A Generalized Bin Packing Problem for parcel delivery in last-mile logistics

Abstract In this paper, we present a new problem arising at a tactical level of setting a last-mile parcel delivery service in a city by considering different Transportation Companies (TC), which differ in cost and service quality. The courier must decide which TCs to select for the service in order to minimize the total cost and maximize the total service quality. We show that the problem can be modeled as a new packing problem, the Generalized Bin Packing Problem with bin-dependent item profits (GBPPI), where the items are the parcels to deliver and the bins are the TCs. The aim of the GBPPI is to select the appropriate fleet from TCs and determine the optimal assignment of parcels to vehicles such that the overall net cost is minimized. This cost takes into account both transportation costs and service quality. We provide a Mixed Integer Programming formulation of the problem, which is the starting point for the development of efficient heuristics that can address the GBPPI for instances involving up to 1000 items. Extensive computational tests show the accuracy of the proposed methods. Finally, we present a last-mile logistics case study of an international courier which addresses this problem

The Generalized Bin Packing Problem with bin-dependent item profits

In this paper, we introduce the Generalized Bin Packing Problem with bin-dependent item profits (GBPPI), a variant of the Generalized Bin Packing Problem. In GBPPI, various bin types are available with their own capacities and costs. A set of compulsory and non-compulsory items are also given, with volume and bin-dependent profits. The aim of GBPPI is to determine an assignment of items to bins such that the overall net cost is minimized. The importance of GBPPI is confirmed by a number of applications. The introduction of bin-dependent item profits enables the application of GBPPI to cross-country and multi-modal transportation problems at strategic and tactical levels as well as in last-mile logistic environments. Having provided a Mixed Integer Programming formulation of the problem, we introduce efficient heuristics that can effectively address GBPPI for instances involving up to 1000 items and problems with a mixed objective function. Extensive computational tests demonstrate the accuracy of the proposed heuristics. Finally, we present a case study of a well-known international courier operating in northern Italy. The problem approached by the international courier is GBPPI. In this case study, our methodology outperforms the policies of the company

Online fulfillment: f-warehouse order consolidation and bops store picking problems

Fulfillment of online retail orders is a critical challenge for retailers since the legacy infrastructure and control methods are ill suited for online retail. The primary performance goal of online fulfillment is speed or fast fulfillment, requiring received orders to be shipped or ready for pickup within a few hours. Several novel numerical problems characterize fast fulfillment operations and this research solves two such problems. Order fulfillment warehouses (F-Warehouses) are a critical component of the physical internet behind online retail supply chains. Two key distinguishing features of an F-Warehouse are (i) Explosive Storage Policy – A unique item can be stored simultaneously in multiple bin locations dispersed through the warehouse, and (ii) Commingled Bins – A bin can stock several different items simultaneously. The inventory dispersion profile of an item is therefore temporal and non-repetitive. The order arrival process is continuous, and each order consists of one or more items. From the set of pending orders, efficient picking lists of 10-15 items are generated. A picklist of items is collected in a tote, which is then transported to a packaging station, where items belonging to the same order are consolidated into a shipment package. There are multiple such stations. This research formulates and solves the order consolidation problem. At any time, a batch of totes are to be processed through several available order packaging stations. Tote assignment to a station will determine whether an order will be shipped in a single package or multiple packages. Reduced shipping costs are a key operational goal of an online retailer, and the number of packages is a determining factor. The decision variable is which station a tote should be assigned to, and the performance objective is to minimize the number of packages and balance the packaging station workload. This research first formulates the order consolidation problem as a mixed integer programming model, and then develops two fast heuristics (#1 and #2) plus two clustering algorithm derived solutions. For small problems, the heuristic #2 is on average within 4.1% of the optimal solution. For larger problems heuristic #2 outperforms all other algorithms. Performance behavior of heuristic #2 is further studied as a function of several characteristics. S-Strategy fulfillment is a store-based solution for fulfilling online customer orders. The S-Strategy is driven by two key motivations, first, retailers have a network of stores where the inventory is already dispersed, and second, the expectation is that forward positioned inventory could be faster and more economical than a warehouse based F-Strategy. Orders are picked from store inventory and then the customer picks up from the store (BOPS). A BOPS store has two distinguishing features (i) In addition to shelf stock, the layout includes a space constrained back stock of selected items, and (ii) a set of dedicated pickers who are scheduled to fulfill orders. This research solves two BOFS related problems: (i) Back stock strategy: Assignment of items located in the back stock and (ii) Picker scheduling: Effect of numbers of picker and work hours. A continuous flow of incoming orders is assumed for both problems and the objective is fulfillment time and labor cost minimization. For the back-stock problem an assignment rule based on order frequency, forward location and order basket correlations achieves a 17.6% improvement over a no back-stock store, while a rule based only on order frequency achieves a 12.4 % improvement. Additional experiments across a range of order baskets are reported