Mastering Hard Operations Analytics Case Studies: A Step-by-Step Guide
Operations analytics is a fascinating field that applies advanced analytical techniques to optimize key business processes and decisions. From streamlining supply chains to maximizing resource utilization, the opportunities to drive efficiency and performance through operations research are nearly endless.
One of the most powerful tools in the operations analytics toolkit is the transportation algorithm. While it may sound technical and intimidating, the underlying concepts are actually quite intuitive. In essence, the transportation problem is all about optimally matching supply and demand to minimize total costs or time.
To illustrate this, let‘s dive into a challenging operations analytics case study focused on optimizing call center staffing. We‘ll formulate the problem, explore different solution methods, and unpack key insights to take your operations research skills to the next level.
The Call Center Conundrum
Imagine you‘re managing a call center with 1,000 agents, each with different training and skills. Incoming calls span four distinct categories (X, Y, Z and W) based on the nature of the customer query. Your goal is to assign agents to queries in a way that minimizes the total time to resolve all calls.
Here‘s what you know:
- The 1,000 agents are split across 6 skill sets (A, B, C, D, E, F) based on their training
- Each skill set has a different number of agents (e.g. 200 in set A, 100 in set C)
- Calls arrive in different proportions by category (e.g. 20% X, 35% W)
- The time for an agent from a given skill set to handle a certain category of call varies (e.g. set A takes 10 min for X calls)
With 1,000 total calls matching the 1,000 agents, this is a balanced transportation problem. The key is determining how to assign agents to calls to minimize total resolution time.
Formulating the Transportation Model
To solve this as a transportation problem, we first need to formulate the objective function and constraints. The objective is to minimize the total time T spent across all agent-call assignments.
Mathematically, this looks like:
MIN T = Sum(i,j) t(i,j) * x(i,j)
Where:
- i = skill sets (A, B, C, D, E, F)
- j = call types (X, Y, Z, W)
- t(i,j) = time for skill set i to resolve call type j
- x(i,j) = number of agents from skill set i assigned to call type j
The constraints are:
- Each agent must be assigned to only one call type
- Each call must be handled by only one agent
- All calls must be resolved
- Agent assignments can‘t exceed the number in each skill set
With the problem formulated, we‘re ready to solve it. While linear programming is one option, let‘s explore some simpler solution methods specific to transportation problems.
Navigating the North-West Corner
The North-West Corner Rule (NWCR) is the simplest way to find an initial feasible solution. We start in the upper left (north-west) corner of the cost matrix, allocate the maximum possible amount to that cell, then cross out the corresponding row or column and proceed to the next cell.
Applying NWCR to our example yields the following assignments:
- 200 A agents to X calls
- 200 B agents split 100 to Y and 100 to Z
- 100 C agents to Y
- 100 D agents to Z
- 250 E agents to W
- 150 F also to W
The total resolution time comes to 7,550 minutes. Not terrible, but definitely room for improvement. NWCR doesn‘t consider the actual times, so it‘s rarely optimal.
Optimizing with Minimum Cost
The Minimum Cost Method (MCM) improves on NWCR by incorporating the time matrix. We find the smallest time across all skill-call combinations with remaining supply and demand, make the maximum assignment there, cross out the row or column, and repeat.
With MCM, the optimal allocations shift to:
- 200 X calls to 100 D and 100 E agents
- 300 Y split across 100 A, 150 B and 50 C
- 150 Z to 100 A and 50 B
- 350 W across 100 C, 100 E and 150 F
This cuts total time nearly in half to 3,900 minutes by prioritizing the quickest resolutions. MCM is usually a better starting point than NWCR but still may not find the global optimum.
Perfecting with Penalty Costs
The Penalty Cost Method takes MCM a step further by calculating the "penalty" for not making each assignment. This penalty is the difference between the minimum and next smallest time value for each skill set and call type.
We make the first assignment where the penalty is largest, recalculate penalties with the updated supply and demand, and continue until all agents and calls are exhausted.
In this case, the largest initial penalty is for call type X and skill set D. After making that assignment and updating, the next biggest penalties are skill set E for type W, then C for Y, and so on.
The final penalty cost assignments are:
- X calls get 100 D and 100 A agents
- Y calls get 200 B and 100 C agents
- Z calls get 100 A and 50 E agents
- W calls get 100 A, 100 E and 150 F agents
Total resolution time is 4,400 minutes – slightly worse than MCM but better than NWCR. In general, penalty costs tends to outperform the other methods but it really depends on the specific time values.
Stepping Beyond Stones
While initial feasible solutions are useful, there‘s usually still room to minimize further. More advanced techniques like the Stepping Stone Method and MODI (modified distribution) build on the initial allocations to find the provably optimal final solution.
These methods involve iteratively testing the impact of shifting assignments, identifying negative cycles to "step around", and redistributing until no further improvements are possible. They‘re a bit more involved mathematically, but worth exploring to take your transportation problem skills to the next level.
From Call Centers to the World
This call center staffing example illustrates core principles that generalize to a wide range of operations analytics problems. From classic examples like facility location and vehicle routing to more novel variants in healthcare, finance, and beyond, transportation models are a go-to operations research tool.
The diversity of applications is matched by the variety of solution approaches. While we walked through three common methods here, dozens of others exist – from genetic algorithms to deep reinforcement learning. Each has pros and cons in terms of simplicity, flexibility, computation time, and more.
At the end of the day, the "best" approach depends on your unique problem characteristics and constraints. The most important thing is to deeply understand the concepts so you can adapt them to novel situations. Hopefully this deep dive into a challenging case study has equipped you to do just that!
Conclusion and Key Takeaways
Optimization is the heart of operations analytics, and transportation problems are one of the most powerful tools in the optimization toolbox. By formulating business challenges in terms of supply, demand, costs, and constraints, you can uncover insights and efficiencies that are impossible to find manually.
The key is starting with a solid problem definition. Deeply understanding your objectives, decision variables, and constraints is critical to choosing the right solution approach. From there, it‘s all about balancing model complexity and performance to find the best possible allocation of scarce resources.
Of course, solving the math is only half the battle. The other core skill is translating analytical results into real-world impact. Always strive to complement your technical operations research chops with strong business acumen, communication, and cross-functional collaboration.
Mastering this balance is a career-long journey, but one that‘s immensely rewarding. For more inspiring examples and in-depth explanations of concepts we touched on here, definitely check out additional articles and case studies on this site.
I hope this deep dive into hard operations analytics has been enlightening and empowering. Here‘s to harnessing the power of advanced analytics to optimize our world!
