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We study stochastic clearing systems with a discrete‐time Markovian input process, and an output mechanism that intermittently and instantaneously clears the system partially or completely. The decision to clear the system depends on both quantities and delays of outstanding inputs. Clearing the system incurs a fixed cost, and outstanding inputs are charged a delay penalty, which is a general increasing function of the quantities and delays of individual inputs. By recording the quantities and delays of outstanding inputs in a sequence, we model the clearing system as a tree‐structured Markov decision process over both a finite and infinite horizon. We show that the optimal clearing policies, under realistic conditions, are of the on‐off type or the threshold type. Based on the characterization of the optimal policies, we develop efficient algorithms to compute parameters of the optimal policies for such complex clearing systems for the first time. We conduct a numerical analysis on the impact of the nonlinear delay penalty cost function, the comparison of the optimal policy and the classical hybrid policy (ie, quantity and age thresholds), and the impact of the state of the input process. Our experiments demonstrate that (a) the classical linear approximation of the cost function can lead to significant performance differences; (b) the classical hybrid policy may perform poorly (as compared to the optimal policies); and (c) the consideration of the state of the input process makes significant improvement in system performance.

In this paper, we incorporate shipment scheduling decisions into hub location problems. Our aim is to determine the optimal locations of hubs, hub network structure, and the number of dispatches to operate on the hub network as well as the time period of dispatching each vehicle from a hub. We develop three mixed-integer programming models for different versions of this problem, depending on whether holding costs are incorporated and whether the vehicles are of different types. We investigate the impact of shipment scheduling decisions and holding costs on hub network configurations, routing decisions, and total cost of the network. We solve the models on instances from a new dataset with real data.

Quantity discounts have been broadly examined in decisions on the sale or purchase of goods. The analysis of coordinating the discount decisions for the retailer (buyer), the wholesaler (supplier), and the public transportation service provider (Less-Than-Truckload carrier), however, is still in its infancy. In this paper, we develop a tri-level programming approach to coordinate the three supply chain members' decisions on discount policies, when the demand is sensitive to the change in price. Both decentralized and centralized scenarios are examined, and a heuristic algorithm is presented to assist the three parties in establishing their discount schemes in a decentralized environment. Through a series of comprehensive numerical experiments based on the linear demand, we show that the price-sensitivity is a key motivation, for all parties, especially the carrier, to offer discounts. Specifically for the wholesale quantity discount, the data analyses also illustrate the different purposes and corresponding structures for the decentralized and centralized cases. For the former case, the discount is quantity-based, which encourages the buyer to increase the size of each order; while for the latter case, the discount is volume-based, which is used to boost the annual demand. The significant improvements to each party and to the entire supply chain resulting from the discount coordination are also demonstrated under various situations.

We examine a coordinated capacitated lot-sizing problem for multiple product families, where demand is deterministic and time-varying. The problem considers set-up and holding costs, where capacity constraints limit the number of individual item and family set-up times and the amount of production in each period. Using a strong reformulation and relaxing the demand constraints, we improve both the upper and lower bounds using a combination of Benders decomposition and an evolutionary algorithm, followed by subgradient optimisation. Through computational experiments, we show that our method consistently achieves better bounds, reducing the duality gap compared to other single-family methods studied in the literature.

We consider the shipment consolidation and freight forwarding problem under two discount schemes: the system-wide and the double-discount. In the system-wide scheme, the cost associated with one flight does not only depend on the quantity of freight assigned to that flight, but also on the total freight assigned to other flights operated by the same carrier. In the double-discount scheme, there are cost savings based on the quantity shipped on a given flight on top of the system-wide discount. We propose models based on multi-commodity network flow formulations that take into account practical aspects such as cargo unsplitability, shipment volume and over-declaration. We propose solution methodologies based on Lagrangian relaxation and local branching. Numerical testing reveals the efficiency of the approaches presented and sheds light on some managerial implications. We find that freight forwarders do not only reduce costs from the system-wide and the double-discount schemes, but are also likely to engage with fewer airlines, thus reducing administrative fees.

