Shipment Consolidation Policy Research Articles

Inbound replenishment and outbound dispatch decisions under hybrid shipment consolidation policies: An analytical model and comparison

We investigate operational decisions in a distribution warehouse facing stochastic demand and incurring fixed and linear transportation costs for the inbound inventory replenishment and outbound dispatch decisions. In order to realize scale economies associated with transportation both on the outbound and inbound sides, dispatch schedules and replenishment decisions at the warehouse must be synchronized over time. Immediate delivery policies on the outbound side are not financially viable because outbound dispatch operations will benefit from temporal shipment consolidation. Our focus in this setting is the analytical modeling of hybrid shipment consolidation policies and their comparison to the time-based and quantity-based counterparts. To this end, we propose analytical (exact and approximate) methods to compute and compare the cost under hybrid policies relative to its alternatives. Since shipment consolidation impacts customer waiting and inventory holding, we also investigate the average delay per order and average inventory per time unit as two important metrics of the distribution operation’s performance, along with the annual cost. We compare these metrics among the alternative under hybrid, time-based, and quantity-based policies. The comparison then allows us to offer an explicit analytical comparison of long-run average cost under these three policies without needing to solve the corresponding optimization problems. Notably, our results offer an analytical characterization of relative cost performance (vis-a-vis the numerical comparison available in the literature) and demonstrate the implications of alternative shipment consolidation policies regardless of the values of model parameters. The results are of practical value in the context of the design and operation of an integrated framework for inventory-transportation systems.

Evaluation and control of inventory distribution systems with quantity based shipment consolidation

AbstractJoint consideration of inventory and shipment decisions is an important aspect of obtaining economically and environmentally sustainable distribution systems. We consider this issue in the context of a one‐warehouse‐multiple‐retailer inventory system with quantity‐based shipment consolidation to groups of nonidentical retailers facing Poisson demand. The system is centralized, with free information sharing and access to real‐time point of sale data. Thus, demand information at the retailers is immediately conveyed upstream to the warehouse without any fixed ordering costs. However, fixed costs associated with handling and transporting goods from the warehouse to the retailers are reflected in the shipment consolidation policy. Stock replenishments at the warehouse are made from an outside supplier/manufacturer according to an (R, Q) policy. For this system, we derive an exact recursive method for determining the inventory level distributions at the retailers. This allows us to evaluate the expected inventory and shipment costs, fill‐rates, and transport emissions for the entire system. We also show how to optimize the system by providing bounds on the optimal shipment quantities and the warehouse reorder level.

Stochastic inventory routing with time-based shipment consolidation

Inspired by the retail industry, we consider a stochastic inventory routing problem where retailers are replenished from a central warehouse using a time-based shipment consolidation policy. Such a time-based dispatching policy, where retailers facing stochastic demand are repetitively replenished at fixed times, is essential in practice. It allows for easy incorporation with dependent up- and downstream planning problems such as personal staffing and warehouse operations, and has become a standard part of transportation contracts. We provide a new chance-constrained model that determines an optimal clustering of retailers in groups, their associated routing and shipment interval, and each retailers’ optimal inventory level. A newly developed branch-price-and-cut algorithm solves our model to optimality. Its efficiency comes from a tailored labeling algorithm for solving the pricing problem that relies, among others, on an optimality pruning criterion based on the approximate solution of a 0,1-knapsack problem. Computational experiments show that our exact method can solve instances of up to 60 retailers to optimality. Besides, we accommodate practitioners by providing a fast heuristic that provides excellent solutions with an optimality gap of less than 1%. Finally, we show that incorporating uncertainty already in the planning process is essential for stochastic inventory routing with time-based shipment consolidation, as it results in overall cost-savings of 7.7% compared to the current state-of-the-art.

