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Annals of Operations Research (2021) 304:427–451431Holzapfel et al. (2018) consider the problem of assigning multi SKUs to warehousesbelonging to different types available to retail companies, which is highly related to ourproblem. They propose a MIP model that accounts for interdependencies between inboundtransportation, outbound transportation, and in-store logistics, for capital tied up in inventories, and for differences in picking costs between the warehouses, which extends thedependences considered by Lovell et al. (2005). The warehouse network is similar to ours,but the problem is not under E-commerce and the company operates a warehouse, insteadof renting. Furthermore, we consider time- sensitive demand, which is important in theE-commerce environment. Guerriero et al. (2013) address the product allocation problemin a multi-layer warehouse with compatibility constraints, and present a linear model toreduce delivery times, inventories and total logistics costs, while also raising service levels.Similar studies include Tsiakis et al., Scott et al. (Fay & Xie, 2014; Tsiakis & Papageorgiou, 2008).Our literature review indicates the following findings. First, the problems of warehouseselection and allocating products to specific warehouses are essential planning tasks andan optimal allocation will lower costs. Second, although E-commerce dominates warehouse lease business, very few quantitative models are available for studying warehouserent under E-commerce. To the best of our knowledge, there is no directly related quantitative decision model available in the literature that considers the scenario that we focus on.Therefore, we develop a model that accounts for various interdependencies among factorsin the multiple-product allocation problem in rented online fulfillment warehouses and conduct sensitivity analyses to obtain strategic managerial insights. Our research is intended tosupport operations managers in making decisions on product allocation to specific warehouses of different types, and in finding the answer to the questions raised in Sect. 1.3  Problem background and OWPIn this section, we provide the OWP background and describe the decision problem. First,we describe the sales network structure using a real-world case. Second, we describe theprocesses that are affected by the multiple-product allocation decision and focus on theunderlying dependencies and cost drivers.3.1  Characterization of the supply network structureIn traditional retail supply networks, large batches of products flow from various warehouses to bricks-and-mortar retailers, who sell to end consumers (Kuhn & Sternbeck,2013). In E-commerce supply networks, single or smaller batches of products flow fromsupplier warehouses to consumers directly by third-party logistic services, thereby shortening the intermediate links of supply networks between suppliers and consumers (Johnson& Whang, 2002). One of the links in the supply network can be the rental of a warehousefrom an OWP.In our case, three different types of warehouses that service different sizes of geographic areas, namely, the supplier, the regional and the local warehouse. A supplier warehouse (SW, e.g., manufacturers, industrial warehouses or wholesale warehouses) mightserve all of the consumers in a large country, such as China. A regional warehouse (RW)serves consumers in a region, which may consist of several provinces in the country. Alocal warehouse (LW) serves consumers in a smaller area, such as a single province or an13

432Annals of Operations Research (2021) 304:427–451agglomeration. Regional warehouses (RW) and local warehouses (LW) are similar to warehouses in some retail supply networks (Kuhn & Sternbeck, 2013). The underlying structureof the supply network in a specific region is shown in Fig. 2.A LW usually takes less than 24 h to deliver the product, while for a RW and a SW, thetime is 2–3 days and 4–7 days, respectively. When consumers place orders, they are shownfrom which type of warehouse the product will be shipped and an estimated delivery time.Unlike e-commerce retailers that offer the consumer an option to pay more for faster shipping, for example, Amazon.com (Ma, 2017), the sellers in our case do not offer the consumer such shipping options.Shortages at RWs and LWs are permitted. The consumer demand from a specific areais first met by the LW, if there is no LW or its inventory is in shortage, the demand willdecrease according to consumer time sensitivity and the remaining demand will be met bya RW. Further, if there is no RW or its inventory is in shortage, the demand will drop again,and the remaining demand will be met by the SW eventually. A shortage at the SW is notpermitted, because that means the total production capacity would not be capable of meeting the demand.3.2  Processes involved in the product allocation decisionIn the supply network, processes include transportation, shelving products, storing products, picking orders, delivery and return. Each process belongs to a particular subsystem,i.e., (1) inbound transportation, (2) warehousing, (3) outbound transportation and delivery,and (4) return. We examine the cost drivers in each subsystem, as well as the interactionsof the subsystems and their related decisions. These subsystems are analyzed next.Fig. 2  The underlying network structure of the supply network13

