Operations Research and Logistics: Leach Distributors Case Study

This assignment presents a comprehensive case study on Leach Distributors, focusing on the application of linear programming to optimize container usage for packaging. The student formulates the optimization problem by defining decision variables, an objective function (maximizing profit), and constraints related to packing material and time. The solution utilizes Microsoft Excel Solver to determine the optimal number of each container class (A, K, and T) to maximize profit while adhering to resource restrictions. The implications of resource constraints are analyzed, and the benefits of linear programming in a manufacturing context are discussed, highlighting its role in profit maximization, efficient resource utilization, and addressing bottlenecks. The conclusion summarizes the findings, emphasizing the optimal container quantities and the achievement of maximum profit within the given constraints. References to relevant academic sources are also provided.

OPERATIONS RESEARCH
AND LOGISTICS CASE
STUDY TASK REFERRED
DEFERRED
CASE STUDY A – LEACH DISTRIBUTORS

TABLE OF CONTENTS
• INTRODUCTION
• Formulation of Optimizing problem
• Decision variables
• Objective function
• Constraints
• Non-negativity restrictions
• Statement of assumption
• Steps involved in Excel Solver
• Solution obtained through Microsoft Solver
• Implications of resource restrictions for Leach Distributors
• Selection and analysis of linear programming application
• Benefits of Linear programming in Manufacturing
• Conclusion
• References

INTRODUCTION
• Linear programming is a mathematical model through which the best outcome whether it
to maximize profit or minimize costs is achieved by representing the linear relationships
between objective function and constraints.
• In this presentation, by applying the linear programming model, the number of each class
of containers to be used by Leach Distributors for packaging during standard shipment
will be determined.

Formulation of optimization problem by
defining objective function and constraint
equations

PROBLEM FORMULATION
Decision variables
• X = Number of class A container to be used
• Y = Number of class K container to be used
• Z = Number of class T container to be used
Objective function
• Maximize,
• Z = $9X + $7Y + $15Z
Constraints
• Subject to,
• Packing material
• 2X + 1Y + 3Z </= 130
• Packing time
• 2X + 6Y + 4Z </= 240

NON – NEGATIVITY RESTRICTIONS
X>/= 0, Y>/= 0, Z>/= 0

STATEMENT OF ASSUMPTIONS
• Conditions of certainty
• Linearity
• Additivity
• Divisibility
• Conditions for non – negativity variables
• Finiteness
• Condition for optimal solution

STEPS INVOLVED IN EXCEL SOLVER

USING MICROSOFT SOLVER FOR SOLVING
FORMULATED LINEAR PROGRAMMING PROBLEM

IMPLICATIONS OF LEACH DISTRIBUTOR’S
RESOURCE RESTRICTION
• Resource restrictions for the Leach Distributor are as follows:
• Total available packing material = 130 pounds
• Total available packing time = 240 hours
• Optimal number of each class of container to pack each week for Leach Distributor are as follows:
• A class “A” container = 0
• A class “K” container = 14
• A class “T” container = 39

CONT.
X Y Z
1 13 39
Total
Profits 9 7 15 678.5714 Available
packing materials 2 1 3 130.7143 130
Packing time 2 6 4 234.2857 240
• Implications if 1 unit of class “A” container will be used in place of class “K”
container

CONT.
• Implications if 1 unit of class “A” container will be used in place of class “T” container
X Y Z
1 14 38
Total
Profits 9 7 15 677 Available
packing
materials
2 1 3 130 130
Packing time 2 6 4 238 240