Trade-offs in the landside operations of air cargo hubs: Horizontal cooperation and shipment consolidation policies considering capacitated nodes

Landside operations in air cargo terminals consist of many freight forwarders (FFWs) delivering and picking up cargo at the capacity-constrained loading docks at the airport's ground handlers' (GHs) facilities. To improve the operations of the terminal and take advantage of their geographical proximity a small set of FFWs can build a coalition to consolidate stochastically-arriving shipments and share truck fleet capacity while other FFWs continue bringing cargo to the terminal in a non-cooperative manner. Results from a detailed discrete-event simulation model of the cargo landside operations in Amsterdam Aiport showed that all operational policies had trade-offs in terms of the average shipment cycle time of coalition FFWs, the average shipment cycle time of non-coalition FFWs, and the total distance traveled by the coalition fleet, suggesting that horizontal cooperation in this context was not always beneficial, contrary to what previous studies on horizontal cooperation have found. Since dock capacity constitutes a significant constraint on operations in air cargo hubs, this paper also investigates the effect of dock capacity utilization and horizontal cooperation on the performance of consolidation policies implemented by the coalition. Thus, we built a general model of the air cargo terminal to analyze the effects caused by dock capacity utilization without the added complexity of landside operations at Amsterdam Airport to investigate whether the results hold for more general scenarios. Results from the general simulation model suggest that, in scenarios where dock and truck capacity become serious constraints, the average shipment cycle times of non-coalition FFWs are reduced at the expense of an increase in the cycle times of FFWs who constitute the coalition. A good balance among all the performance measures considered in this study is reached by following a policy that takes advantage of consolidating shipments based on individual visits to GH.

Inventory management with advance demand information and flexible shipment consolidation

In this paper, we study a stochastic single-item, single-stage inventory system, in which orders from several production facilities are placed at one warehouse. An (R, Q) policy is applied to control the inventory at the warehouse, and orders arrive according to a Poisson process and include a due date such that some information about future demand is available. This advance demand information (ADI) can be used to adapt a time-based shipment consolidation policy applied to replenish stock at the production facilities. We develop a model to incorporate flexible deliveries, indicating that orders can be shipped before their due date if sufficient reserved transportation capacity is available. We derive analytical, approximate expressions for the expected inventory and shipment costs and therefore enable the evaluation of different inventory and shipment policies including outbound transportation capacities. We additionally show how to compute the optimal policy parameters and conduct a detailed numerical study. Our computational experiments indicate that our approximation works extremely well, with an average total cost deviation of 0.20%, and finds optimal policy parameters in more than 90% of our instances. In line with existing research, we can show that ADI leads to large cost reductions. However, the main cause of the cost reduction is the flexible delivery option. To be able to completely utilize this option, even larger safety stocks are obtained compared to systems without ADI, but savings due to a more efficient transportation policy far exceed the cost increase due to higher safety stocks.

Optimal shipment consolidation and dynamic pricing policies for perishable items

Considering a firm who operates multiple stores to sell perishable items with limited inventory, we build a multi-location inventory model to explore the optimal dynamic pricing and shipment consolidation policies. The optimal consolidation and continuous-time dynamic pricing policies are obtained by solving the corresponding optimization problem based on optimal control theory. The optimal strategies derived show that the firm should take penetration pricing policy and select a subset of stores with high market potentials. Compared to cases of static pricing and non-consolidation, both dynamic pricing and shipment consolidation policies can enhance the firm’s profitability, while they exert substitutable effects. Furthermore, the heterogeneity of stores, price sensitivity of demands, deteriorating property of items, holding cost and delivery cost all highlight the importance of consolidation. Additionally, the optimal dynamic price exhibits non-monotonicity with respect to deterioration rate and holding cost.

Freight delivery in a Physical Internet Supply Chain: an applied optimisation model with peddling and shipment consolidation

The delivery of goods (freight) accounts for the major cost and emissions in logistics systems worldwide. The effective management of the supply chain requires logistical efficiency and sustainability. Several logistics performance measurements such as distances driven and fuel efficiency are also indicators of sustainability. As an emerging paradigm, the Physical Internet (PI) addresses logistical, societal, and sustainability goals. However, the question remains whether some aspects of logistical efficiency in traditional logistics could be incorporated into the PI paradigm. To this effect, we examine how peddling, a consolidation strategy in traditional logistics, can enhance PI supply chain. Specifically, we formulate optimisation models and study the case of a Mexican automotive supply chain from both the PI and traditional logistics perspectives by comparing three different configurations; namely, Model P built on PI, Model S based on conventional standard peddling, and Model H, a hybrid. The hybrid Model H is optimised in a two-phase solution framework. We show via the case of a Mexican automotive supply chain that Model H outperforms others on average distance travelled and truck utilisation. Thereby, it is concluded that appropriate peddling and shipment consolidation policies may enhance PI supply chain logistics performance.

