James H. Bookbinder

An integrated inventory–transportation system with modified periodic policy for multiple products

Abstract Efficient management of a distribution system requires an integrated approach towards various logistical functions. In particular, the fundamental areas of inventory control and transportation planning need to be closely coordinated. Our model deals with an inbound material-collection problem. An integrated inventory–transportation system is developed with a modified periodic-review inventory policy and a travelling-salesman component. This is a multi-item joint replenishment problem, in a stochastic setting, with simultaneous decisions made on inventory and transportation policies. We propose a heuristic decomposition method to solve the problem, minimizing the long-run total average costs (major- and minor-ordering, holding, backlogging, stopover and travel). The decomposition algorithm works by using separate calculations for inventory and routing decisions, and then coordinating them appropriately. A lower bound is constructed and computational experience is reported.

Transfer Optimization in a Transit Network

Transfer optimization attempts to minimize the overall inconvenience to passengers who must transfer between lines in a transit network. Bus trips are scheduled to depart from their terminal so as to minimize some objective function measuring that inconvenience. In this paper, the transit network is assumed to be given, and the scheduled headway is treated as fixed on each line. We denote by t i the departure time of the first bus on line i . { t i } are termed “offset times,” and constitute the decision variables of our model. To take into account stochastic travel times of buses, our treatment of transfer optimization employs a simulation procedure in combination with an optimization model. That model turns out to be a relaxation of the Quadratic Assignment Problem. It can incorporate a wide range of objective functions (measures of overall passenger disutility) and a variety of policies for holding buses at a transfer point. In the case where buses are not held at all, we show, for a number of different objective functions and transit networks, the negative consequences of optimizing transfers with a deterministic bus-travel-times assumption, if these travel times are in fact random variables. Suggestions are then made for future research.

Estimation of inventory re-order levels using the bootstrap statistical procedure

It can be difficult to set the reorder point in an inventory system because often one does not have much knowledge of the lead-time demand (LTD)distribution. A frequent practice is to assume a “standard” distribution, such as the Normal. The reorder point is then taken as the p-th fractile of that standard distribution, where (1 −p) is the specified probability of stockout during a replenishment cycle. When the desired service level p is high and the “true” LTD distribution is skewed, previous research has shown that the reorder point and inventory costs are strongly affected by the shape of the assumed LTD distribution. Ideally, no assumptions about this distribution should be necessary. One such “distribution-free” approach is the bootstrap procedure. Beginning with a single sample W = {x1x2,…,xn} of lead-time demand, the bootstrap repeatedly samples with replacement from W, A family of bootstrap samples of size n is thereby created, each sample furnishing an estimate Xp∗ of the p-th fractile of the LTD...

Comparison of Asian and European logistics systems

This research compares the logistics systems of Asia and Europe and categorises them into distinct levels of logistics excellence. First, the context in Asia and in Europe is summarized. Then, attributes of a world‐class logistics system are proposed. By applying cluster analysis to data from authoritative sources, we objectively segregate European and Asian logistics systems into three logistics tiers. There are several surprises, the main one being that the UK is classified Tier 2 (not as favourable as Tier 1). A prioritized set of attributes that the UK could improve on to qualify for the Tier 1 group is suggested. Sensitivity analyses are conducted to determine changes to the classifications. After finding that the top‐ranking logistics systems of Europe and Asia are from Denmark and Singapore, respectively, those two countries are studied in detail to draw logistics lessons applicable elsewhere.

Probabilistic Modeling of Freight Consolidation by Private Carriage

A program of freight consolidation is a systematic attempt to decrease total transportation cost between a given origin and destination. Fewer shipments of larger weight are dispatched, while recognizing the inventory carrying cost of holding the first-arriving orders before dispatching the combined load. Here we employ probabilistic modeling to choose the maximum holding time and desired dispatch quantity. We obtain practical decision rules for temporal consolidation for transportation in ones own truck. Final results are expressed visually through a nomograph (four inked graphs) relating decision variables, probability and demand parameters, and objective-function values. The nomograph permits an intuitive sensitivity analysis.

