Applying Mixed Integer Linear Programming to decide on the location of a new warehouse and its corresponding delivery distribution plan.

Background

The packaging industry plays a crucial role in supply chain management, ensuring products are efficiently transported from production to consumers. Company P, a local potato chip brand, operates within this sector, packaging its products in cans and bags at three separate plants. These goods are then sent to a central warehouse for quality checks before distribution to five retail partners. With a significant sales increase anticipated over the next three years, Company P is facing the challenge of expanding its warehousing capabilities to keep pace with rising demand.

Current Supply Chain

The information provided illustrates the capacity of each plant and the requirements of each retailer. The primary factor influencing the decision-making process is the impact of the delivery quantities on the overall cost, which are influenced by the varying degrees of transportation costs for the northern, current, and southern regions.

Problem Statement

Company P needs to determine the most cost-effective strategy for expanding its warehousing capacity in response to projected sales growth. To match this upsurge, the upper management is faced with the following potential remedies:

• Building a regular warehouse in the northern region.
• Building a smaller warehouse in either the northern or southern region.
• Expand the current warehouse that doubles its capacity.

The objective is to select the option and location that will minimize delivery costs while considering that each warehouse has a specified capacity constraint and building multiple warehouses must not go over the prescribed capital budget.

Methodology and Solution Strategy

The case study qualifies as an optimization problem, specifically a linear programming problem, as it involves the objective of minimizing total costs while following specific constraints in budget and capacity.

The formulation above is known as a Mixed Integer Linear Programming (MILP) problem because it involves optimizing a linear objective function subject to linear constraints. It incorporates both continuous and integer decision variables, distinguishing it from pure linear programming, which only deals with continuous variables. MILP problems are typically used in scenarios requiring discrete decisions, such as scheduling or resource allocation.

With this “format”, we create 6 complex sets of MILP formulation, where each corresponds to a warehousing structure (shown in the table below). The idea is to compare the costs across the next 3 years

Recommendations and Impact

A regular warehouse up north and a smaller warehouse down south yield the lowest delivery costs in general as compared to having only one additional warehouse in either regions. It was also shown that expanding the current warehouse is a bad decision since it will later incur high delivery costs.

When only planning for the next year, the company may quickly realize that small warehouses in the northern and southern regions are enough since the option has a cheaper delivery and construction cost compared to a regular warehouse in the north and a small warehouse in the south. But in a much long-term perspective, the latter will ultimately outperform the rest as demands further increase.

Proposed Distribution Plan for 2004

To prepare for the next three years, below shows the supply chain for 2004 that will only expect minimal changes from the plants and to the retailers as 2005 and 2006 come.