Construct A Model of Shipping Costs

Posted: August 25th, 2021

Student’s Name

Professor’s Name

Course

Date

Construct A Model of Shipping Costs

Consider two points, such that point x is the source and point y is the destination. The shipping problem can be modeled in the form of linear programming where the objective function aims at minimizing the shipping costs subject to supply and demand as constraints (Jansson and Shneerson, 143).

Let;      A_x be the quantity available at the source, x

            B_y bethe quantity of the goods required at destination y

            C_xy is the cost per unit incurred to ship the commodity from the origin to its destination, y.

Z_xy represents the quantity shipped from the origin xto destination y.

Mathematically, this problem can be modelled as follows;

Minimize total cost, K =

            Subject to;

Sum of Zxy= A_x, x =1, 2…m

                Zxy = B_y, y=1, 2…n

Zxy > 0, for all x and y.

Hence, if P is the plant or factory from which goods are manufactured while T represents the warehouse goods are shipped, then;

Let Zxy be the number of goods that are shipped from Pi to warehouse T_ij and that C_xy is the unit cost for shipping goods from P_i to warehouse T_j, the model objective function would be;

Minimize the shipping cost,

K = β₀+ β₁ c₁₁z₁₁+ β₂ c₁₂z₁₂+ β₃ c₁₃z₁₃+ β₄ c₂₁z₂₁+ β₅ c₂₂x₂₂+ β₆ c₂₃x₂₃+Ф

K is the total cost, which is the dependent variable. C and Z are independent variables whose change causes a relative change in K, the total cost.

Subject to:

Supply constraints,

S₁ = z₁₁+ z₁₂+ z₁₃

S₂ = z₂₁+ z₂₂+ z₂₃

S₃ = z₃₁+ z₃₂+ z₃₃

Demand Constraints,

D₁ = z₁₁+ z₁₂+ z₁₃

D₂ =z₂₁+ z₂₂+ z₂₃

D₃ =z₃₁+ z₃₂+ z₃₃

Assumptions in the models;

It is assumed that; Zxy >= for all the values of x and y

In addition, average supply available at the source is equal to average demand in the destination areas, that is, D₁+ D₂+ D₃= S₁+ S₂+ S₃.

According to (Mudambi et al., 17),  cost modelling  is important to shipping companies as it helps identify particular factors that contribute to costs, labor and direct materials required in completing activities in production.

Works Cited

Jansson, J. O., and D Shneerson. Liner Shipping Economics. Dordrecht: Springer Netherlands, 1987. Print.

Mudambi, Ram, and Martin J. Ricketts. The Organization of the firm: international business perspectives. London: Routledge, 1998. Print.