Transportation Problem Solver • web app with Excel interface by Stelling Consulting

Transportation problem description and example

In a transportation problem, demand should be met by supply against minimal transportation costs. The table below shows demand, supply and the transportation cost per quantity for each supply-demand connection. In this example, total demand (350) equals total supply (350). Total supply may exceed total demand, but can never be less, otherwise the problem can not be solved! The application will warn you if in your input the total supply is less than total demand.

Demo data

COST PER QUANTITY		SUPPLY
COST PER QUANTITY		14	15	16	18	9	4	7	15	20	232
DEMAND	40	334	356	336	18	45	795	59	291	89	585
	14	285	234	805	283	440	325	957	330	796	600
	26	431	965	600	241	190	417	117	916	631	436
	18	763	719	550	396	200	619	689	514	108	874
	10	484	933	792	607	322	548	851	715	802	272
	30	816	611	225	79	851	425	841	481	500	903
	18	899	391	165	155	657	231	757	730	48	282
	8	922	320	661	38	726	760	150	891	483	407
	4	316	504	123	587	938	706	382	729	547	310
	6	751	37	825	754	140	323	229	592	571	914
	6	117	706	414	674	275	703	395	315	115	891
	12	498	898	858	498	187	411	717	353	560	368
	18	169	470	643	433	132	652	898	719	555	444
	2	840	336	860	577	112	292	422	294	411	474
	20	935	569	443	639	523	549	60	415	409	791
	32	753	614	610	426	136	578	118	335	751	494
	20	83	572	108	570	241	946	651	762	790	40
	36	167	838	963	299	362	90	843	39	50	45
	28	517	657	914	79	678	811	173	364	930	593
	2	746	440	747	392	946	456	560	462	798	462

Optimal quantities: total costs are 102587

OPTIMAL QUANTITIES		SUPPLY
OPTIMAL QUANTITIES		14	15	16	18	9	4	7	15	20	232
DEMAND	40				4	9			2	2	23
	14	1	9				4
	26										26
	18									18
	10										10
	30			16	14
	18										18
	8										8
	4										4
	6		6
	6	6
	12										12
	18	7									11
	2										2
	20							7	13
	32										32
	20										20
	36										36
	28										28
	2										2

With r referring to row, and c to column, and X_rc to the transport quantity from Supply_r to Demand_c, and C_rc to the transport cost per quantity from Supply_r to Demand_c the LP problem can be formulated as:

Minimize Σ C_rc × X_rc , subject to
Σ X_rc ≥ Demand_c ∀ c

Σ X_rc ≤ Supply_r ∀ r

X_rc ≥ 0 ∀ r,c

Input

Oversupply

Enter data tab or semicolon separated.

Top-left cell = MIN (minimize costs) 1^st row = supply quantities 1^st column = demand quantities All other cells = transport cost per quantity

Solution

Initialisation method

Amount of cases

The solution will appear here, once run.

Visual supply chain network design case (random)

The random case will contain 10 warehouses and 1000 customers, with transportation costs per quantity = distance between warehouse and customer (instead of random costs). Generated input will appear under section 2. Hidden logic within that input enables below visualizations.

Oversupply

Final solution

Costs: Index:

Initial solution VOGEL

Costs: Index:

Initial solution STELLING

Costs: Index: