Building Blocks of Supply Planning Solutions: Supply Chain Solver Methods

Michael Jermann Manager, PwC Switzerland 08/12/22

Are you facing the challenge of having to transform your supply planning processes? The pandemic has prompted many supply chain leaders to improve their planning processes and invest in new software solutions to enhance future resilience. This trend is further accelerated by the move to S/4HANA, the new version of SAP, which many companies are using as an opportunity to re-evaluate existing operating models.

Against this backdrop, this white paper series takes a look at supply planning solutions. Supply planning refers to the tactical planning process of creating production, capacity utilisation, distribution and material requirement plans based on a forecast of demand. These plans form the input into more detailed scheduling systems in the short-term operational environment. Most software offerings in this space bring a core platform of capabilities that is then configured to a product that fits the customer’s specific needs. Supply organisations therefore play a critical role in shaping these solutions by formulating clear functional requirements. This paper zooms in on the foundational building blocks, and instead of giving a broader view of capabilities discusses these topics in greater detail. The intention is to make these aspects of the supply planning tool more tangible and foster a deeper awareness of the critical design decisions on your transformation journey. This is important, because the design of these components of your planning tool has a fundamental impact on the overall solution. Moreover, as these building blocks touch on almost every function of the tool, it’s critical to get the design right the first time to avoid costly rework during the implementation. Your business’s specific functional requirements in this area might also have an impact on your selection of vendor.

Pick the solver best suited to your problem

The driving force in any supply planning tool is the underlying method that translates business objectives in the form of input parameters into calculated outcomes such as a production or distribution plan. These methods, which we refer to as “solvers”, can be classified into two categories: mathematical optimisation (such as linear programming) and heuristics. Depending on your business environment, one might be more suited than the other or a hybrid approach might be needed. To make this decision, it’s critical to understand what problems your planning teams have to solve before the plans are handed over to operational teams and systems downstream (i.e. scheduling). From our experience, this exercise is aided greatly by a base understanding of how the different methods approach problem solving

How does mathematical optimisation work?

In the mathematical optimisation method, planners define costs for all relevant planning activities as an input for the solver. These include the costs of producing, shipping or storing products. Besides these supply costs, planners capture profitability and service level priorities. Here it is common for solutions to look at profitability from an opportunity cost perspective, for example by considering product profitability via a penalty cost for failing to meet demand. Inventory policies are similarly taken account of via penalty costs for a failure to achieve targeted stock levels. In addition to cost parameters, planners define constraints such as production and transport capacity limits. These can be hard constraints, meaning the solver is prevented from exceeding these limits, or soft constraints, meaning the solver starts incurring costs once limits are breached. Depending on your industry, various other additional parameters, such as production lead times, may be included.

These input parameters are then run through a mathematical function. This function considers the costs that the planner has provided across the full supply network (for example by considering costs across all manufacturing sites) as well as across the full planning horizon (for example by considering time-varying costs or decisions to produce earlier or later). The solver aims to find the lowest cost solution within the given constraints.

How does heuristics work?

Whereas planners define costs using the optimisation approach, planners using heuristics define planning sequences based on best practices or rules of thumb. Normally there are multiple sequences, each of which tackles specific parts of a plan. For example, it is common for sales demand to be solved first, with target stock levels solved thereafter. With heuristics, more sequences are likely to exist in the solve run, and it is critical to gain transparency from your solution provider on this set-up. Apart from this crucial distinction, other parameters are handled similarly to mathematical optimisation.

To illustrate this solving process, let’s look at a possible example in the manufacturing industry. The heuristics solver starts its solving process by looking at locations with demand for the first product in the defined solve order for the first time-bucket. Let’s assume this demand is mapped to a distribution centre (DC). Should there be insufficient stock at the DC, the solver checks available transportation lanes that can replenish the DC from other locations. In the case of multiple lanes, the solver picks the one that the planner has defined as the first priority (via a rule of thumb). The solver then travels upstream on this lane to arrive at a manufacturing site. At this site, the solver checks available production lines and transportation lanes to other locations, again picking the prioritised option. In the event that a hard capacity constraint stops the solver from planning the full demand on the production line, the solver checks secondary options, travelling back downstream, if necessary, to choose alternate paths. If there are no available options, the solver reports the demand as lost. As you can see, a heuristic works sequentially, analysing the situation for each node individually.

What are the pros and cons of each method?

These solvers approach problems fundamentally differently and come with their advantages and disadvantages. Mathematical optimisation is superior when it comes to handling trade-offs, as the solver dynamically considers relative cost differences across the entire network and time horizon. This is illustrated in Figure 1, where the optimiser considers the costs of all demands when deciding which customer to fulfil from where. The user does not have to predefine the solve order, but only needs to provide the costs for each option. Based on this, the solver can make the cost-optimal decision on its own. In heuristics, planners need to tell the solver as an input what rule to follow. In this example we prioritised the different sourcing options based on the cost. As the heuristics solver solves by demand, we also need to provide it with a sequence in which the demands are solved. Again, here we will assume as a rule of thumb that the premium customer should be solved first, followed by the retailer and then the wholesaler. Now that we have given the solver an input on what rules to follow, let us look at the result.