Annals of Operations Research (2021) 304:427–4514333.2.1  Inbound transportationInbound transportation comprises transportation tasks between the SW and the RW orLW. The source–destination links are a result of the product assignment. For the manufacturers in our case, inbound transportation is mainly fulfilled by third-party logisticsservices, which are slower, but much cheaper than standard express services. Logisticcompanies have similar charging rules. Shipment of products under the standard physical volume (SPV, a function of length,width, height, and weight) is charged by weight and distance Shipment of products over the SPV is charge by volume and distanceSmall products, such as clothes, that are well under the SPV, may have the same shipping cost for one or several. However, for products over the SPV, such as a refrigerator,the shipping cost scales with the number of products. Consequently, transportation costsare most efficient for products with high sales and low physical volumes.When choosing to rent space from RW or LW, there are minimum rental costs forspace and for holding inventory. Rentals are not cost efficient when sales volume is lowfor products with low physical volumes and value. To simplify our case, we assume thattransportation from the manufacturer to each RW or LW is in batches. We also assumethat the cost per product and quantity of product shipped are independent of each other.3.2.2  WarehousingAfter products are received in the RW or LW warehouse, they are labeled and stored ina storage space rented by sellers until an order comes. Then they are picked, packed andsent to the sorting center for outbound transportation and delivery. In this subsystem,the following cost drivers should be considered. Rentals are charged by cubic meters per period. There is a minimum size of rentals. The service of receiving products is charged per-unit to cover counting, labeling,carrying to the storage space, and shelving. Holding inventory is charged per-unit of product in inventory at the beginning of theperiod. There is a minimum charge for holding inventory. The service of order fulfilment is charged by per-order to cover order printing,invoicing, picking, packing, and sending to the sorting center. Order picking is oftenresponsible for more than 50% of the total warehouse cost (De Koster et al., 2007).Differences in the warehousing costs may occur due to different technologies applied,labor costs and geographical areas. In addition, we only consider orders with a singleproduct. For orders with several different products or a batch product, the order pickingcost per-product would be lower.13

434Annals of Operations Research (2021) 304:427–4513.2.3  Outbound transportation and deliveryThis subsystem comprises transportation and delivery tasks between warehouse andconsumer. Since LW serves a specific area, RW and SW serve all areas in the region,the outbound relations are predetermined. The transportation volumes depend on salesand inventory. Shipping from a LW usually takes one day and costs the least, whichimproves consumer service (Keh & Shieh, 2001). In contrast, shipping from a SWlocated far away from the consumer would take 4–7 days and cost the most for delivery. The cost of outbound transportation and delivery is the greatest of the four subsystems, and the delivery time has a significant influence on consumer satisfaction (Ma,2017). Thus, the cost and time of outbound transportation including last-mile deliveryare highly relevant to the distribution of warehouses. The primary purpose of supplynetwork segmentation is to decrease the cost and time spent on outbound transportationand delivery.Online sellers present two different charging policies for outbound transportation and delivery: shipping fees or shipping free (Gümüş et al., 2013). Shipping fees mean the consumerwould pay for the cost, which is especially significant for products with low value and highweight and volume. Free shipping is frequently offered by online sellers when the total valueof the order is above a certain threshold price. In our case, we only consider orders with asingle product, so free shipping will be offered when the price of the product is above thethreshold.3.2.4  ReturnE-commerce presents much higher return rates than traditional trade, especially with the generous return policies offered by online sellers (de Araújo et al., 2018). Although return rateshave been steadily rising in recent years, it is treated as a certain proportion of sales in oneperiod by many analytical models of e-commerce (Altug & Aydinliyim, 2016; Bonifield et al.,2010; Shang et al., 2017). In this paper, we also follow this mode. For simplicity, we requirethat the return is sent back to the original warehouse where the product is shipped out and thereturn request is initiated in the same cycle.The cost of a return covers services of logistics from consumer to warehouse, includingthe inbound services of receiving products at the warehouse (“product re-inbound”). Generally, online consumers are granted a full refund or partial refund (Shang et al., 2017). Consumers enjoy a full refund when the return reasons are the seller’s mistakes, such as, productquality issues, logistics damage, missing parts, and mis-matches with descriptions. Followingimprovements in product quality and service, most product returns are now due to consumerbehavior-related reasons. For example, consumers may not be satisfied with the purchasedproducts, may not understand how to use the products, or may regret an impulsive purchase(Li et al., 2014). In such cases, the consumer bears the cost of logistics service back to thewarehouse and sellers cover the cost of product re-inbound, and we assume such arrangementsfor returns in our model.13

Annals of Operations Research (2021) 304:427–4514354  ModelingIn the present section, we develop a decision support model for product allocation tospecific warehouses of the different types (SW, RW, and LW). Section 4.1 describesproblem description and model assumptions, and then Sect. 4.2 defines indices, parameters and decision variables. The objective function and constraints of the model arefinally outlined in Sect. 4.3.4.1  Problem description and model assumptionsBased on our problem background, the problem is described as the follows: given theOWP environment, the online direct seller needs to solve the following problem simultaneously to maximize the profit: (1) which warehouse of three types in OWP will bechosen and how much space will be rented from the selected warehouses; (2) how doesthe seller allocate their multiple products among the rented warehouses, considering different warehouse rent and picking costs, inbound and outbound transportation cost; (3)how does the seller fulfill the demands from different regions/areas, taking into accountof time-sensitive demands.We make the following assumptions which are reasonable according to the real-worldcases, such as JD.com Inc., Tmall.com Inc. in China.(1) There are no relationships among the regional warehouses in our real-world cases.Thus, to simplify our model and focus our problem, we consider the case with onesupplier warehouse from an unspecified region, one regional warehouse and severallocal warehouses in the same region as the regional warehouse.(2) Warehouses are seller-managed inventories: replenishment decisions are made at theend of each period and fulfilled at the beginning of the next period.(3) Warehouses have enough space available for all our scenarios. There is no upper bound,but there is a lower bound on sizes of spaces for rent.(4) Transportation cost and lead time for the product are equal among warehouses at thesame level, and therefore there is no need for optimizing for these costs. This assumption is following the policy of a real logistics company that charges for transportationbased on regions of the origin and the destination, instead of an exact distance.(5) Demands for all products from each area are known in the period. The demands thatare unsatisfied from a lower level warehouse can be partially fulfilled by an upper levelwarehouse, depending on the consumer’s time sensitivity.4.2  NotationThe parameters of the proposed model include given demand, lead time, transportationcost, order handling cost, and others listed in Table 1. The decision variables includewhether to rent space in each warehouse, quantity of product to stock in each, and otherslisted in Table 1.13

