An Optimal Mixed Batch Shipment Policy for Multiple Items in a Single-Supplier Multiple-Retailer Integrated System

This study addresses mixed batch shipment policy with common replenishment cycle for multiple items in a single-supplier multiple-retailer integrated system. The supplier produces multiple items on a single facility under a common replenishment cycle and delivers products to retailer utilizing a mixed batch shipment policy. The objective is to determine the optimal replenishment cycle, the number of shipments, and the structure of mixed shipment, all of which minimize the integrated total cost per unit time. The single-item isolation model is constructed first, and the single-item isolation model is then integrated into the single-item integration model. Moreover, the single-item integration model is integrated into the multi-item integration model. The minimum total cost model is transformed into a maximum replenishment cycle model to optimize the structure of the mixed batch shipment. The replenishment cycle division method is then developed to obtain the optimal solutions to the subject problem. Examples are presented to illustrate the procedures involved in the replenishment cycle division method.     

Airfreight forwarder shipment planning: A mixed 0–1 model and managerial issues in the integration and consolidation of shipments

The planning and management of air cargo logistics is a complex endeavor, involving collaboration of multiple logistics agents to deliver shipments timely, safely and economically. Airfreight forwarders are third-party brokers/operators who coordinate and manage cargo shipments for their clients. It is important for a forwarder to develop a shipment plan to evaluate the possible integrations and consolidations, to assess whether shipments can meet their respective target delivery dates, and to estimate the amount of costs involved. In this paper, we formulate a forwarder’s shipment planning problem as a mixed 0–1 LP. Effects of integration and consolidation – on the timely delivery of shipments during any phase of the shipping process – are explicitly addressed. A forwarder’s in-house capacity, as well as the available capacity of its partners and sub-contracting agents, are incorporated. We also consider the target cost for a shipment. Based on the special characteristics of the model, we design a customized tabu-search algorithm. We also provide an illustrative case to examine several managerial issues.     

Truck dock assignment problem with operational time constraint within crossdocks

In this paper, we consider a truck dock assignment problem with an operational time constraint in crossdocks where the number of trucks exceeds the number of docks available. The problem feasibility is affected by three factors: the arrival and departure time window of each truck, the operational time for cargo shipment among the docks, and the total capacity available to the crossdock. The objective is to find an optimal assignment of trucks that minimizes the operational cost of the cargo shipments and the total number of unfulfilled shipments at the same time. We combine the above two objectives into one term: the total cost, a sum of the total dock operational cost and the penalty cost for all the unfulfilled shipments. The problem is then formulated as an integer programming (IP) model. We find that as the problem size grows, the IP model size quickly expands to an extent that the ILOG CPLEX Solver can hardly manage. Therefore, two meta-heuristic approaches, Tabu Search (TS) and genetic algorithm (GA), are proposed. Computational experiments are conducted, showing that meta-heuristics, especially the Tabu search, dominate the CPLEX Solver in nearly all test cases adapted from industrial applications.     

Planning and consolidating shipments from a warehouse

A typical warehouse or distribution centre ships material to various customer locations across the country, using various modes of transportation. Each mode has different constraints on size of shipment, different cost structures and different transportation times. Typically, for a given warehouse there are certain customer locations that receive frequent shipments of material. It is often possible, therefore, for the warehouse to consolidate different orders for the same customer location into a single shipment. The transportation mode and the day of shipment must be chosen such that the consolidated shipment meets the size constraints and arrives within an agreed-upon ‘delivery window’. In preparing a warehouse distribution plan, a planner seeks to achieve transportation economies of scale (by consolidating two or more orders into fewer shipments) while levelling the workload on warehouse resources and ensuring that material arrives at a customer location during the acceptable delivery window.The problem of deciding what shipments to make daily can be formulated as a set partitioning problem with side constraints. This paper describes a heuristic solution approach for this problem. Computational experiments using actual warehouse select activity indicate that, for moderate-size problems, the heuristic produces solutions with transportation costs that are within a few percent of optimal. Larger problems found in practice are generally too large to be solved by optimal algorithms; the heuristic easily handles such problems. The heuristic has been integrated into the transportation planning system of a leading distributor of telecommunications products.     

