## Minimizing the Cost of Transportation

Read this article. The study employed a transportation model to find the minimum cost of transporting manufactured goods from factories to warehouses. As you read, think of some factors that can greatly increase transportation and logistics time.

### Review of Some Literatures

The transportation problem was formalized by the French mathematician.

Charnes et al., developed the Stepping Stone Method which provides an alternative way of determining the simplex-method information.

Dantzig used the simplex method in the transportation problem as the Primal simplex transportation method. An initial basic feasible solution for the transportation problem can be obtained by using the North West corner Rule, Least-cost or the Vogel's Approximation method. Harold Kuhn developed and publishes the Hungarian method which is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal the vest dual method. This method was originally invented for the best assignment of a set of persons to a set of jobs. It is a special case of transportation problem. Roy and Gelders solved a real life distribution problem of a liquid bottled product through a 3-stage logistic system; the stages of the system are plant-depot, depot-distributor and distributor-dealer. They modelled the customer allocation, depot location and transportation problem as a 0-1 integer programming model with the objective function of minimization of the fleet operating costs, the depot setup costs, and delivery costs subject to supply constraints, demand constraints, truck load capacity constraints, and driver hours constraints. Arsham et al., introduced a new algorithm for solving the transportation problem. The proposed method used only one operation, the Gauss Jordan pivoting method, which was used in simplex method. The final table can be used for the post optimality analysis of transportation problem. This algorithm is faster than simplex, more general than stepping stone and simpler than both in solving general transportation problem. Tzeng et al., solved the problem of how to distribute and transport the imported Coal to each of the power plants on time in the required amounts and at the required quality under conditions of stable and supply with least delay. They formulated a LP that Minimizes the cost of transportation subject to supply constraints, demand constraints, vessel constraints and handling constraints of the ports. The model was solved to yield optimum results, which is then used as input to a decision support system that help manage the coal allocation, voyage scheduling, and dynamic fleet assignment. Das et al., focused on the solution procedure of the multi-objective transportation problem where the cost coefficients of the objective functions, and the source and destination parameters are expressed as interval values by the decision maker. They transformed the problem into a classical multi-objective transportation problem so as to minimize as the interval objective function. They defined the order relations that represent the decision maker's preference between interval profits. They converted the constraints with interval source and destination parameters into deterministic one. Finally, they solved equivalent transformed problem by fuzzy programming technique.

A.C. Caputo et al., presented a methodology for optimally planning long-haul road transport activities through proper aggregation of customer orders in separate full-truckload or less-than- Truck load shipments in order to minimize total transportation costs. They have demonstrated that evolutionary computation techniques may be effective in tactical planning of transportation activities. The model shows that substantial savings on overall transportation cost may be achieved adopting the methodology in a real life scenario. Chakraborty A. And Chakraborty M. Studied cost-time minimization in a transportation problem with fuzzy parameters: a case study. They proposed a method for the minimization of transportation cost as well as time of transportation when the demand, supply and transportation cost per unit of the quantities are fuzzy. The problem is modelled as multi objective linear programming problem with imprecise parameters. Fuzzy parametric programming has been used to handle impreciseness and the resulting multi objective problem has been solved by prioritized goal programming approach. A case study has been made using the proposed approach. Dhakry N. S. and Bangar A. Studied Minimization of Inventory and Transportation Cost Of an Industry -A Supply Chain Optimization. The results they obtained from the transportation-inventory models show that the single DC and regional central stock strategies are more cost-efficient respectively compared to the flow-through approach. It is recommended to take the single DC and the regional central stock strategies for slow moving and demanding products respectively: Minimizing inventory & transportation cost of an industry: a supply chain optimization. Yan Q. and Zhang Q. The Optimization of Transportation Costs in Logistics Enterprises with Time-Window Constraints. They presents a model for solving a multiobjective vehicle routing problem with soft time-window constraints that specify the earliest and latest arrival times of customers. If a customer is serviced before the earliest specified arrival time, extra inventory costs are incurred. If the customer is serviced after the latest arrival time, penalty costs must be paid. Both the total transportation cost and the required fleet size are minimized in this model, which also accounts for the given capacity limitations of each vehicle. The total transportation cost consists of direct transportation costs, extra inventory costs, and penalty costs. This multi objective optimization is solved by using a modified genetic algorithm approach. The output of the algorithm is a set of optimal solutions that represent the trade-off between total transportation cost and the fleet size required to service customers. The influential impact of these two factors is analyzed through the use of a case study. Edokpia, R.O. and Amiolemhen, P.E. Studied Transportation cost minimization of a manufacturing firm using genetic algorithm approach. The data they obtained were analyzed and formulated into a transportation matrix with three routes and ten depots which were coded into strings after which the GA was applied to generate optimal schedules for six to nine depots that optimize the total transportation cost, revealing marked savings when compared with the company's current evaluation method. The cost savings reduced as the number of depots in the generated schedules increased with the six-depot schedule having the highest cost saving of N347, 552 daily.

The aim of this study is to minimize the cost of shipping cement from BUA cement factories to the various warehouses (Dealers).