Crowdsourced delivery systems have created many new industry last-mile delivery solutions and have received some attention in the academic literature. In this review paper, we analyze the current industry status of this emergent concept and provide a classification of available platforms based on their matching mechanisms, target markets and compensation schemes. We review the operations research (OR) literature explicitly addressing this topic and assess the realism of the assumptions, and applicability to real-world applications. We also compare the management decisions within crowdsourced delivery systems to well-studied OR problems in the literature, and pinpoint new challenges that arise in the context of crowdsourced delivery. The purpose of this paper is to identify key elements of such systems that distinguish them from other transportation systems, to ultimately shed light on some promising research directions.

A dual-toll policy, considering a multi-degree fuzzy incident rate, is proposed to mitigate the risk caused by hazardous material (hazmat) transportation in a road network. To address several carriers transporting multiple hazmat types, we use a bi-level programming formulation. The upper and lower levels, respectively, exemplify decision problems faced by the regulators (regional and local governments) and travelers (hazmat and non-hazmat). The contributions of this paper are threefold. • In addition to the total network risk, our model includes risk equity (minimization of the maximum link risk). This makes the spatial distribution of risk closer to homogeneous. • We propose a new definition of risk measurement, based on the integration of a fuzzy incident rate and population exposure, together with the transportation time. This new definition better reflects the uncertain nature of actual transportation situations. • We construct a new real-world transportation network based on data from the City of Nanchang, China. Empirical distances, travel times, population densities, and applicable regulations are incorporated in this network of 32 nodes and 102 arcs. Our model is solved, based upon the preceding figures and toll values that are consistent with Chinese national standards. To solve the model effectively, a genetic-algorithm-based methodology is employed, along with a piecewise linearization method and a Frank-Wolfe approach. Employing both the well-known Sioux-Falls network and the new, larger network, case studies are presented. If distinct hazmat tolls are imposed on differing hazmat types, those case studies enable managerial insights, derived from the dual toll policy, when incident possibilities vary.

We analyze the problem faced by a logistics provider that dispatches shipment orders (parcels or larger packages) of two order classes, viz. expedited and regular. Shipment orders arrive according to a compound Poisson process for each class. Upon an arrival, the logistics provider may continue consolidating arriving orders by paying a holding cost. Alternatively, the provider may dispatch, at a fixed cost, a vehicle containing (a portion of) the load consolidated so far. In addition, the provider must specify the composition of each dispatch by allocating (rationing) the volume of the vehicle between expedited and regular shipment orders. We model this problem as a continuous-time Markov Decision Process and minimize the expected discounted total cost. We prove the existence of quantity-based optimal threshold policies under particular conditions. We also structurally analyze the thresholds of these optimal policies. Based on these structural properties, we develop an efficient solution approach for large problem instances which are difficult to solve using the conventional policy-iteration method. For two real-life applications, we show that the quantity-based threshold policies derived using the proposed approach outperform the time policies used in practice. (C) 2018 Elsevier B.V. All rights reserved.

Nestle Canada currently uses 32 routes that serve over 4,500 customers in the Greater Toronto Area (GTA). This study aims to quantify Nestlé's costs and benefits of modifying their ice cream supply chain to incorporate night-time deliveries, while providing a framework for the regulatory, conceptual, and inertial obstacles to implementation. Employing Nestlé's customer data set, we created routing software to determine the proportion of customers who must be willing to accept deliveries outside of normal working hours so that the change would be financially feasible. Based upon a literature review we found that, before proceeding, the following qualitative factors should be considered: safety, sustainability, regulatory concerns, truck noise, traffic, and congestion. Reduction of 3–10 percent in the number of routes may result from switching a suitable proportion of deliveries to night-time, achieving the minimum fleet size when 50–60 percent of locations are served on night routes. The operation of both night-time and daytime deliveries would enable an increase in truck utilization, thus decreasing the number of vehicles required. Recommendations for success of night-time deliveries include preparation of a safety plan, procurement of plate trucks, noise-abatement techniques, and the development of a noise-monitoring program.