Operations planning for a multi-stage kanban system

A multi-stage production line which operates under a just-in-time production philosophy with linear demand is considered here. The first workstation processes the raw materials after receiving them from suppliers, a kanban mechanism between the workstations transports the work-in-process to the succeeding workstation, and after processing them, delivers the finished products to a buyer or a warehouse. The problem is to find optimally the number of raw material orders, kanbans circulated between workstations, finished goods shipments to the buyers, and the batch size for each shipment (lot). A cost function is developed based on the costs incurred due to the raw materials, the work-in-process between workstations, and the finished goods. Optimal number of raw material orders that minimizes the total cost is obtained, which is then used to find the optimal number of kanbans, finished goods shipments, and the batch sizes for shipments. Numerical examples are used to demonstrate the computations of optimal parameters, and to configure the kanban mechanism on a timescale. Several avenues for future research are also indicated.     

Design of intermodal logistics networks with hub delays

In an intermodal hub network, cost benefits can be achieved through the use of intermodal shipments and the economies of scale due to consolidation of flows at the hubs. However, due to limited resources at the logistics hubs, shipment delays may affect the service performance. In this research hub operations are modeled as a GI/G/1 queuing network and the shipments as multiple job classes with deterministic routings. By integrating the hub operation queuing model and the hub location-allocation model, the effect of limited hub resources on the design of intermodal logistics networks under service time requirements is investigated. The managerial insights gained from a study of 25-city road-rail intermodal logistics network show that the level of available hub resources significantly affects the logistics network structure in terms of number and location of hubs, total network costs, choice of single-hub and inter-hub shipments and service performance.     

Optimal production plans and shipment schedules in a supply-chain system with multiple suppliers and multiple buyers

This research addresses an optimal policy for production and procurement in a supply-chain system with multiple non-competing suppliers, a manufacturer and multiple non-identical buyers. The manufacturer procures raw materials from suppliers, converts them to finished products and ships the products to each buyer at a fixed-interval of time over a finite planning horizon. The demand of finished product is given by buyers and the shipment size to each buyer is fixed. The problem is to determine the production start time, the initial and ending inventory, the cycle beginning and ending time, the number of orders of raw materials in each cycle, and the number of cycles for a finite planning horizon so as to minimize the system cost. A surrogate network representation of the problem developed to obtain an efficient, optimal solution to determine the production cycle and cycle costs with predetermined shipment schedules in the planning horizon. This research prescribes optimal policies for a multi-stage production and procurements for all shipments scheduled over the planning horizon. Numerical examples are also provided to illustrate the system.     

The freight consolidation and containerization problem

In today’s global free market, third-party logistics providers (3PLs) are becoming increasingly important. This paper studies a problem faced by a 3PL operating a warehouse in Shanghai, China, under contract with a major manufacturer of children’s clothing based in the United States. At the warehouse, the 3PL receives textile parcel shipments from the suppliers located in China; each shipment is destined for different retail stores located across the United Sates. These shipments must be consolidated and loaded into containers of varying sizes and costs, and then sent along shipping routes to different destination ports. An express company, such as UPS and FedEx, unloads the shipments from the containers at the destination ports and distributes them to their corresponding stores or retailers by parcel delivery. The objective is to find an allocation that minimizes the total container transportation and parcel delivery costs. We formulate the problem into an integer programming model, and also propose a memetic algorithm approach to solve the problem practically. A demonstration of a good solution to this problem was a decisive factor in the awarding of the contract to the 3PL in question.     

Optimal production and shipment models for a single-vendor–single-buyer integrated system

This paper develops a more general production-inventory model for a single-vendor–single-buyer integrated system. Unlike the hitherto existing production-inventory models for the vendor–buyer system, the present model neither requires the buyer’s unit holding cost greater than the vendor’s nor assumes the structure of shipment policy. Secondly, the model is extended to the situation with shortages permitted, based on shortages being allowed to occur only for the buyer. Thirdly, the paper also presents a corresponding production-inventory model for a deteriorating item for the integrated system. The solution procedures are provided for finding the optimal production and shipment policies and illustrated with numerical examples. Three significant insights are shown: (1) no matter whether the buyer’s unit holding cost is greater than the vendor’s or not, the present model always performs best in reducing the average total cost as compared to the hitherto existing models; (2) if the buyer’s unit holding cost is less than the vendor’s, the optimal shipment policy for the integrated system will only comprise shipments with successive shipment sizes increasing by a fixed factor. It is different from that obtained by Hill [Hill, R.M., 1999. The optimal production and shipment policy for the single-vendor single-buyer integrated production-inventory problem. International Journal of Production Research 37, 2463–2475] for the opposite case; (3) when designing a single-vendor–single-buyer integrated system, making the buyer’s unit holding cost lower than the vendor’s is more beneficial to the system if shortages are not permitted to occur; otherwise it just reverses.     

Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: A harmony search algorithm

In this paper, a multi-buyer multi-vendor supply chain problem is considered in which there are several products, each buyer has limited capacity to purchase products, and each vendor has warehouse limitation to store products. In this chain, the demand of each product is stochastic and follows a uniform distribution. The lead-time of receiving products from a vendor to a buyer is assumed to vary linearly with respect to the order quantity of the buyer and the production rate of the vendor. For each product, a fraction of the shortage is backordered and the rest are lost. The ordered product quantities are placed in multiple of pre-defined packets and there are service rate constraints for the buyers. The goal is to determine the reorder points, the safety stocks, and the numbers of shipments and packets in each shipment of the products such that the total cost of the supply chain is minimized. We show that the model of this problem is of an integer nonlinear programming type and in order to solve it a harmony search algorithm is employed. To validate the solution and to compare the performance of the proposed algorithm, a genetic algorithm is utilized as well. A numerical illustration and sensitivity analysis are given at the end to show the applicability of the proposed methodology in real-world supply chain problems.     

Real-time order tracking for supply systems with multiple transportation stages

This paper presents a stochastic model that evaluates the value of real-time shipment tracking information for supply systems that consist of a retailer, a manufacturer, and multiple stages of transportation. The retailer aggregates demand for a single product from end customers and places orders on the manufacturer. Orders received by the manufacturer may take several time periods before they are fulfilled. Shipments dispatched by the manufacturer move through multiple stages before they reach the retailer, where each stage represents a physical location or a step in the replenishment process. The lead time for a new order depends on the number of unshipped orders at the manufacturer’s site and the number and location of all shipments in transportation. The analytic model uses real-time information on the number of orders unfulfilled at the manufacturer’s site, as well as the location of shipments to the retailer, to determine the ordering policy that minimizes the long-run average cost for the retailer. It is shown that the long-run average cost is lower with real-time tracking information, and that the cost savings are substantial for a number of situations. The model also provides some guidelines for operating this supply system under various scenarios. Numerical examples demonstrate that when there is a lack of information it is better for the retailer to order every time period, but with full information on the status in the supply system it is not always necessary for the retailer to order every time period to lower the long-run average cost.     

Economic selection of process mean for single-vendor single-buyer supply chain

Process mean selection for a container-filling process is an important decision in a single-vendor single-buyer supply chain. Since the process mean determines the vendor’s conforming and yield rates, it influences the vendor–buyer decisions regarding the production lot size and number of shipments delivered from the vendor to buyer. It follows, therefore, that these decisions should be determined simultaneously in order to control the supply chain total cost. In this paper, we develop a model that integrates the single-vendor single-buyer problem with the process mean selection problem. This integrated model allows the vendor to deliver the produced lot to buyer in number of unequal-sized shipments. Moreover, every outgoing item is inspected, and each item failing to meet a lower specification limit is reprocessed. Further, in order to study the benefits of using this integrated model, two baseline cases are developed. The first of which considers a hierarchical model where the vendor determines the process mean and schedules of production and shipment separately. This hierarchical model is used to show the impact of integrating the process mean selection with production/inventory decisions. The other baseline case is studied in the sensitivity analysis where the optimal solution for a given process is compared to the optimal solution when the variation in the process output is negligible. The integrated model is expected to lead to reduction in reprocessing cost, minimal loss to customer due to the deviation from the optimum target value, and consequently, providing better products at reduced cost for customers. Also, a solution procedure is devised to find the optimal solution for the proposed model and sensitivity analysis is conducted to investigate the effect of the model key parameters on the optimal solution.     

Intermodal shipments as recourse in logistics disruptions

This research deals with the flexibility of transportation systems when faced with disruptions. A network optimization model is used to investigate the feasibility of using intermodal shipments as recourse to disruptions in a transportation network. In a study of US interstate highways and intermodal rail networks, performance of over-the-road and intermodal shipments is compared under different disruption scenarios. The results show that the topology of US transportation system and locations of existing intermodal terminals provide required path redundancies and a strategic benefit for intermodal shipments to bypass disrupted regions with lower costs and competitive shipment times compared to rerouted road shipments.     

An Algorithmic Framework for Routeing LTL Shipments

One way of reducing the unit cost of shipment by a motor carrier is to consolidate many LTL (less-than-truck-load) shipments. Explicit information on the route structure is a prerequisite to the understanding of the costs of the services provided and to the planning of the allocation of the equipment and personnel among the terminals. In this paper, an approach for routeing the LTL shipments is presented and is applied to a hypothetical network. Solution results of this example show that the algorithm offers an efficient and reasonably accurate method for the routeing of LTL shipments via the intermediate terminals.     

