在第2天的预测销售总量 490.38,4554.75,3040.29,498.07,2500.67,1052.02; % 以此类推，填写第3~7天的预测销售总量 506.55,4724.39,3197.76,449.89,2895.68,1041.47; 519.04,4495.37,3025.57,426.07,3079.82,983.91; 408.42,4461.56,2761.41,426.77,3033.27,889.95; 391.04,4474.64,3171.31,472.90,3008.13,798.36; ]; %构建目标函数系数向量 f = -sales_forecast(:); % 将销售总量转换为目标函数系数向量的负数

% 成本加成倍数 cost_multiplier = [1.02, 1.02, 1.02, 1.02, 1.02, 1.02]; % 品类1~6的成本加成倍数

% 构建不等式约束矩阵和右侧向量 A = [7,6]; b = [7,1];

% 销售总量的约束 for i = 1:size(sales_forecast, 2) A = blkdiag(A, eye(size(sales_forecast, 1))); % 每个品类的约束矩阵为单位矩阵 b = [b; sales_forecast(:, i)']; % 每个品类的约束右侧向量为预测的销售总量 end

% 成本加成定价的约束 A = [A; -diag(cost_multiplier)]; % 成本加成定价的约束矩阵为对角矩阵的负数 b = [b; zeros(size(cost_multiplier))]; % 成本加成定价的约束右侧向量为0

% 构建变量的上下界 lb = zeros(size(f)); % 变量下界为0 ub = []; % 变量上界为无穷大

% 使用线性规划函数求解优化问题 [x, ~, exitflag] = linprog(f, A, b, [], [], lb, ub);

if exitflag == 1 % 输出补货数量和定价策略 replenishment = reshape(x, size(sales_forecast, 1), size(sales_forecast, 2)); pricing = cost_multiplier'; disp('补货数量：'); disp(replenishment); disp('定价策略：'); disp(pricing); disp(['商超的最大收益为：', num2str(-f'*x)]); else disp('无法找到最优解！'); end