In the international air cargo business, freight is usually consolidated into containers, called Unit Load Devices (ULDs). The transportation charge of a ULD depends on whether the total weight exceeds a certain threshold, called the pivot weight. If the total load tendered by a freight forwarder is less than the pivot weight, it gets charged at the under-pivot rate. Any portion of the load that exceeds the pivot weight is charged at the over-pivot rate. This scheme is adopted for safety reasons to avoid the overloading of ULDs. We formulate a mixed integer program, and propose four solution methodologies for the air-cargo consolidation problem under the pivot-weight scheme (ACPW). These are exact solution approaches based on branch-and-price, a best-fit decreasing loading heuristic, and two extended local branching heuristics (a multi-local tree search and a relaxation-induced neighborhood search). The local branching heuristic with relaxation-induced neighborhood search is found to outperform other approaches in terms of solution quality and computational time. Problems with up to 400 shipments and 80 containers are solved to within 3.4% of optimality in less than 20min.

This article studies the dispatch of consolidated shipments. Orders, following a batch Markovian arrival process, are received in discrete quantities by a depot at discrete time epochs. Instead of immediate dispatch, all outstanding orders are consolidated and shipped together at a later time. The decision of when to send out the consolidated shipment is made based on a “dispatch policy,” which is a function of the system state and/or the costs associated with that state. First, a tree structured Markov chain is constructed to record specific information about the consolidation process; the effectiveness of any dispatch policy can then be assessed by a set of long-run performance measures. Next, the effect on shipment consolidation of varying the order-arrival process is demonstrated through numerical examples and proved mathematically under some conditions. Finally, a heuristic algorithm is developed to determine a favorable parameter of a special set of dispatch policies, and the algorithm is proved to ...

The truck plant of General Motors of Canada produces 60 trucks/hour, 2 shifts/day, in a highly automated factory employing 3,200 people. Flow in the paint shop is prone to bottlenecks when there is a large ratio of two- to monotone jobs. (Two-tone jobs require a second pass through the paint shop.) The shop has four major control points (two conveyor crossovers and two significant conveyor intersections), where decisions for routing jobs can greatly impact paint-shop performance. A simulation model is developed and refined to determine a set of “best” rules for those control points, dynamic rules reflecting input variables, and current system status. The paint-shop simulation model is employed to study overall throughput and time in the system for various control rules, as functions of product mix and the rates of automotive processing and repair. Conclusions are drawn regarding the influence of those rules on the conveyor crossovers and intersections.

Although it is an essential link in any supply chain, transportation is often neglected in inventory decisions. In reordering decisions, for example, this omission may well result in unexpected losses, as transportation and quantity discounts can be tricky. In this paper, we study the problem of optimal coordination of these discounts from the perspectives of the parties who offer them, rather than of those who take them. Using a non-cooperative model of a three-party supply chain, we show that cooperation can benefit each member individually, and the supply chain overall. In fact, cooperation can generate a non-empty core – that is, there may be a surplus that can be allocated so that all parties and all coalitions of parties, are induced to continue to cooperate. We provide a detailed algorithm, based on the Shapley value, to allocate the surplus fairly and illustrate it with numerical examples.

Less-Than-Truckload (LTL) carriers generally serve geographical regions that are more localized than the inter-city line-hauls served by truckload carriers. That localization can lead to urban freight transportation routes that overlap. If trucks are traveling with less than full loads, there typically exist opportunities for carriers to collaborate over such routes. We introduce a two stage framework for LTL carrier collaboration. Our first stage involves collaboration between multiple carriers at the entrance to the city and can be formulated as a vehicle routing problem with time windows (VRPTW). We employ guided local search for solving this VRPTW. The second stage involves collaboration between carriers at transshipment facilities while executing their routes identified in phase one. For solving the second stage problem, we develop novel local search heuristics, one of which leverages integer programming to efficiently explore the union of neighborhoods defined by new problem-specific move operators. Our computational results indicate that integrating integer programming with local search results in at least an order of magnitude speed up in the second stage problem. We also perform sensitivity analysis to assess the benefits from collaboration. Our results indicate that distance savings of 7---15 % can be achieved by collaborating at the entrance to the city. Carriers involved in intra-city collaboration can further save 3---15 % in total distance traveled, and also reduce their overall route times.

