Sử dụng công cụ Solver trong MS Excel để giải bài toán tối ưu

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Đối với việc tìm lời giải cho bài toán tối ưu (optimal problem) khó khăn lớn nhất khi đã biết được thuật toán là chi phí tính toán rất lớn do dữ liệu cần xử lý (tính toán) và số phương án ứng viên (candidate solution) quá nhiều. Vì vậy, việc tính toán thủ công để tìm phương án tối ưu trong thực tế là không khả thi. Để giải quyết khó khăn này, MS Excel đã xây dựng công cụ Solver giúp giải các bài toán tối ưu. Bài viết này giới thiệu cách sử dụng công cụ Solver để tìm phương án tối ưu thông qua một số bài toán tối ưu quen thuộc như bài toán vận tải, bài toán nguyên vật liệu sản xuất. Do bài viết chỉ tập trung vào việc minh họa cách sử dụng Solver để tìm phương án tối ưu nên không trình bày lại chi tiết cách giải các bài toán này. Các bài toán này thường được trình bày rất chi tiết trong môn học Qui hoạch tuyến tính.

Qui trình để giải các bài toán tối ưu sử dụng Solver thực hiện theo các bước sau:

1. Xây dựng hàm mục tiêu (Objective Function)
2. Xây dựng các ràng buộc (Constraints)
3. Tổ chức dữ liệu trên bảng tính Excel
4. Sử dụng Solver để tìm phương án tối ưu

1. Ví dụ chung về bài toán tối ưu

Giả sử ta có hàm mục tiêu và các ràng buộc của bài toán tối ưu được thiết lập như sau:

Sử dụng Solver để tìm phương án tối ưu cho bài toán trên.

Như vậy bước thiết lập hàm mục tiêu và các ràng buộc đã xong, bước tiếp theo là tổ chức dữ liệu trong bảng tính Excel và thực hiện Solver

Tổ chức dữ liệu trong Excel  cho bài toán trên như sau:

Chú ý giá trị khởi tạo cho các biến x1, x2, x3, x4 (vùng chứa phương án tìm kiếm B4:E4) ban đầu là 0.

 Sau khi tổ chức dữ liệu như trên, ta sử dụng Solver để tìm phương án tối ưu như sau:

Vào Menu Tools chọn Solver (nếu trong Menu Tools chưa có công cụ Solver thì vào Menu Tools chọn Add-ins chọn Solver add- in để cài thêm công cụ solver). Hộp thoại Solver xuất hiện, thiết lập các tham số cho solver như sau:

Giải thích các tham số:

Set Target Cell: Ô chứa giá trị hàm mục tiêu (F5)

Equal to: Chọn Max, tìm giá trị max của hàm mục tiêu

By changing Cells: Các ô chứa phương án tối ưu cần tìm ($B$4:$E$4)

Subject to the Constraints: Chứa các ràng buộc của hàm mục tiêu. Gồm 4 ràng buộc như đã cho.

phương án tối ưu là (0,3,0,0.8) và giá trị hàm mục tiêu đạt giá trị lớn nhất là 36.

Để có thêm thông tin chi tiết về phương án tối ưu, chọn Keep Solver Solution, trong mục Reports chọn Answer như sau:

2. Ví dụ về bài toán vận tải

Lập phương án vận chuyển xăng từ 4 kho xăng đến 5 trạm tiêu thụ với chi phí vận chuyển, lượng xăng dự trữ tại mỗi kho và nhu cầu tiêu thụ xăng tại mỗi trạm được cho như bảng dưới đây sao cho tổng chi phí vận chuyển là nhỏ nhất.

Lập hàm mục tiêu và các ràng buộc cho bài toán vận tải

 

Tổ chức dữ liệu trong bảng tính Excel như sau

Sử dụng Solver để tìm phương án tối ưu để vận chuyển xăng với chi phí nhỏ nhất

 

Phương án tối ưu

Phương án vận chuyển tối ưu là (0,0,0,4,0;0,4,0,0,2;7,3,0,0,0;0,0,7,3,0), chi phí vận chuyển nhỏ nhất là 227

3. Bài toán sản xuất

Một nhà máy dự định sản xuất 5 loại sản phẩm S_j (j=1,5). Tất cả 5 loại sản phẩm này đều sử dụng 4 loại nguyên vật liệu NVL_i (i=1,4). Lợi nhuận của mỗi sản phẩm và dự trữ của từng loại nguyên vật liệu được cho như bảng sau:

Hãy tìm phương án sản xuất các sản phẩm để có được tổng lợi nhuận là lớn nhất.

Xây dựng hàm mục tiêu và các ràng buộc cho bài toán

Sử dụng Solver để tìm phương án sản xuất tối ưu

Kết quả

Số lượng  từng loại sản phẩm sản xuất để đạt được lợi nhuận tối đa là (200,0,0,0,200). Lợi nhuận đạt được là 124000.

bác giúp em giải một số bài toán được không ạ :(( em làm bài kiểm tra mà không sao làm được giúp em với

Em học AddIn này cách đây 5 năm và bây giờ mới ứng dụng Thầy ah. Quá tuyệt vời, lại free ! :D

By changing Cells: Các ô chứa phương án tối ưu cần tìm ($B$4:$E$4) Dòng này em chưa biết nhập sao em ra các ký tự không giống, chỉ cho em với ạ

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