Browsing by Subject "Assortment planning"

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Open Access
Assortment planning considering split orders
(2021-08) Söylemez, Duygu
When multi-item orders cannot be satisﬁed through a single shipment stemming from not having all the items in an order in the same warehouse, the cost of packaging and transportation increases and the delivery of the orders can be delayed. In this regard, split order problem is one of the most signiﬁcant challenges that the online retailers face. As the capacities of the warehouses are limited, it is not possible to stock every item in every warehouse. To minimize the number of orders that cannot be satisﬁed in a single shipment, it is important to determine how the limited capacities of the warehouses should be allocated to items or it is necessary to decrease the transportation costs through consolidating the split orders. Since this problem is NP-hard, the previous studies in the literature are based on heuristic algorithms. In this study, exact and heuristic methods have been examined to solve large scale problems. Some of the heuristic algorithms oﬀered uses the LP relaxation of the model provided by Jehl et al.(2018). In this sense, the analytical characterization of the optimal solution of the LP relaxation has also been revealed. It is proved that the allocation variables can only take three diﬀerent values at most one being fractional. It is shown that this solution can be found without actually solving the LP relaxation by beneﬁting from an algorithm oﬀered in literature to solve 0-1 fractional programming problems. Moreover, it is proved that a similar characterization is preserved for multiple warehouses or when a central depot with unlimited capacity and a forward distribution center are considered together. Additionally, the working principle of the greedy ranking algorithm oﬀered in the literature is theoretically justiﬁed and a dynamic version of this algorithm is developed. To evaluate the performance of the heuristic algorithms oﬀered and the run time of the integer programming problem, an extensive numerical study has been conducted. The change in the diﬃculty level of the problem based on the plant capacity, the number of orders, and the number of stock keeping units (SKU) is scrutinized. Furthermore, the assortment allocation problem is modeled together with the consolidation problem. The performance of the model is evaluated through comparing its solution to the solution obtained through solving two problems consecutively.
Open Access
Assortment planning framework with substitution and complexity cost
(2021-08) Sönmez, Dilara
While increasing product variety may have a positive eﬀect on market share, it may lead to diﬃculties in product management and forecasting, leading to increase in inventory holding costs. In addition, as a result of increased setup times, eﬃciency decreases. In this study, we propose two methods to help a multi-national tire manufacturer manage their assortment to ﬁnd a balance be-tween variety and sales. The ﬁrst method evaluates the marginal complexity cost of a set of new products so that a data-driven decision can be made to introduce or not to introduce new products. The second method determines the set of tires to be included in the assortment that increases the total proﬁt. To account correctly for the partial sales revenue losses due to discontinued products, we estimate the fractions of demands substituted by the products left in the assort-ment. Customer no-purchase information were unobserved, as well as the exact timings of stock-outs and sales up to those times. Also, market share information for a particular group of tires for the company were unavailable. Based on these incomplete data, the substitution probabilities were estimated using an iterative method. The solutions were iterated on to ﬁnd the set of substitution probabilities that best ﬁt the data. Discontinued products are expected to save from complex-ity costs due to production capacity losses because of frequent break times. The complexity cost is a set function that accounts for the interactions between the products during manufacturing processes, as well as the variety in the product portfolio. In order to estimate the break time savings, a machine learning model was used, and an algorithm was designed to measure the eﬀect of a set of products being discontinued. For the periods in which the machines work in full capacity, the additional proﬁt due to potential new sales was also considered. This value and the conversion cost saved due to discontinued products were added to the proﬁt function. The predictions from the machine learning model and the other costs are used to formulate a large-scale assortment optimization problem with a complex objective function. The assortment problem is solved using genetic algo-rithm. The results show that the new assortment obtained through our analysis has between 3.8% and 15.2% less products than the initial assortment. The new assortment leads to additional proﬁt between 0.6% and 4.6% of the company’s annual income. The results also show that considering complexity costs in assort-ment decisions leads to substantially diﬀerent assortments and additional savings in comparison to those obtained without their considerations.
Open Access
Assortment planning in transshipment systems
(2015-08) Dağ, Hilal
Assortment planning, i.e., determining the set of products to offer to customers is a challenging task with immediate effects on profitability, market share and customer service. In this thesis, we study a multiple location assortment planning problem in a make-to-order environment. Each location has the exibility to access others' assortments by transshipping products he/she does not keep. This allows them to offer higher variety and increase sales without increasing costs associated with assortment. Customer behavior is defined using exogenous demand model where each arriving customer to a location chooses a product with an exogenous probability among all possible options. In our multiple location setting, we assume that the customer has access to the complete assortment in all locations. If a customer's requested product is not available in that customer's assigned location but available in another location, the firm ships the product to the customer at the same price and incurs a transshipment cost. If his/her first choice product is not offered by any of the locations then he/she switches to a substitute product, which can be either satisfied from customer's assigned location, or by transshipment. Otherwise, it is lost. The problem is then to determine the assortment in each location such that the total expected profit is maximized. We first show that the optimal assortments are nested, i.e., the assortment of a location with a smaller market share is a subset of the assortment of a location with a larger market share. We then show that while the common assortment is in the popular set (i.e., some number of products with highest purchase probabilities), the individual assortments do not necessarily have this property. We also derive a sufficient condition for each assortment to be in the popular set. In the final part of the thesis, we conduct an extensive numerical study to understand the effects of various parameters such as assortment cost and transshipment cost on optimal assortments and effects of allowing transshipments on resulting assortments compared to a no-transshipment system. Finally, we introduce an approximation algorithm that benefits from the structural properties obtained in this study and also test its performance with extensive numerical analyses.
Embargo
Multi-plant manufacturing assortment planning in the presence of transshipments
(Elsevier BV, 2023-05-31) Dolgan, Nagihan Çömez; Dağ, Hilal; Ünver, Nilgün Fescioğlu; Şen, Alper
In this study, we consider the assortment planning problem of a manufacturing firm with multiple plants. Making a plant capable of producing a product is costly, therefore the firm cannot manufacture every product in every plant. In case a customer’s order in a particular region is not available in the closest plant, another plant can ship the product using transshipment, but at an extra transportation cost. If a demanded product is not produced in any plant, substitution from first choice to a second choice is also considered, which can be either satisfied by the closest plant, or by transshipment. The problem is to jointly determine assortments in all plants such that total profit after assortment and transshipment costs is maximized. The resulting problem is complex as transshipments and substitutions are intertwined to affect assortment decisions. We show that the optimal assortments are nested, i.e., the assortment of a plant with a smaller market share is a subset of the assortment of a plant with a larger share. The common assortment of all locations is shown to be in the popular set (i.e., no leapfrogging in product popularities), and a sufficient condition on substitution rate is derived for each individual assortment to be in the popular set. We conduct an extensive numerical study to understand the effects of allowing transshipments on resulting assortments. Moreover, we introduce approximate assortment planning algorithms that benefit from the derived structural properties, which are shown to generate near-optimal assortments in a broad range of instances tested.