ANALYTICAL RESULTS ON THE SERVICE PERFORMANCE OF STOCHASTIC CLEARING SYSTEMS

Stochastic clearing theory has wide-spread applications in the context of supply chain and service operations management. Historical application domains include bulk service queues, inventory control, and transportation planning (e.g., vehicle dispatching and shipment consolidation). In this paper, motivated by a fundamental application in shipment consolidation, we revisit the notion of service performance for stochastic clearing system operation. More specifically, our goal is to evaluate and compare service performance of alternative operational policies for clearing decisions, as quantified by a measure of timely service referred to as Average Order Delay ($AOD$). All stochastic clearing systems are subject to service delay due to the inherent clearing practice, and $\textrm {AOD}$ can be thought of as a benchmark for evaluating timely service. Although stochastic clearing theory has a long history, the existing literature on the analysis of $\textrm {AOD}$ as a service measure has several limitations. Hence, we extend the previous analysis by proposing a more general method for a generic analytical derivation of $\textrm {AOD}$ for any renewal-type clearing policy, including but not limited to alternative shipment consolidation policies in the previous literature. Our proposed method utilizes a new martingale point of view and lends itself for a generic analytical characterization of $\textrm {AOD}$, leading to a complete comparative analysis of alternative renewal-type clearing policies. Hence, we also close the gaps in the literature on shipment consolidation via a complete set of analytically provable results regarding $\textrm {AOD}$ which were only illustrated through numerical tests previously.

Controlling distribution inventory systems with shipment consolidation and compound Poisson demand

We consider a one-warehouse-multiple-retailer inventory system where the retailers face stochastic customer demand, modelled as compound Poisson processes. Deliveries from the central warehouse to groups of retailers are consolidated using a time based shipment consolidation policy. This means that replenishment orders have to wait until a vehicle departures, which increases the lead time for the retailers and therefore also the safety stock. Thus, a trade-off exists between expected shipment costs and holding costs. Our aim is to determine the shipment intervals and the required amount of safety stock for each retailer and the warehouse to minimize total cost, both for backorder costs and fill rate constraints. Previous work has focused on exact solutions which are computationally demanding and not applicable for larger real world problems. The focus of our present work is on the development of computationally attractive heuristics that can be applied in practice. A numerical study shows that the proposed heuristics perform well compared to the exact cost minimizing solutions. We also illustrate that the approaches are appropriate for solving real world problems using data from a large European company.

A perishable product shipment consolidation model considering freshness-keeping effort

Based on Quality-based policy and Quantity-and-Quality-based policy proposed in this paper, the corresponding perishable products shipment consolidation stochastic models by integrating freshness-keeping effort decision are formulated. For each policy, analytical results give conditions and expressions of adopting these policies and freshness-keeping effort. Numerical experiments show: (i) the positive effect of fresh investment on cost, (ii) the changing tends of policy parameters, freshness-keeping efforts and cost based on all parameters, (iii) the superiority of Quantity-and-Quality-based policy over Quality-based policy in most operational environment and (iv) the cost improvement under Quantity-and-Quality-based policy than other existing shipment consolidation policies.

Shipment Consolidation Policy under Uncertainty of Customer Order for Sustainable Supply Chain Management

With increasing concern over the environment, shipment consolidation has become one of a main initiative to reduce CO2 emissions and transportation cost among the logistics service providers. Increased delivery time caused by shipment consolidation may lead to customer’s order cancellation. Thus, order cancellation should be considered as a factor in order uncertainty to determine the optimal shipment consolidation policy. We develop mathematical models for quantity-based and time-based policies and obtain optimality properties for the models. Efficient algorithms using optimal properties are provided to compute the optimal parameters for ordering and shipment decisions. To compare the performances of the quantity-based policy with the time-based policy, extensive numerical experiments are conducted, and the total cost is compared.

