# Supply Chain

Supply Chain Management became a popular term in the mid-1990s but, even today, no clear definition of the term has emerged. Instead, for most academics and practitioners, supply chain management is a broad term that covers many functions, including but not limited to manufacturing, warehousing, and transportation, as well as supplier relationship management, inventory management, pricing, and customer service.

As globalization has increased the scope and the complexity of supply chains, developing a supply chain strategy has become critical to a company's success. For some companies, a supply chain strategy that operates across multiple areas is necessary to achieve competitive advantage. For other companies, a supply chain strategy that focuses on a single area is sufficient to achieve operational excellence. In either case, optimization plays an important role.

This case studies collection highlights discrete optimization models in three areas that fall under the umbrella of supply chain: manufacturing, location analysis, and transportation. Please note that not all of the topics are serious in nature!

### Manufacturing

• Cutting Stock Problem
Given paper rolls of fixed width and a set of orders for rolls of smaller widths, the objective of the Cutting Stock Problem is to determine how to cut the rolls into smaller widths to fulfill the orders to minimize the scrap.
• Project Scheduling with CPM
Given a list of activities required to complete a project along with the duration of each activity and the dependencies between activities, the objective of the Critical Path Method (CPM) is to determine the sequence of activities that minimizes the latest completion time.

### Location Analysis

• Air Ambulance Reassignment Problem
The objective of the Air Ambulance Reassignment Problem is to determine a minimum cost assignment of helicopters to sites to satisfy the projected demand for the next time period.
• Quadratic Assignment Problem (interactive NEOS demo)
The objective of the Quadratic Assignment Problem is to assign $n$ facilities to $n$ locations in such a way as to minimize the assignment cost, which is a function of flow and distance.
• Nurse Practitioner Staffing (interactive NEOS demo)
The objective of the Nurse Practitioner Staffing Problem is to determine the optimal number of nurse practitioners to hire in order to maximize the number of patients served at nursing facilities.

### Transportation

• Bar Crawl Optimization Problem
The objective of the Bar Crawl Optimization Problem is to select a set of bars and determine an ordering of them in such a way as to maximize the total benefit minus the total distance subject to a budget constraint.
• Multiple Traveling Salesman Problem
The Multiple Traveling Salesman Problem (mTSP) is a generalization of the Traveling Salesman Problem (TSP) in which more than one salesman is allowed. Given a set of cities, one depot where $m$ salesmen are located, and a cost metric, the objective of the $m$TSP is to determine a tour for each salesman such that the total tour cost is minimized and that each city is visited exactly once by only one salesman.
• Woodman's Grocery Delivery Problem
This case study demonstrates how supermarkets can make use of ridesharing vehicles to augment their delivery fleet and how to develop a model that routes both the supermarkets vehicles and the ridesharing vehicles to satisfy customer demands. The problem can be modeled as a Heterogeneous Fleet Vehicle Routing Problem with Time Windows (HVRPTW).