We can immediately see that if we just go solving the premium customer first, the outcome will be more costly compared with the mathematical optimisation approach. This is because too much volume of the premium customer will be planned on Plant 1, thereby triggering costly overflows for the retail and wholesale customer to Plant 2. To improve the outcome, we would have to tweak the business rule, for example by solving the retailer’s and wholesaler’s demand ahead of the premium customer demand. This is a very simple situation, and more complex use cases might exist for your business. This example illustrates the way static rules in heuristics can lead to suboptimal planning. An optimiser arrives at a cost-optimal outcome by solving for the entire network as part of a mathematical function whilst a heuristics solution solves order by order based on rules of thumb that might require frequent revisions in volatile environments.

While mathematical optimisation can generate cost-optimal outcomes, this is only true if they are maintained properly, which is not always straightforward. Costs are often partially – or sometimes even fully – artificial, as they “monetise” factors that are not easily quantifiable. For example, demand penalty costs would not only have to account for the margin contribution of the product, but also the strategic value of the product’s customers or the importance of the product’s category from a market share perspective. It is our experience that these artificial costs often reflect a priority instead of a true cost impact. Also bear in mind that it is not only the single cost for a product and activity that is relevant, but how these costs relate to other costs, thereby defining the priority order in trade-off decisions. With increasing number of objectives, it becomes trickier to consistently maintain the correct relationship across products and cost objectives. Therefore, it is crucial to put sound processes in place to regularly review these parameters.

It can also be more challenging to explain the solve output of the mathematical algorithm. In heuristics, this is simplified somewhat, as the planner can predefine the solve priorities. Also, plan changes can generally be more easily identified and explained in heuristics thanks to the sequential nature of the solve (versus the fully interconnected approach in mathematical optimisation). This interconnected solve approach in mathematical optimisation can also result in more widespread changes plan over plan. This can pose a challenge for logistics organisations when plant or production line allocations frequently change, thereby preventing executional fine-tuning for increased efficiency. Heuristics results are generally more consistent and localised, as a heuristic solves in a siloed, node-by-node approach.

A significant risk of mathematical approaches is that with an increased level of complexity the solver runtime can increase substantially. This can throw a curveball into planning processes if a solve run requires several hours to calculate. A strong solver performance is crucial, especially given the increased complexity that comes with an end-to-end view of the supply chain and the need to simulate scenarios rapidly. There have been advances in speeding up the runtime of mathematical solvers. For example, the latest solver from Gurobi improved its performance by 43% from 2019 to 20211. However, heuristics still has the edge on speed in many cases. Knowing these strengths and weaknesses, many service providers offer hybrid solutions where mathematical optimization is combined with heuristics.

How do I pick the right approach for my supply chain?

We recommend that at the beginning of the planning transformation journey, supply chain leaders thoroughly assess what problems the system will have to solve in detail. It’s critical to capture all use cases, the frequency with which they occur and their impact on operations. A key success factor in running this exercise is to bring together technical and functional expertise to avoid bias and ensure the right questions are asked. This reflection allows companies to gain a better understanding of what type of solver capabilities are needed and can help you understand what an end-to-end planning approach in your transformation journey truly means, thereby allowing you to formulate a more tangible product vision. This approach will also allow companies to make more informed vendor selections, creating better process blueprints and driving a smoother transformation journey overall.

Where are you likely to need support?

In this, Part 1 of our white paper series on the building blocks of supply planning solutions, we’ve examined the role of the solvers. Solvers, the underlying method that translates business objectives into calculated outcomes, fall into two categories: mathematical optimisation and heuristics. Whether you choose one or the other or a hybrid form depends on your business environment. The decision involves understanding the problems your planning teams are having to solve from both a business and a technology (solver) perspective, as well as the pros and cons of each approach. External support at this point can help you formulate a more tangible product vision and apply the relevant functional and technical know-how across the different phases of the project. It could include best practice guidance in areas such as:

Blueprinting: Collating and analysing solver use cases from both a technical and functional angle to establish clear expectations of what types of problems the solution will need to solve
Vendor selection: Evaluating vendors for the best possible solve model to address your functional needs
Implementation: Translate the business needs into a detailed functional design as well as setting the right initial costs and orders of priority for the solvers
Change management: Helping establish a data governance model to ensure parameters are maintained properly by your planners

Part 2

Supply Chain Solver Methods.
In this, Part 2 of our white paper series on the building blocks of supply planning solutions, we’ve looked at how you can design your digital distribution network for resilience. A digital distribution network consists of supply and demand nodes as well as the transportation lanes that connect these locations.

Read article

#social#