Single-Source Multi-Period Problem Model with Active Constraints-Based Approach Algorithm

In this paper, we introduce the multi-period single sourcing problem as an assignment problem. The multi- period single-sourcing problem in this research is seen as a problem of finding assignments, from time to time to obtain the minimum possible total transportation and inventory costs for distributing goods to customers. The case considered in this problem is the case of placing inventory items that are distributed to customers online, so this case is seen as a non-polynomial or NP hard problem that requires a solution algorithm, and the algorithm we offer is a direct search algorithm to solve the problem. multi period single sourcing. The direct search algorithm offered is the Branch and Price algorithm which was developed for Generalized Assignment Problems (GAP) to a much more complete class of problems, called CAP (Convex Assignment Problems). We offer this algorithm because the results it will obtain are more optimal, the computing time is superior, and it shows greater stability, that is, fewer outliers are observed. Specifically, we generalize the strategy of separating nonbasic variables from their constraints, combined with using active constraint methods to solve the Generalized Assignment Problem (GAP) into a Convex Assignment problem. Then, identification of important subclasses of the problem is carried out, which contains many variations of multi- period single sourcing problems, as well as GAP variants. The final result we found is an active depth-based single source multi-period model that can minimize the damage to the optimal integer solution for solving the MPSSP convex problem

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

Lp-Based Artificial Dependency for Probabilistic Etail Order Fulfillment

We consider an online multi-item retailer with multiple fulfillment facilities and finite inventory, with the objective of minimizing the expected shipping cost of fulfilling customer orders over a finite horizon. We approximate the stochastic dynamic programming formulation of the problem with an equivalent deterministic linear program, which we use to develop a probabilistic fulfillment heuristic that is provably optimal in the asymptotic sense. This first heuristic, however, relies on solving an LP that is exponential in the size of the input. Therefore, we subsequently provide another heuristic which solves an LP that is polynomial in the size of the input, and prove an upper bound on its asymptotic competitive ratio. This heuristic works by modifying the LP solution with artificial dependencies, with the resulting fractional variables used to probabilistically fulfill orders. A hardness result shows that asymptotically optimal policies that are computationally efficient cannot exist. Finally, we conduct numerical experiments that show that our heuristic's performance is very close to optimal for a range of parameters.http://deepblue.lib.umich.edu/bitstream/2027.42/108712/1/1250_ASinha.pd

Decision models for fast-fashion supply and stocking problems in internet fulfillment warehouses

Internet technology is being widely used to transform all aspects of the modern supply chain. Specifically, accelerated product flows and wide spread information sharing across the supply chain have generated new sets of decision problems. This research addresses two such problems. The first focuses on fast fashion supply chains in which inventory and price are managed in real time to maximize retail cycle revenue. The second is concerned with explosive storage policies in Internet Fulfillment Warehouses (IFW). Fashion products are characterized by short product life cycles and market success uncertainty. An unsuccessful product will often require multiple price discounts to clear the inventory. The first topic proposes a switching solution for fast-fashion retailers who have preordered an initial or block inventory, and plan to use channel switching as opposed to multiple discounting steps. The FFS Multi-Channel Switching (MCS) problem then is to monitor real-time demand and store inventory, such that at the optimal period the remaining store inventory is sold at clearance, and the warehouse inventory is switched to the outlet channel. The objective is to maximize the total revenue. With a linear projection of the moving average demand trend, an estimation of the remaining cycle revenue at any time in the cycle is shown to be a concave function of the switching time. Using a set of conditions the objective is further simplified into cases. The Linear Moving Average Trend (LMAT) heuristic then prescribes whether a channel switch should be made in the next period. The LMAT is compared with the optimal policy and the No-Switch and Beta-Switch rules. The LMAT performs very well and the majority of test problems provide a solution within 0.4% of the optimal. This confirms that LMAT can readily and effectively be applied to real time decision making in a FFS. An IFW is a facility built and operated exclusively for online retail, and a key differentiator is the explosive storage policy. Breaking the single stocking location tradition, in an IFW small batches of the same stock keeping unit (SKU) are dispersed across the warehouse. Order fulfillment time performance is then closely related to the storage location decision, that is, for every incoming bulk, what is the specific storage location for each batch. Faster fulfillment is possible when SKUs are clustered such that narrow band picklists can be efficiently generated. Stock location decisions are therefore a function of the demand arrival behavior and correlations with other SKUs. Faster fulfillment is possible when SKUs are clustered such that narrow band picklists can be efficiently generated. Stock location decisions are therefore a function of the demand behavior and correlations with other SKUs. A Joint Item Correlation and Density Oriented (JICDO) Stocking Algorithm is developed and tested. JICDO is formulated to increase the probability that M pick able order items are stocked in a δ band of storage locations. It scans the current inventory dispersion to identify location bands with low SKU density and combines the storage affinity with correlated items. In small problem testing against a MIP formulation and large scale testing in a simulator the JICDO performance is confirmed

Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints

Production planning on multiple parallel machines is an interesting problem, both from a theoretical and practical point of view. The parallel machine lotsizing problem consists of finding the optimal timing and level of production and the best allocation of products to machines. In this paper we look at how to incorporate parallel machines in a Mixed Integer Programming model when using commercial optimization software. More specifically, we look at the issue of symmetry. When multiple identical machines are available, many alternative optimal solutions can be created by renumbering the machines. These alternative solutions lead to difficulties in the branch-and-bound algorithm. We propose new constraints to break this symmetry. We tested our approach on the parallel machine lotsizing problem with setup costs and times, using a network reformulation for this problem. Computational tests indicate that several of the proposed symmetry breaking constraints substantially improve the solution time, except when used for solving the very easy problems. The results highlight the importance of creative modeling in solving Mixed Integer Programming problems.Mixed Integer Programming;Formulations;Symmetry;Lotsizing

Vehicle Dispatching and Routing of On-Demand Intercity Ride-Pooling Services: A Multi-Agent Hierarchical Reinforcement Learning Approach

The integrated development of city clusters has given rise to an increasing demand for intercity travel. Intercity ride-pooling service exhibits considerable potential in upgrading traditional intercity bus services by implementing demand-responsive enhancements. Nevertheless, its online operations suffer the inherent complexities due to the coupling of vehicle resource allocation among cities and pooled-ride vehicle routing. To tackle these challenges, this study proposes a two-level framework designed to facilitate online fleet management. Specifically, a novel multi-agent feudal reinforcement learning model is proposed at the upper level of the framework to cooperatively assign idle vehicles to different intercity lines, while the lower level updates the routes of vehicles using an adaptive large neighborhood search heuristic. Numerical studies based on the realistic dataset of Xiamen and its surrounding cities in China show that the proposed framework effectively mitigates the supply and demand imbalances, and achieves significant improvement in both the average daily system profit and order fulfillment ratio

Design and optimization of an explosive storage policy in internet fulfillment warehouses

This research investigates the warehousing operations of internet retailers. The primary physical process in internet retail is fulfillment, which typically involves a large internet fulfillment warehouse (IFW) that has been built and designed exclusively for online sales and an accompanying parcel delivery network. Based on observational studies of IFW operations at a leading internet retailer, the investigations find that traditional warehousing methods are being replaced by new methods which better leverage information technology and efficiently serve the new internet retail driven supply chain economy. Traditional methods assume a warehouse moves bulk volumes to retail points where the bulks get broken down into individual items and sold. But in internet retail all the middle elements of a supply chain are combined into the IFW. Specifically, six key structural differentiations between traditional and IFW operations are identified: (i) explosive storage policy (ii) very large number of beehive storage locations (iii) bins with commingled SKUs (iv) immediate order fulfillment (v) short picking routes with single unit picks and (vi) high transaction volumes with total digital control. In combination, these have the effect of organizing the entire IFW warehouse like a forward picking area. Several models to describe and control IFW operations are developed and optimized. For IFWs the primary performance metric is order fulfillment time, the interval between order receipt and shipment, with a target of less than four hours to allow for same day shipment. Central to achieving this objective is an explosive storage policy which is defined as: An incoming bulk SKU is exploded into E storage lots such that no lot contains more than 10% of the received quantity, the lots are then stored in E locations anywhere in the warehouse without preset restrictions. The explosion ratio Ψo is introduced that measures the dispersion density, and show that in a randomized storage warehouse Ψoo\u3e0.40. Specific research objectives that are accomplished: (i) Develope a descriptive and prescriptive model for the control of IFW product flows identifying control variables and parameters and their relationship to the fulfillment time performance objective, (ii) Use a simulation analysis and baseline or greedy storage and picking algorithms to confirm that fulfillment time is a convex function of E and sensitive to Ǩ, the pick list size. For an experimental problem the fulfillment time decrease by 7% and 16% for explosion ratios ranging between Ψo=0.1 and 0.8, confirming the benefits of an explosive strategy, (iii) Develope the Bin Weighted Order Fillability (BWOF) heuristic, a fast order picking algorithm which estimates the number of pending orders than can be filled from a specific bin location. For small problems (120 orders) the BWOF performes well against an optimal assignment. For 45 test problems the BWOF matches the optimal in 28 cases and within 10% in five cases. For the large simulation experimental problems the BWOF heuristic further reduces fulfillment time by 18% for Ǩ =13, 27% for Ǩ =15 and 39% for Ǩ =17. The best fulfillment times are achieved at Ψo=0.5, allowing for additional benefits from faster storage times and reduced storage costs