Exact Analysis of Divergent Inventory Systems with Time-Based Shipment Consolidation and Compound Poisson Demand

Sustainable and efficient management of a distribution system requires coordination between transportation planning and inventory control decisions. In this context, we consider a one warehouse multi-retailer inventory system with a time-based shipment consolidation policy at the warehouse. This means that there are fixed costs associated with each shipment, and retailer orders are consolidated and shipped periodically to groups of retailers sharing the same delivery routes. Customer demand is compound Poisson distributed and unsatisfied demand at each stock point is backordered and allocated on a first-come first-served basis. The system is centralized and inventory levels are reviewed continuously. The warehouse has access to real-time inventory information from the retailers, and uses a (R, nQ) policy to replenish from an outside supplier/manufacturer. We derive the exact probability distributions for the inventory levels at the retailers, and use these to obtain exact expressions for the system’s expected shipment, holding and backorder costs, its average inventory levels, and fill rates. Based on the analytical properties of the objective function, we construct an optimization procedure by deriving bounds on the optimal reorder levels and shipment intervals both for single-item and multi-item systems.

다수 고객 통합전략을 활용하는 생산 및 물류계획 수립

This paper considers an integrated one-vendor multi-buyer production-inventory model where the vendor manufactures multiple products in lot at their associated finite production rates. In the model, it is allowed for each product to be shipped in lot to the buyers even before the whole product production is not completed yet. Each product lot is dispatched to the associated buyer in a number of shipments. The buyers consume their products at fixed rates. The objective is to the production and shipment schedules in the integrated system, which minimizes the total cost per unit time. The total cost consists of production setup cost, inventory holding cost and shipment cost. For the model, an iterative optimal solution procedure with shipment consolidation policy incorporated. It is then tested through numerical experiments to show how efficient and effective the shipment consolidation policy is.

On the service performance of alternative shipment consolidation policies

In order to compare the performances of alternative shipment consolidation policies, we develop closed-form expressions of the distribution of the maximum waiting time and the average order delay. We examine the tradeoff between the expected delivery frequency, as measured by the expected shipment consolidation cycle length, and the average order delay. The previous analytical results regarding shipment consolidation are aimed at optimizing the performances of alternative policies using cost-based criteria whereas our results are useful under service-based criteria.

Joint shipment consolidation and inventory decisions in a two-stage distribution system

This study is motivated by a problem that an industrial distributorship faced while distributing automotive spare parts to service and repair centers. Considering the problem encountered, we present an analytical model for joint inventory and shipment consolidation decisions in a two-stage distribution system with a single distribution center, multiple non-identical retailers, and an outside supplier. The retailers face stochastic end-customer demand and use continuous review to replenish inventories. On the other hand, the distribution center uses a periodic review policy and employs a time-based shipment consolidation policy to dispatch retailers’ accumulated orders at the end of each consolidation cycle. We present an exact optimization technique to compute the optimal replenishment quantity at the distribution center, order-up-to level at retailers, and a shipment consolidation cycle length to measure the effects of inventory at retailers on the overall performance. Finally, we perform numerical experiments to measure the impact of various parameters on the overall distribution system.

Evaluation of stock allocation policies in a divergent inventory system with shipment consolidation

In this paper we consider a one-warehouse N-retailer inventory system characterized by access to real-time point-of-sale data, and a time based dispatching and shipment consolidation policy at the warehouse. More precisely, inventory is reviewed continuously, while a consolidated shipment (for example, a truck) to all retailers is dispatched from the warehouse at regular time intervals. The focus is on investigating the cost benefits of using state-dependent myopic allocation policies instead of a simple FCFS (First-Come-First-Serve) rule to allocate shipped goods to the retailers. The analysis aims to shed some light on when, if ever, FCFS is a reasonable policy to use in this type of system? The FCFS allocations of items to retailers are determined by the sequence in which retailer orders (or equivalently customer demands) arrive to the warehouse. Applying the myopic policy enables the warehouse to postpone the allocation decision to the moment of shipment (from the warehouse) or the moments of delivery (to the different retailers), and to base it on the inventory information available at those times. The myopic allocation method we study is often used in the literature on periodic review systems.

