Optimal Supply Chain Model: Highway Concrete Aggregates

A supply chain is a network of physical or virtual products flowing between suppliers, distribution centers, and customers. Product movements within the network are determined by management. Supply chain managers need to consider cost, speed, risk, and other factors when deciding how to deliver products. An optimum supply chain attains the best progress toward the goal with minimum risk to the fulfillment of the customer's order.

This article seeks to show the use of supply chain concepts in planning a county’s public works highway construction. The scope includes concrete aggregate sourcing, grading, and delivery to the construction site. Linear programming was used as the optimization platform (1)(2). A determination of the best supply chain configuration is performed whenever changes to supply chain assumptions are made.

The construction of concrete highway involves the preparation of the road bed and the pouring of the concrete mix. This slurry consists of a specific combination of cement, coarse aggregate, fine aggregate, and water. The best mixture is that combination of ingredients that results in the specified strength while pouring readily into slabs of concrete.

Natural or crushed rocks give concrete its basic strength while fine aggregates and cement fill the interstices and bind everything into a hard solid structure. Water makes the mix workable but an excess will result in weak concrete. Indeed, any deviation of these components from the standards set by the American Society of Testing Materials or ASTM makes for an unworkable mix or a weak concrete pavement.

The Concrete Aggregate Supply Plan

The county’s highway construction project will require 21,000 cubic yards of aggregates following the 1:2:4 ratio of cement, coarse aggregates, and fine aggregates. Two commercial suppliers, s1 and s2 will deliver 4,000 and 3,000 cubic yards of graded aggregates, respectively. These add up to 33% of the total aggregate requirement. The rest of the aggregate requirements are met from the County’s quarry and sand and gravel pits. County properties s3, s4, s5, and s6 supply 3,000, 3,300, 2,700 and 5,000 cubic yards, respectively.

The optimized plan by the construction team has a total delivered cost of $4,016,080. Of this amount, $1,488,600 is out-of-pocket cash paid to commercial suppliers. The remainder of the cost is estimated from the County’s accounting system.

The Optimized Supply Plan Under Source Risk

The biggest risk to the county’s highway construction project is the capacity of its aggregate processing operation at s6. The construction team believes there is a significant chance the facility can only supply a lower 2,000 cubic yards of graded aggregates rather than the planned 5,000 cubic yards. Upon the county’s request, the commercial suppliers pledged extra capacity for the project.

The supply chain model was optimized after the supply constraints were modified. This time, the two commercial suppliers, s1 and s2 each deliver 5,000 cubic yards of graded aggregates. This time, 48% of total aggregates are supplied by commercial producers. The rest of the requirements will be made up by delivery from the county’s quarry and sand and gravel pits. Properties s3, s4, s5, and s6 supply 3,000, 3,300, 2,700, and 2,000 cubic yards of aggregates, respectively.

While this optimized plan under risk has a lower total cost of $3,977,280, the county actually paid less out-of-pocket cash of $2,237,000 to commercial suppliers.

Conclusion

An optimized supply chain model on a linear programming platform allows quick evaluation of system performance while considering risks to the delivery of quality products to the customer. As a managerial tool for performing network risk analysis, spreadsheet interfaced optimization platforms are easy to use and are conveniently available at minimal costs (3)(4)(5).

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Analytical

Linear programming optimization platforms perform mathematical operations on a system of linear equations. One of the equations defines the objective function and the rest are equations that constrain the objective function. Each iteration of the platform's mathematical operations produces a solution. Optimization is achieved when the latest solution is the highest for maximizing objective functions or the lowest for minimizing objective functions. The analysis in this article used the Solver (3), a linear programming platform Add-In of Microsoft Excel. The model that is fully illustrated in the exhibit below has six decision variables in the objective function and five equations of constraint. A more comprehensive supply chain model covering a greater scope of highway construction can be developed in the Solver with its capacity to consider 200 decision variables.

By Mgmtlaboratory.com staff. 2023

References

1. Optimal Social Service Resource Planning. www.mgmtlaboratory.com. February 2019.

2. Diversity and the Modern Portfolio Theory. www.mgmtlaboratory.com. August 2023.

3. Solver. Microsoft Excel. A (free) mathematical programming Add-in in Excel that accommodates 200 decision variables and 100 constraints.

4. What’sBest!  Solver Suite, Lindo Systems Inc. This $195 spreadsheet app. accommodates 500 decision variables and 250 constraints. The purchaser will have a permanent license.

5. Analytic Solver.  Frontline Systems Inc. This extension of the Solver in Microsoft Excel accommodates up to 8.000 decision variables. The purchaser will have a subscription license of $495 for the first year.