Area: Fashion Retail
Problem class: MIP (Stock Redistribution)

Managing Retail Stock Distribution at Premium Shoe Manufacturer Goertz


As a medium sized fashion producer and retailer, Goertz regularly faces the challenge of how to redistribute stock across 150 retail stores. A newly developed solution with a GAMS model at its core helps Goertz to intelligently redistribute stock multiple times during the sales season. With the new solution, Goertz has been able to increase stock availability and at the same time shave off an average of seven days of each redistribution cycle. Goertz technical staff was able to independently implement the model in less than two months.


Goertz is a traditional premium shoe manufacturer, founded in 1875 in the city of Hamburg in Northern Germany, where it is still headquartered today. In addition to designing and manufacturing shoes, Goertz also operates its own chain of 150 retail stores throughout Germany, with over 3000 employees. Goertz offers around 7000 different styles of shoes for sale. Like most fashion products, the produced styles change between seasons and from year to year. Given this fluctuating product portfolio, it makes no economic sense to hold large volumes of stock in a central warehouse, because the chances of not selling all sizes of a particular style of shoe by the end of a season are great. Instead, Goertz uses its 150 retail stores as a large, distributed warehouse, where the complete inventory is always on display.

The Problem

Shoe styles are present in stores at the beginning of a season without any gaps in sizes. However, those gaps accumulate throughout the season, as more and more pairs of shoes are sold. Once more than two sizes of a style have been sold out in a particular store, the whole style of shoes is flagged as “incomplete” for that store in the Enterprise Resource Planning (ERP) system. Keeping the number of these incomplete styles as small as possible is both in the interest of the retailer as well as in the interest of the customers.

Goertz have developed a complex redistribution scheme to achieve this goal of minimal gaps throughout the sales season. In this scheme, stores send the remaining sizes of an incomplete style back to the central distribution warehouse. After processing in the warehouse, individual sizes of shoes are then redistributed to stores with demand, prioritizing stores with a high sales probability throughout the remainder of the sales season. This scheme allows the company to react to the unforeseeable nature of the sales success of different shoes in different stores, but it is costly and slow. Transport, inventorization, and redistribution add expense, and the typical turnaround time for shoes undergoing this redistribution scheme is between 7﹘14 days, during which the affected shoes cannot be sold.

The challenge of managing stock levels across multiple locations in a more efficient way had Goertz look into mathematical optimization techniques. The aim was development of a new solution to the problem that would maintain or exceed their high standards, while at the same time minimizing cost and turnaround time.

Given the fact that the central warehouse was the point which introduced most of the cost and delays, the experts at Goertz developed an idea to cut out the warehouse and instead implement a direct store-to-store redistribution system. With 7000 different styles in 150 stores, the number of possible combinations for redistributing shoes between stores is extremely high. But with a well defined set of business constraints, a mixed integer problem could be established in GAMS to solve the problem:

Optimization Objectives

Maximize overall availability of complete size ranges
Across all stores, the number of incomplete styles should be as small as possible after redistribution.
Minimize the total transport cost
The number of individual deliveries should be as small as possible.
Prioritise high volume stores
Depending on their location, some stores perform better than others for certain styles. The redistribution scheme prioritizes those stores which are more likely to sell particular styles during the remainder of the sales season.

Business Constraints

Avoid incomplete size ranges
If an incomplete style is sent out from a store, then all sizes should be sent out to clear the shelf space.
Avoid very small transports
Only schedule a transport between two stores, if at least five pairs of shoes can be sent.
Limit burden on the sending stores
Since the redistribution has to be handled by store staff in addition to their other duties, each origin store must send to 10 different destination stores at most.


For selecting an optimization solution, a key consideration for Goertz was ease of integration into their existing IT infrastructure. Here, GAMS’ flexibility and range of available interfaces is a great advantage. To integrate GAMS with as little friction as possible, a set of R routines was written, which pull data from the different company planning and warehousing databases for pre-processing. Processed data is then passed to the developed GAMS model via GDX files. The results from the GAMS run are then read back into R and after checking for plausibility fed into the ERP system. The ERP system in turn generates the individual transport instructions for each store.

The core of the solution is a mixed integer model formulated in GAMS. This model can be solved by CPLEX in approximately 90 minutes on standard workstation hardware (3 CPUs, 32 GB RAM) for the complete Goertz inventory.

The Implementation
Fig 3. Schematic representation of the optimization solution. The GAMS model is called by a set of custom R scripts which pull and sanitise data from the various company databases and then feed the data into the optimization. The results are again collected by R scripts and transferred to the ERP system, which in turn generates the individual transport instructions.


The optimization results allowed Goertz to dramatically increase the number of fully available shoe styles across all stores: A redistribution of around 6% of the total stock between stores resulted in an increase of fully available styles by 22%. Figure 4 shows the results for one style of shoe. Because of the low store-to-store shipping volumes, a standard courier service can be utilised for transportation.

Contrary to expectations, each store benefits from the scheme, even those which have to send out more shoes than they receive, because in the end even they have more complete styles than before. In summary, a successful solution was implemented by the team of Goertz experts in a short period of time. All project goals and objectives have been achieved, with the redistribution time reduced from 7-14 days to 2-5 days, thus increasing the opportunities for sales.

Fig 4. Effect of the direct store-to-store redistribution scheme on availability of one product style across all stores. Before the redistribution (left), a highly fragmented availability of the style across all stores is apparent. After redistribution, the number of stores with incomplete availability of the style has been reduced from 80 to 18.

About Goertz

Goertz is a traditional premium shoe manufacturer, founded in 1875 in the city of Hamburg in Northern Germany, where it is still headquartered today. In addition to designing and manufacturing shoes, Goertz also operates its own chain of 150 retail stores throughout Germany, with over 3000 employees.