Inventory control in divergent supply chains with time‐based dispatching and shipment consolidation

AbstractThis article analyses a divergent supply chain consisting of a central warehouse and N nonidentical retailers. The focus is on joint evaluation of inventory replenishment and shipment consolidation effects. A time‐based dispatching and shipment consolidation policy is used at the warehouse in conjunction with real‐time point‐of‐sale data and centralized inventory information. This represents a common situation, for example, in various types of vendor managed inventory systems. The main contribution is the derivation of an exact recursive procedure for determining the expected inventory holding and backorder costs for the system, under the assumption of Poisson demand. Two heuristics for determining near optimal shipment intervals are also presented. The results are applicable both for single‐item and multiitem systems. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 59–71, 2011

Environmental assessment of shipment release policies

PurposeA program of shipment consolidation (SCL) is the purposeful intervention by management to regularly combine several small shipments so that a larger load may be dispatched on the same vehicle. SCL decisions traditionally have been based upon minimization of total logistics costs (inventory plus transportation). The paper aims to answer the following research question: given the environmental implications of vehicle emissions as a function of load weight, are the familiar SCL policies still optimal?Design/methodology/approachNonlinear expressions relating carbon dioxide (CO2) emissions to vehicle weight, and parameterized by trip length and average travel speed, were derived from published experimental data. Those expressions were included in a simulation model that assessed the environmental impact, in addition to the logistics cost, of the policies concerning when to release a consolidated load.FindingsFor short holding times, the quantity policy performs best in terms of both logistics cost and pollution reduction. In the case of low‐order arrival rates and long holding times, the time policy is best at reducing emissions and logistics costs. However, the best dispatch policy conflicts in terms of pollution reduction and logistics cost minimization for the following cases: moderate holding times and long holding times combined with high‐order arrival rates. In these cases, it is necessary to consider the speed of travel, trip length and unit cost of emissions when evaluating the policies.Research limitations/implicationsA carbon trading market appears to be on the horizon in several industries, which will establish a price per unit weight for CO2 emissions and make it beneficial to minimize the total cost (including emissions) of the network. This research only considers CO2 pollution, but future investigations could also consider other pollutants such as nitrogen oxides, carbon monoxide and volatile organic carbons.Practical implicationsSCL policies can include a “green logistics” component that is based on empirical data.Originality/valueOne undesirable consequence of transportation by truck is CO2 emissions. However, the impact can be lessened, while still emphasizing total logistics cost per load, with our simulation‐based results for shipment release policies.

An integrated model for stock replenishment and shipment scheduling under common carrier dispatch costs

We examine a joint inventory replenishment and shipment scheduling problem that arises in the context of a vendor-managed inventory (VMI) arrangement. Since a temporal shipment consolidation policy is being implemented, the inventory requirements at the vendor are affected by the timing and quantity of shipment release. The vendor’s problem is to determine an integrated policy for inventory replenishment and shipment release and to set its parameters. We develop analytical models for computing such integrated policies where it is economical to use common carriage for outbound transportation. We propose algorithmic approaches to set the optimal policy parameter values.

An analytical model for computing the optimal time-and-quantity-based policy for consolidated shipments

The logistics literature reports that three different types of shipment consolidation policies are popular in current practice. These are time-based, quantity-based and Time-and-Quantity (TQ)-based consolidation policies. Although time-based and quantity-based policies have been studied via analytical modeling, to the best of the authors knowledge, there is no exact analytical model for computing the optimal TQ-based policy parameters. Considering the case of stochastic demand/order arrivals, an analytical model for computing the expected long-run average cost of a consolidation system implementing a TQ-based policy is developed. The cost expression is used to analyze the optimal TQ-based policy parameters. The presented analytical results prove that: (i) the optimal TQ-based policy outperforms the optimal time-based policy; and (ii) the optimal quantity-based policy is superior to the other two (i.e., optimal time-based and TQ-based) policies in terms of cost. Considering the expected maximum waiting time as a measure of timely delivery performance, however, it is numerically demonstrated that the TQ-based policies improve on the quantity-based policies significantly with only a slight increase in the cost.