Increased competition in business environments requires that firms provide not only quality but also timely service with minimal cost. Offering a delivery-time guarantee may increase the demand for a product or service, or allow the firm to charge a price premium. This paper investigates the effects of different pricing schemes for a Third Party Logistics (3PL) provider. The 3PL tenders a consolidated load to a carrier that line-hauls over a certain origin–destination lane. In a price- and time-sensitive logistics market, we derive the optimal quotations that should be made for price and delivery-time, with the objective of maximizing the profit rate of the 3PL provider. We propose four easy-to-use temporal pricing schemes, and derive the corresponding optimal length of shipment consolidation cycles and the prices. Depending on the logistics market parameters, we show that charging according to an order’s time of arrival is not necessarily the best pricing scheme. Various managerial insights and numerical examples with sensitivity analysis are provided.

We study the freight forwarder’s shipment planning problem in an airfreight forwarding network where a set of cargo shipments have to be transported to given destinations. We provide mixed integer programming formulations that use piecewise-linear cargo rates and account for volume and weight constraints, flight departure/arrival times, as well as shipment-ready times. After exploring the solution of such models using CPLEX, we devise two solution methodologies to handle large problem sizes. The first is based on Lagrangian relaxation, where the problems decompose into a set of knapsack problems and a set of network flow problems. The second is a local branching heuristic that combines branching ideas and local search. The two approaches show promising results in providing good quality heuristic solutions within reasonable computational times, for difficult and large shipment consolidation problems.

Quantity discounts are a useful mechanism for coordination. Here we investigate such discounts from the supplier's perspective, both from a non-cooperative game-theoretical approach and a joint decision model. Taking into account the price elasticity of demand, this analysis aids a sole supplier in establishing an all-unit quantity discount policy in light of the buyer's best reaction. The Stackelberg equilibrium and Pareto optimal solution set are derived for the non-cooperative and joint-decision cases, respectively. Our research indicates that channel efficiency can be improved significantly if the quantity discount decision is made jointly rather than non-cooperatively. Moreover, we extend our model in three directions: (1) the product is transported by a private fleet; (2) the buyer may choose to offer her customers a different percentage discount than that she obtained from the supplier; and (3) the case of heterogeneous buyers. Numerical case studies are employed throughout the paper to illustrate the practical applications of the models presented and the sensitivity to model parameters.

Consider a family of SKUs for which the supplier will offer a quantity discount, according to the aggregate purchases of the product group. Management of those items is based on the modified periodic policy. From the supplier's point of view, what are the optimal parameters (breakpoint and discount percentage)? For deterministic demand, we discuss the cases in which demand is both constant and price-sensitive. First as a noncooperative Stackelberg game, and then when the two parties make the discount and replenishment decisions jointly, we illustrate the impact of price-sensitivity and joint decision making on the supplier's discount policy.

This article studies the dispatch of consolidated shipments. Orders arrive to a depot at discrete time epochs following a discrete time batch Markov arrival process (BMAP). The weight of an order is measured in discrete units and may be correlated with the arrival time. As soon as the total weight of the accumulated orders reaches a threshold, which is a function of the time elapsed since the last dispatch, all orders are consolidated and a shipment is dispatched. A discrete time Markov chain for the accumulated weight of orders in the system is introduced and analyzed. The distributions of the accumulated weight at an arbitrary time, total accumulated weight in a consolidation cycle, and excess of weight per shipment are obtained. By introducing an absorption Markov chain and a terminating Markovian arrival process, we find the distributions of the consolidation cycle length, the waiting time of an arbitrary order, and the number of orders that occur in a cycle. An efficient computational procedure is de...

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.

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 tim...

Firms such as Wal-Mart and Campbell's 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 customer's order quantity, the vendor's production quantity, hence the parties’ individual and total costs...