Vehicle routing considerations in distribution system design

Abstract In Distribution System Design, one minimizes total costs related to the number, locations and sizes of warehouses, and the assignment of warehouses to customers. The resulting system, while optimal in a strategic sense, may not be the best choice if operational aspects such as vehicle routing are also considered. We formulate a multicommodity, capacitated distribution planning model as anon-linear, mixed integer program. Distribution from factories to customers is two-staged via depots (warehouses) whose number and location must be chosen. Vehicle routes from depots to customers are established by considering the “fleet size and mix” problem, which also incorporates strategic decisions on fleet makeup and vehicle numbers of each type. This problem is solved as a generalized assignment problem, within an algorithm for the overall distribution/routing problem that is based on Benders decomposition. We furnish two version of our algorithm denoted Technique I and II. The latter is an enhaancement of the former and is employed at the users discretion. Computer solution of test problems is discussed.

Random lead times and expedited orders in (Q,r) inventory systems

This paper considers inventory models of the order-quantity/order-point type, or (Q,r) models. In general the control parameters (Q and r) depend on both the demand process and the replenishment lead time. Although many studies have treated lead time as constant, focusing solely on demand, a (Q,r) model with stochastic lead time could be a building block in Supply Chain Management. Variability in lead times between successive stages is often what disturbs supply chain coordination.In a two stage system with a constant demand rate, we will concentrate on lead time as a random variable, and develop two probabilistic models. In the first, lead T is exogenous. Lead time is made endogenous in the second stochastic model through an “expediting factor” τ, the constant of proportionality between random variables T (the expedited lead time) and T (ordinary lead time): T = τT. For expedited orders (τ 1. The second model thus has three decision variables (Q, r, τ).For each model, we show that the expected cost per unit time is jointly convex in the decision variables and obtain the global minimizer. Numerical examples are given. Sensitivity analyses are conducted with respect to the cost parameters, and suggestions are made for future research.

Markovian Decision Processes in Shipment Consolidation

Shipment consolidation is a logistics strategy that combines two or more orders or shipments so that a larger quantity can be dispatched on the same vehicle. This paper discusses a discrete-time Markovian decision process (MDP) approach for determining when to release consolidated loads. We assume that the shipper controls the timing of each load dispatch. Thus, whenever a customer places an order, a choice must be made between dispatching this order (plus all others waiting) immediately, or continuing to consolidate until at least the arrival of the next order. Our MDP models of shipment consolidation consider movement by for-hire transportation (common carriage) or by a firms own vehicles (private fleet). Small but realistic numerical examples illustrate the application of these models and the data-aggregation issues that must be resolved. Two minimization criteria are considered: cost per unit time, or cost per hundredweight per unit time. For private carriage, the optimal policy is of the control-limit type; for common carriage, it may not be. These potential differences in form of the optimal policy are true for either objective function. The possibly contrasting optimal policies are interpreted in light of the costs encountered by an industrial firms private fleet compared to the freight charges of a public trucking company.

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.

Calculating the benefits of vendor managed inventory in a manufacturer-retailer system

Firms such as Wal-Mart and Campbells Soup have successfully implemented vendor managed inventory (VMI). Articles in the trade press and academic literature often begin with the premise that VMI is ‘beneficial’; but beneficial to which party and under what conditions? We consider in this paper a vendor V that manufactures a particular product at a unique location. That item is sold to a single retailer, the customer C. Three cases are treated in detail: independent decision making (no agreement between the parties); VMI, whereby the supplier V initiates orders on behalf of C; and central decision making (both vendor and customer are controlled by the same corporate entity). Values of some cost parameters may vary between the three cases and each case may cause a different actor to be responsible for particular expenses. Under a constant demand rate, optimal solutions are obtained analytically for the customers order quantity, the vendors production quantity, hence the parties’ individual and total costs in the three cases. Inequalities are obtained to delineate those situations in which VMI is beneficial.