Posted: August 25th, 2021
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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; Ax be the quantity available at the source, x
By bethe quantity of the goods required at destination y
Cxy is the cost per unit incurred to ship the commodity from the origin to its destination, y.
Zxy 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= Ax, x =1, 2…m
Zxy = By, 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 Tij and that Cxy is the unit cost for shipping goods from Pi to warehouse Tj, 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.
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