SYNOPTIC ABSTRACTDifferent valuations of the same service can provide profit opportunities to the service provider, by differentiating premiums for varying types of customers. However, the success of revenue management in such a market environment heavily depends on the quality of the market research on customer segmentation. We model and analyze customer equilibrium segmentation behavior in a closed system where service is provided by either of two centers. The perceived qualities of service depend on the type of pricing scheme to which the customer subscribes. The analysis is based upon a stochastic single period model where the customers are all privately informed. Some structural results are obtained and a numerical example is given for a 3-class system, with various managerial insights.

Vendor-managed inventory (VMI) and consignment inventory (CI) are supply-chain sourcing practices between a vendor and customer. VMI allows the vendor to initiate orders on behalf of the customer. This presumably benefits the vendor who can then make replenishment decisions according to her own preferences. In CI, as in the usual independent-sourcing approach to doing business, the customer has authority over the timing and quantity of replenishments. CI seems to favor the customer because, in addition, he pays for the goods only upon use. Our main aim is to analyze CI in this supply chain under deterministic demand, and provide some general conditions under which CI creates benefits for the vendor, for the customer, and for the two parties together. We also consider similar issues for the combined use of CI and VMI.

This paper addresses a hub-and-spoke network problem for railroad freight, where a central planner is to find transport routes, frequency of service, length of trains to be used, and transportation volume. Hub-and-spoke networks, often found in air freight, have not been favoured by railways in the past. Such a structure could be profitable, however, if there exist concentrated freight flows on some service links. We formulate a linear integer programming model whose objective function includes not only the typical operational cost, but also cost due to the transit time spent by freight in the network. We then develop heuristic algorithms to solve large scale instances occurring in rail freight systems in France plus Italy; Germany; and a 10-country European network. By assuming that every node is equipped with consolidation capability, we let the final solution naturally reveal potential hub locations, the impact of several of which is studied by sensitivity analysis.

North American Free Trade Agreement (NAFTA), the free-trade agreement between Canada, Mexico and the United States, has caused North American companies to consider inclusion of Mexico in their supply chain. The lower Mexican wages may offset the additional transportation costs; capital-intensive operations are preferably still done in the United States or Canada. With a consumer base focused in the United States, can an organisation leverage the benefits of NAFTA to their individual advantage? This paper aims to show how, through a real-world example, overall supply chain costs (total system costs of inventory, transportation and facilities) can be minimised under those circumstances. We formulate and solve a mixed-integer programming model to find the optimal supply chain for Tectrol Inc., a manufacturer of power supplies. In the first case, components produced in Canada undergo final assembly in the United States, followed by distribution there. The second case is a ‘NAFTA’ supply chain: the Canadian components are converted to sub-assemblies in Mexico, processed in finishing plants across the US border, then shipped through distribution centres to the final customer. Model solutions indicate in each instance where to locate finishing plants and distribution centres, and how many of each there should be. Results provide Tectrol (hence other manufacturers) some general guidelines on distribution and supply chain decisions in the NAFTA context.

Cross-docking replaces traditional warehousing, enabling continuous flow of items without storage. Here we model location-distribution networks, that include cross-docking facilities, to obtain the latter's impact on the supply chain. We formulate optimization models to minimize total cost in three multi-echelon networks, each model generalizing the preceding one. The first includes a single manufacturer, one product type, and multiple customers. Cross-docks are to be located between origin and destinations. Besides solving optimally, a tool for quantitative analysis of direct-shipment decisions is developed. The second model considers more than one product: We determine a cost-effective sequence of items for indirect shipment (via cross-docks). Finally, in a network with multiple origins, optimal solutions are obtained for 40 medium-sized and larger examples.

Most studies on supply chain management have taken an “inventory” point of view: The chain, supplier → manufacturer → major manufacturer , is thus analyzed as a series of production-inventory decisions. Although correct, that approach neglects issues on the transportation between nodes, thereby missing important opportunities for cost savings and optimization. Here we focus on the substantial economies of scale in transportation. These occur when merchandise is shipped in one’s own truck (private carriage), or when transport is performed by a public, for-hire trucking company (common carriage). As a result, better inventory replenishment between successive echelons may have less impact than improved transportation decisions. This is especially true when the latter include a strategy for shipment consolidation, the policies whereby several small orders will be held as they accumulate, then dispatched as a single, combined load. In the present paper, we apply renewal theory to two strategies commonly utilized in practice. For the case of a quantity policy we obtain the optimal target weight before dispatch, while for a time policy, we calculate the optimal length of each consolidation cycle (maximum holding time for any order). These strategies are analyzed for private carriage and then for common carriage. Particular situations are studied graphically and numerically; general results are expressed in the form of propositions.

