@@ -2179,7 +2179,6 @@ The [**Assignment Problem**]() aims to allocate *n* tasks to *n* agents (machine
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2182- 🏄🏄🏄🏄🏄
21832182
21842183## 1. [ Hungarian Method] ( ) (Step by Step):
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@@ -2235,10 +2234,15 @@ The [**Assignment Problem**]() aims to allocate *n* tasks to *n* agents (machine
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2237+ 🏄🏄🏄🏄🏄
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2239- ## Step 1: Set Up the Excel Spreadsheet
2239+ ### [ Step 1] ( ) : Set Up the Excel Spreadsheet
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2241- ### 1. Enter the Cost Matrix
2241+ <br >
2242+
2243+ #### [ 1.1] ( ) : Enter the Cost Matrix
2244+
2245+ <br >
22422246
22432247| | B | C | D |
22442248| -----| ------| ------| ------|
@@ -2247,9 +2251,15 @@ The [**Assignment Problem**]() aims to allocate *n* tasks to *n* agents (machine
22472251| T2 | 1 | 3 | 2 |
22482252| T3 | 5 | 2 | 4 |
22492253
2254+ <br >
2255+
22502256- Place this table in cells ** B2: D4 ** .
22512257
2252- ### 2. Create the Decision Variable Table
2258+ <br >
2259+
2260+ #### [ 1.2] ( ) : Create the Decision Variable Table
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2262+ <br >
22532263
22542264| | G | H | I |
22552265| -----| ------| ------| ------|
@@ -2258,20 +2268,31 @@ The [**Assignment Problem**]() aims to allocate *n* tasks to *n* agents (machine
22582268| T2 | x21 | x22 | x23 |
22592269| T3 | x31 | x32 | x33 |
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2271+ <br >
2272+
22612273- Place this table in ** G2: I4 ** .
22622274- These cells will be filled with 0 or 1 by the Solver (1 = assigned, 0 = not assigned).
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2264- ### 3. Calculate the Total Cost
2276+ <br >
2277+
2278+ ### [ 1.3] ( ) : Calculate the Total Cost
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22662280In cell ** K2** , enter:
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2282+
22682283``` bash
22692284=SUMPRODUCT(B2:D4, G2:I4)
22702285```
22712286
22722287This formula multiplies each assignment by its cost and sums the total.
22732288
2274- ### 4. Add Row and Column Sums for Constraints
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2290+ <br >
2291+
2292+
2293+ #### [ .4] ( ) : Add Row and Column Sums for Constraints
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2295+ <br >
22752296
22762297#### Row Sums (Each Task Assigned Once)
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@@ -2285,9 +2306,10 @@ This formula multiplies each assignment by its cost and sums the total.
22852306- In ** H5** : ` =SUM(H2:H4) `
22862307- In ** I5** : ` =SUM(I2:I4) `
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2309+
22882310<br >
22892311
2290- ## Step 2: Configure Excel Solver
2312+ ### [ Step 2] ( ) : Configure Excel Solver
22912313
229223141 . ** Go to** : Data > Solver
229323152 . ** Set Objective** :
@@ -2304,17 +2326,22 @@ This formula multiplies each assignment by its cost and sums the total.
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23052327<br >
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2307- ## Step 3: Solution Example
2329+ ### [ Step 3] ( ) : Solution Example
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23092331After running Solver, you should get a solution like:
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2333+ <br >
2334+
2335+
23112336| | M1 | M2 | M3 | Row Sum |
23122337| -----| ----| ----| ----| ---------|
23132338| T1 | 1 | 0 | 0 | 1 |
23142339| T2 | 0 | 0 | 1 | 1 |
23152340| T3 | 0 | 1 | 0 | 1 |
23162341| Col Sum| 1| 1 | 1 | |
23172342
2343+ <br >
2344+
23182345- ** Task 1 → Machine 1** (cost 2)
23192346- ** Task 2 → Machine 3** (cost 2)
23202347- ** Task 3 → Machine 2** (cost 2)
@@ -2325,27 +2352,33 @@ After running Solver, you should get a solution like:
23252352
23262353## Excel Table and Formula Summary
23272354
2355+ <br >
2356+
23282357| | M1 | M2 | M3 | Row Sum |
23292358| -----| ------| ------| ------| ---------|
23302359| T1 | G2 | H2 | I2 | J2 |
23312360| T2 | G3 | H3 | I3 | J3 |
23322361| T3 | G4 | H4 | I4 | J4 |
23332362| Col Sum| G5 | H5 | I5 | |
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2364+ <br >
2365+
23352366- ** Total Cost:** ` =SUMPRODUCT(B2:D4, G2:I4) `
23362367- ** Row Sums:** ` =SUM(G2:I2) ` , etc.
23372368- ** Column Sums:** ` =SUM(G2:G4) ` , etc.
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23392370<br >
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2341- ### [ Result ] ( ) :
2372+ ### [ Step 4 ] ( ) : Result
23422373
23432374** The optimal assignment is:**
23442375- Task 1 to Machine 1 (cost 2)
23452376- Task 2 to Machine 3 (cost 2)
23462377- Task 3 to Machine 2 (cost 2)
23472378
2348- ### [ ** Total minimum cost:** 6] ( )
2379+ <br >
2380+
2381+ ### ** Total minimum cost:** [ 6] ( )
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