Optimizing stock replenishment in fashion retailers

4 • Mobility and Transportation 55 4.1 OPTIMIZING STOCK REPLENISHMENT IN FASHION RETAILERS Jesús Muñuzuri Sanz and Alicia Robles-Velasco ABSTRACT In the current paradigm, where rapid evolution of the retail industry is seen, especially in textile companies, general product assignment in any distribution and supply chain, consisting of a main warehouse and several locations, can mean an important challenge. The replenishing process in shops centers all its attention on dynamically optimizing the inventory of shops attending to a wide range of products, starting from a sales prevision of previous periods. In this context, the objective of this work is centered on optimizing replenishing work in shops for non-perishable goods which lose value as time passes. INTRODUCTION Replenishing in shops must satisfy independent flow demands, in methods and time, allowing covering the demands of shops without increasing their associated warehousing costs. Different sectors (for example, textile) have specific casuistry facing a shortage of any product. In normal conditions, this is penalized, but on certain occasions, this effect is not that subject to accusation because customers opt for different equivalent products from another shop of the same company or they acquire them via web channels. Nevertheless, the fashion sector is subject to the strong depreciation of the product (end of the season), because it has not been sold during the season for which it was designed. This means that unsold stocks are available at prices with large discounts, greatly reducing the profit margin. The objective of this work is to optimize the replenishment in shops, guaranteeing maximum product availability and rotation, and so, reducing costs, especially those derived from excess storage or, on the contrary, the costs of 56 AI Knowledge Transfer stock shortages. Therefore, a version conjugating two different metaheuristics has been implemented: particle swarm optimization (PSO) for updating solutions and Simulated Annealing to calculate the changes experienced in the solution, in addition to limiting simulation time. STATE OF THE ART Currently, the shop replenishment problem has been repeatedly discussed to improve the planning and optimization of the supply chain and retail commerce. Nevertheless, only some researchers, such as Iannone et al. (2013), focus their attention on the textile sector and all its casuistry: extensive product and customer catalog, high rate of rotation, highly unpredictable, as well as seasonal and impulsive demand. Pan et al. (2009) consider batch economic models subject to market changes or seasonality. Along this line, Grewal, Enns, and Rogers (2015) assess the sensitive price variation dominated by the randomness and seasonality of demand. Searching for demand prediction, Anily and Hassin (2013) focus on heterogeneous behavior of customer decision. Outside of the textile sector, other works, such as Coelho and Laporte (2014) who focus on the reestablishment and replenishing of perishable or deteriorating products in shops should be highlighted. Lee (1987) calculates the minimum cost of an inventory with transfers for replacement n shops, located in the same territorial area, optimizing the expected number of pending orders. Later, Kukreja et al. (2001) add the casuistry of shops located in different territorial regions. Rudi, Kapur, and Pyke (2001) study a periodic review system with the restocking of two shops after knowing the demand for the period but before it is satisfied. On the other hand, Archivald (2007) develops an inventory system based on a multi-location model with periodic reviews for different industrial environments. He focuses on quantifying the optimal decisions of transfers between locations according to the moment in which movements are allowed. On the other hand, Minner, Silver, and Robb (2003) develop heuristics to define the convenience or not of restocking or moving items in a continuous multi-location review inventory where shortages are allowed. Elaborating along this line, Axsäter (2003) implements a replenishing policy where the shop with a shortage can obtain products from other shops that have less stock shortage costs. The paper of Martino, Iannone, and Packianather (2016) has been used for reference in this development, as a guide to define the model and its equations, as well as the study of the shop replacement problems. 4 • Mobility and Transportation 57 CONTRIBUTION The issue contemplated in this study is about shop inventory and replenishment management for a multi-product model with multiple locations and over various time periods. The main objective of the problem is to maximize profitability, understood as the difference between total income and costs. Among the main considered hypotheses, we can mention the following: • Each shop will receive an order from the central warehouse at the start of each period. The order will consist of different typologies of products. • The periods can be defined as a range of days, weeks, months, or years. • This means that the products are not perishable but do suffer from devaluation over time. • There is an estimated demand prevision based on historical data. Revenue has been defined as the unit sale price of each product in each shop during each period. The sales of each product and in each shop will be estimated as the minimum value between the inventory existing in the previous year and the demand in the current period. The demand of each product, in each shop and for each period, will be a value between the range of sales predictions with an uncertainty threshold of up to 20%. In terms of costs, stock shortage costs can be considered only if the demand to be satisfied is greater than the inventory existing in the previous period; otherwise, it will be nil. The purchase cost is the cost of acquiring all the units of the different orders for each shop and period. The transport cost is considered as separated into two concepts: the fixed-route cost of the vehicle to supply all the shops and the variable cost depending on the distance and type of order to be covered. This means that each vehicle travels back to one shop without visiting any others. Finally, the storage cost is the sum of a fixed inventory maintenance cost per shop and a variable cost evaluable by the depreciation of the inventory during the period. Therefore, the proposed optimization problem consists of maximizing the benefit understood as the difference between income and costs, on the condition that purchase costs do not exceed a previously set budget. Artificial Intelligence techniques were used to solve the problem. Specifically, the developed methodology combines PSO metaheuristics where a leader (best solution) sets the direction of solutions group, with Simulated Annealing for 58 AI Knowledge Transfer upward movements and escaping from local optima, accepting or denying the changes produced in the solution. This typology of problems presents many feasible solutions. However, with a finite period, there is no guaranteed convergence with the optimum. Therefore, the best solution until meeting a fixed stop criterion is sought in a maximum number of iterations. The sequence of steps of this methodology is as follows: initially, a demand, a random period, and a current solution are calculated, defining the sales and the inventory for that first solution, which will be the origin of the first vicinity. All the neighbors of vicinity are formed based on a percentage variation of values and periods. This variation can be incremental or decremental in the range between 0% and 40%. Subsequently, each solution will be valued defining its benefit, and the best solution will be updated according to its value. If the change of the current benefit is less than a limit, that change will be accepted updating the current solution. The creation of a new series of solutions has been designed as the weighted measure of the best solution found so far, the current solution and a random solution (the used weights have been fixed by experimentation). ACKNOWLEDGMENTS This project has been carried out in collaboration with the TIER1 Technology and within the Organization Engineering research group. WORKS CITED Anily, S., & Hassin, R. (2013). Pricing, replenishment, and timing of selling in a market with heterogeneous customers. International Journal of Production Economics, 145(2), 672–682. Archibald, T. W. (2007). Modelling replenishment and transshipment decisions in periodic review multilocation inventory systems. Journal of the Operational Research Society, 58(7), 948–956. Axsäter, S. (2003). Evaluation of unidirectional lateral transshipments and substitutions in inventory systems. European Journal of Operational Research, 149(2), 438–447. Coelho, L. C., & Laporte, G. (2014). Optimal joint replenishment, delivery and inventory management policies for perishable products. Computers & Operations Research, 47, 42–52. 4 • Mobility and Transportation 59 Grewal, C. S., Enns, S. T., & Rogers, P. (2015). 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