Suppose that a private carrier delivers to a set of customers and also has a number of (optional) backhaul opportunities. It wants to choose the best of these, depending on the revenue generated, and insert them in a revised tour. This will be at an expense of deviation from the original tour, because, here, deliveries need not precede backhauls. The problem is to find the mixed tour whose net cost is the lowest, selecting the most profitable backhauls subject to the overall capacity. We thus generalize several other vehicle routing problems with backhauls. A mixed-integer model is developed for the problem. It is based on Miller–Tucker–Zemlin subtour elimination constraints. We address several improvement techniques aimed at increasing computational tractability of the formulation. Computational results show that medium-sized problems can be solved optimally in a reasonable time by using a general-purpose commercial solver. © 2003 Wiley Periodicals, Inc.

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.

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 one's own truck. Final results are expressed visually through a nomograph (four linked graphs) relating decision variables, probability and demand parameters, and objective-function values. The nomograph permits an intuitive sensitivity analysis.

Given an assortment of k products, a retailer must make an important decision on the percentage of space allocated to each of them. Optimization models for this problem have previously shown that an item's space should not simply be given in proportion to its sales or its gross margin (GM). Calculations of Direct Product Profitability (DPP) have improved upon the GM concept, but the present paper is the first (of which we are aware) to integrate the DPP approach into a shelf-space optimization model.

The processing time of large orders is, in many industries, longer than that of small orders. This renders supply lead times in such settings to be increasing in the order size. Yet that pattern is not re#ected in existing inventory control models, especially those allowing for random lead times. This work aims at rectifying the situation. Our setting is an order-quantity/reorder-point model with backordering, where the shortage penalty is incurred per unit per unit time. The processing time of each unit is random; the processing time of a lot is correlated with its size. For the case where lead time is proportional to the lot size, we obtain a closed-form solution. That is, unlike the classical (Q, r) model (where lead time is independent of lot size), no iterations are required here. We also analyze a case where the processing time exhibits economies of scale in the lot size. Finally, we consider a situation where a customer can secure shorter processing times by reserving capacity at the supplier’s manufacturing facility. ( 2000 Elsevier Science B.V. All rights reserved.

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 time 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 time 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 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

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.

This paper obtains the optimal routings for intermodal containerized transport from Canada to Mexico. Such traffic is being stimulated by the North American Free Trade Agreement (NAFTA), but the cost and lead times of feasible routes are not well known. We summarize the links and routes to Mexico on which one or more carriers now operate, and then determine non-dominated tradeoffs between cost and service. Every southbound route from Canada requires a transshipment point in the southern or southwestern U. S. Feasible transshipment points are also candidate locations for a manufacturing ‘twin plant’, a distribution centre, or a transportation hub. Here, as a first step in this bigger problem, a network is constructed between five Canadian origins and three important Mexican destinations. Each link employs available intermodal services whose transit time and transportation cost are obtained through industry sources. A shortest-path algorithm enables calculation of the route requiring least time and the route of minimum cost. Non-dominated time/cost tradeoffs are identified for each origin–destination pair. After including inventory expenses (by parametrizing the unit value of lead time), total-cost curves then eliminate some routing alternatives. Guidelines are provided on the effects of mode, carrier, and O–D locations on selection of intermodal routes to Mexico. Finally, two new intermodal services are proposed and their benefits discussed.

Decision analysis in management science employs concepts from economics such as utility functions and indifference curves. A utility function U models the “satisfaction” that a customer obtains from logistics service. Here U depends on two attributes (lead time, fill rate) whose values more directly represent customer service. The shipper can, at additional cost, improve either or both of these attributes. Constructs and maximizes various utility functions U given a total budget B for distribution service. Finds that without increasing the budget overall logistics service can often be improved from the customer’s point of view. Whether U is additive or multiplicative, a customer’s utility resulting from the optimal lead time and fill rate is typically 20 per cent higher than when those attribute levels are set intuitively (without reference to customer preferences and tradeoffs expressed by U). Gives some introduction to decision analysis (certainty equivalent, risk aversion, …) to aid in understanding the functional forms employed for U and methods of solution, rendering the paper more self‐contained.