Annals of Operations Research (2021) 304:427–451436Table ciijcpijcrijtiDij𝜆jui𝛾jvjpjcjMDecision variablesxijyijzijrisimijnijkThe index of warehouse: i 0, SW; i 1, RW; i 2; LWThe index of product, from 1 to JThe unit cost of inbound transportation for product j from manufacturers to warehouseiThe unit cost of outbound transportation form warehouse i to the corresponding areaThe unit cost of renting space in warehouse i per-periodThe unit cost of holding inventory in warehouse i per-periodThe unit cost of inbound services in warehouse iThe unit cost of order picking in warehouse iThe unit cost of returning product to warehouse iLead time from warehouse i to the corresponding area, usually from 1 to 7 daysDemand to warehouse i for product j per-period corresponding to lead time spent bylocal warehouse;D1j is the total demand to the regional warehouse from areas withoutlocal warehouses in the region𝜆 0, represents lead time sensitivity of demandThe minimum size of a rental unit in warehouse i , usually an integer multiple of cubicmeters0 γ 1, return rate, a proportion of orderUnit volume of product jThe unit price of product j that customers payUnit ordering cost of product jA big number, used for logic constraintsInventory of product j in warehouse i at the beginning of the period ( 0)Quantity of product j fulfilled from warehouse i( 0)Quantity of product j returned to warehouse i( 0)1, if renting space in warehouse i ; 0, otherwiseThe capacity of renting space in warehouse i( 0)Logic binary variableLogic binary variablelogic binary variable4.3  FormulationThe integrated problem is formulated as the following mixed integer programmingmodel.13

437Annals of Operations Research (2021) 304:427–4514.3.1  Objective functionMaxZ IJ ()pj yij zij (i 0 j 0 ( I cwij xij i 0 j 0csi si i 0 IJ IJ JI chij xij i 0 j 0IJ )caij yiji 0 j 0JI ciij xij i 0 j 0JI cpij yij i 0 j 0JI )crij ziji 0 j 0cj yiji 0 j 0(1)The objective function consists of four terms: the first term is the sales revenue. Thesecond term is the transportation cost from the supplier to the warehouse and from thewarehouse to the area. The third term is the warehousing cost associated with rentingspace, holding inventory, inbound services, order picking, and receiving returns. Thefourth term is the total ordering cost of the product. The object is to find the optimalrenting warehouse policy and inventory in order to maximize the total profit.4.3.2  Constraintsui ri si M ri , i I.(2)Constraints (2) ensure that if space is rented in a warehouse, then the capacity will beequal to or greater than the minimum size of rentals in that warehouse.J vj xij si , i I.(3)j 0The constraints ensure that warehouse i has enough available space to store inventoryat the beginning of the period.yij xij , i I, j J.(4)Constraints (4) ensure that quantity of product j fulfilled from warehouse i in theperiod cannot exceed the inventory at the beginning of the period. Note that a shortagein the local or regional warehouse will happen if the demand for warehouse i is higherthan the inventory at warehouse i.J vj (xij yij zij ) si , i I.(5)j 0Constraints (5) ensure that warehouse i has enough rental space available to storeremaining inventory and return products at the end of the period.zij 𝛾j yij , i I, j J.(6)In our case, as shown in constraints (6), we assume that the rate of returns for product j is a proportion of the orders for warehouse i .13

Annals of Operations Research (2021) 304:427–451438The product price is equal for all consumers, which has no influence on order decisions inour case. The quantity of consumer orders is a function of demand and lead time. We assumethat the function is Cobb–Douglas (Palaka et al., 1998; Ray & Jewkes, 2004):f (D, t) D t 𝜆This Cobb–Douglas function will help us to obtain qualitative insights without much analytical complexity. It also has the desirable property that the quantity of orders is higher at ashorter guaranteed lead time.For local warehouses i (i 2) and product j, t 1, the demand is Dij. If xij Dij, the saleis Dij, and all demand is satisfied. Otherwi

To the best of our knowledge, it is the rst research to study multi-echelon online fulll-ment warehouse rent and inventory decisions under the E-commerce supply network. Our main contributions include the following: (1) We present a mixed-integer model for multi-type warehouse selection and multi-ech-elon inventory decisions under E-commerce.