Short-term liner ship fleet planning with container transshipment and uncertain container shipment demand

This paper proposes a short-term liner ship fleet planning problem by taking into account container transshipment and uncertain container shipment demand. Given a liner shipping service network comprising a number of ship routes, the problem is to determine the numbers and types of ships required in the fleet and assign each of these ships to a particular ship route to maximize the expected value of the total profit over a short-term planning horizon. These decisions have to be made prior to knowing the exact container shipment demand, which is affected by some unpredictable and uncontrollable factors. This paper thus formulates this realistic short-term planning problem as a two-stage stochastic integer programming model. A solution algorithm, integrating the sample average approximation with a dual decomposition and Lagrangian relaxation approach, is then proposed. Finally, a numerical example is used to evaluate the performance of the proposed model and solution algorithm.     

A continuous approximation procedure for determining inventory distribution schemas within supply chains

This paper presents an integrated inventory distribution optimization model that simultaneously incorporates the issues of location, production, inventory, and transportation within a supply chain. The objective is to determine the optimal number and size of shipments under varying but commonly practiced production and shipping scenarios. A continuous approximation procedure is proposed to determine the optimal number and size of shipments. Three production and shipping scenarios are investigated and closed form expressions for the optimal number of shipments for each scenario are obtained. A numerical example is presented to demonstrate the usefulness of the model.     

A stochastic periodic review integrated inventory model involving defective items, backorder price discount, and variable lead time

The purpose of this article is to investigate a stochastic integrated supplier-retailer inventory problem. The model analyzed in this article explores the problem of the protection interval, the backorder price discount, the lead time, and the numbers of shipments from the supplier to the retailer in one production run as control variables to widen applications for an integrated periodic review inventory model. We consider the situation in which the supplier and the retailer establish a long-term strategic partnership and contract to jointly determine the best strategy. We assume that the protection interval demand follows a normal distribution. Our objective is to determine the optimal review period, the optimal backorder price discount, the optimal lead time, and the optimal number of shipments from the supplier to the retailer in one production run, so that the joint expected annual total cost incurred has the minimum value. Furthermore, an algorithm of finding the optimal solution is developed. Also, the sensitivity analysis included and a numerical example is given to illustrate the results of the proposed model.     

Genetic algorithms for a supply management problem: MIP-recombination vs greedy decoder

Two variants of genetic algorithm (GA) for solving the Supply Management Problem with Lower-Bounded Demands (SMPLD) are proposed and experimentally tested. The SMPLD problem consists in planning the shipments from a set of suppliers to a set of customers minimizing the total cost, given lower and upper bounds on shipment sizes, lower-bounded consumption and linear costs for opened deliveries. The first variant of GA uses the standard binary representation of solutions and a new recombination operator based on the mixed integer programming (MIP) techniques. The second GA is based on the permutation representation and a greedy decoder. Our experiments indicate that the GA with MIP-recombination compares favorably to the other GA and to the MIP-solver CPLEX 9.0 in terms of cost of obtained solutions. The GA based on greedy decoder is shown to be the most robust in finding feasible solutions.     

An improved solution to the replenishment policy for the EMQ model with rework and multiple shipments

Recently, Chiu et al. (2012) [1] present an alternative optimization procedure to derive the optimal replenishment lot size for an economic manufacturing quantity (EMQ) model with rework and multiple shipments. This inventory model was proposed by Chiu et al. (2011) [2]. Both papers do not consider the determining of the number of shipments. This paper determines both the optimal replenishment lot size and the optimal number of shipments jointly. The solution of this paper is better than the solutions of Chiu et al.  and .     

An integrated inventory model with controllable lead time and distribution‐free demand

The impact of lead time reduction on an integrated periodic review inventory system comprising a single vendor and multiple buyers with a step crashing cost function and service‐level constraints is studied. The probability distribution of demand during the protection period for each buyer is unknown, but the mean and the variance are given. Each production lot of the vendor can be delivered in a number of shipments to all buyers. A minimax distribution‐free procedure with Lagrange multipliers is applied to determining the lead time, the common shipment cycle time, the target levels of replenishments and the number of shipments per production cycle so that the expected total system cost is minimized. Numerical experiments along with sensitivity analysis were performed to illustrate the effects of parameters on the decision and the total system cost. Copyright © 2009 John Wiley & Sons, Ltd.