Automated Guided Vehicles (AGVs) have the flexibility to meet the material handling requirements of asynchronous assembly lines. Furthermore, AGVs can select from among alternative paths in accordance with a prescribed lane selection rule, thereby facilitating the use of parallel server workstations. In this paper, motivated by our work in the automotive industry, several new lane selection rules are proposed. One of these, First Available Server/First Available Buffer/Balanced Work Content (FAS/FAB/BWC), is compared to two existing rules: Alternating Server, and First Available Server/First Available Buffer/Expected Completion Time (FAS/FAB/EC). Three performance measures — job throughput, workload balance among servers, and alteration of input job sequence — are employed. A SIMAN simulation model of a small, asynchronous parallel assembly line is used to study the impact on system performance of both the lane selection rule and the number of parallel servers. Interaction between these two factors is studied through ANOVA. A number of interesting findings are reported for results of the lane selection rules with respect to the three performance measures. Their interpretation is used to motivate further research.

A basic issue in the planning of urban public transport is the determination of headways or inter-dispatch times. During each season, i.e. distinct time-period whose demand characteristics are constant, the following tradeoff must be considered. Dispatching too many vehicles on a route causes high operating costs, while too few vehicles may result in unsatisfactory levels of service. An appropriate policy on headways will help to balance resources between lines (routes) in peak-demand hours and will influence the total number of buses acquired by a transit company. Previous practice in industry usually bases the planning of headways upon satisfying service criteria on a “most-congested segment”. This approach reduces the problem from that of studying a route to that of a single segment (stop), but thereby fails to account for other important information about the line's characteristics. In this article, we develop two new service criteria which consider the line as a whole: (1) “crowding-over-distance” takes into account discomfort resulting from a vehicle carrying too many passengers, and the corresponding distance travelled; and (2) “probability-of-failure”, the frequency with which a waiting passenger fails to board due to lack of space. COD will be analyzed using simulation. POF will be related to a time-dependent Markov chain that is “inhomogeneous” in terms of distance along the route. Optimal headways are those which dispatch the smallest number of buses while meeting the particular service criterion. Models based on each of the two criteria are illustrated and applied to a number of routes of the Israeli transit company, DAN.

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 firm's 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 firm's private fleet compared to the freight charges of a public trucking company.

This article aims to classify and critique the research and applications that have been conducted concerning supply chain management and logistics in Latin America. We assess the countries in Central and South America according to their capabilities in transportation infrastructure and various demographic and economic characteristics. A third objective is to identify additional research opportunities.

A retailer or distributor of finished goods, or the manager of a spare-parts inventory system, must generally forecast the major portion of demand. A specific customer-service level p (fraction of replenishment intervals with no stockout) implies two challenges: achieve the service within a small interval plus or minus, and do so with a minimum-cost investment in inventory. The pth fractile of lead-time demand (LTD) is the reorder point (ROP) for this service measure, and is often approximated by that fractile of a normal distribution. With this procedure, it is easy to set safety stocks for an (s, Q) inventory system. However, Bookbinder and Lordahl [2] and others have identified cases where the normal approximation yields excessive costs and/or lower service than desired. This article employs an order-statistic approach. Using available LTD data, the ROP is simply estimated from one or two of the larger values in the sample. This approach is sufficiently automatic and intuitive for routine implementation in industry, yet is distribution free. The order-statistic method requires only a small amount of LTD data, and makes no assumptions on the form of the underlying LTD distribution, nor even its parameters μ and ρ. We compare the order-statistic approach and the normal approximation, first in terms of customer service and then using a model of expected annual cost. Based upon characteristics of the available LTD data, we suggest a procedure to aid a practitioner in choosine between the normal and order-statistic method. © 1994 John Wiley & Sons, Inc.