Operational planning models for distribution networks

The design and optimisation of a logistic network deals with a wide set of decisions, e.g. the determination of the best location and capacity of the different logistic facilities (production plants, distribution centres, transit points, wholesalers, etc.), the allocation of the product demand coming from customers in presence (or absence) of fractionable flows of material, the determination of the best transportation mode (truck, rail, etc.) as well as loading and routing of vehicles. These decisions involve multiple stages of a distribution network: customers-regional distribution centres (RDC), RDCs-central distribution centres (CDC) and CDCs-production plants and sources, in presence of multiple products and the variable time (i.e. time-dependent product demand and flows of material). This paper presents a top-down methodology that joins the strategic planning, the tactical planning and the operational planning of distribution networks with a special focus on the development of effective heuristic methods to face the vehicle routing problem. Original models and heuristic algorithms for the operational planning are illustrated. The impact of the strategic and tactical decisions on the performance of the operational planning is evaluated by the application of the proposed hierarchical approach to two realistic case studies. Obtained results are illustrated in a what-if experimental analysis conducted on multiple problem settings and realistic scenarios.     

Travel distance estimation and storage zone optimization in a 2-block class-based storage strategy warehouse

Order picking has been considered as the most critical operation in warehousing. Recent trends in logistics demand faster but more reliable order picking systems. The efficiency of an order picking process greatly depends on the storage policy used, i.e. where products are located within the warehouse. In this paper, we deal with the most popular storage policy that is class-based (or ABC) storage strategy. Particularly, we investigate the problem of determining the optimal storage boundaries (zones) of classes in each aisle for manually operated warehouses.

We first propose a probabilistic model that enables us to estimate the average travel distance of a picking tour. We found that the differences between results obtained from simulation and the model were slight. Using the average travel distance as the objective function, we present a mathematical formulation for the storage zone optimization problem. However, the exact approach can handle only small size warehouse instances. To circumvent this obstacle, we propose a heuristic for the problem. Numerical examples we conducted show that the heuristic performs very well in all the cases.     

Multi-commodity warehouse location and distribution planning with inventory consideration

We consider the problem of designing a distribution network for a logistics provider that acquires products from multiple facilities and then delivers those products to many retail outlets. Potential locations for consolidation facilities that combine shipments for cost reduction and service improvements are considered. The problem is formulated with direct shipment and consolidation opportunities. A novel mathematical model is derived to solve a complex facility location problem determining: (i) the location and capacity level of warehouses to open; (ii) the distribution route from each production facility to each retailer outlet; and (iii) the quantity of products stocked at each warehouse and retailer. A genetic algorithm and a specific problem heuristic are designed, tested and compared on several realistic scenarios.     

A heuristic for multi-item production with seasonal demand

A heuristic is developed for a common production/inventory problem characterized by multiple products, stochastic seasonal demand, lost sales, and a constraint on overall production. Heuristics are needed since the calculation of optimal policies is impractical for real-world instances of this problem. The proposed heuristic is compared with those in current use as well as optimal solutions under a variety of conditions. The proposed heuristic is both near optimal and superior to existing heuristics. The heuristic deviated from optimality by an average of 1.7% in testing using dynamic programming as a benchmark. This compares favorably against linear-programming-based heuristics and practitioner heuristics, which deviated from optimality by 4.5 to 10.6%.     

Particle swarm optimization for the multi-period cross-docking distribution problem with time windows

Cross-docking has emerged as a new technique in supply chain management to replace the warehouse concept in the retail industry. This paper proposes a multi-period cross-docking distribution problem that consists of manufacturers, cross-docks and customers. This model is formulated for cases that consider multiple products, consolidation of customer orders and time windows that are available in multiple periods. The objective function is to minimise the total cost, which includes transportation cost, inventory cost and penalty cost. The penalty cost arises when demand remains in each period that cannot be satisfied. To deal with the complexity of the problem, an algorithm is developed based on particle swarm optimisation (PSO) with multiple social learning terms, GLNPSO, with two solution representations. The solution representations are a one-period solution representation (OP-SR) and a multi-period solution representation (MP-SR). The GLNPSO-based algorithm performs well in solving this problem. Moreover, both representations are proven effective when comparing the solution quality and computational time with those results obtained from CPLEX. In terms of quality, the MP-SR solution is better than the OP-SR solution for both stable and fluctuating demand instances. However, MP-SR requires more computational effort than OP-SR.     

A Heuristic Programming Algorithm for Warehouse Location

A new heuristic programming method of solving a particular type of warehouse location problem is presented. The problem is to allocate K or less facilities to N possible locations so as to service M demand centers at minimum cost. The algorithm presented is suitable for hand calculation of medium-size problems (50 × 50) or when computerized will readily solve large-scale problems of the order of (600 × 600); i.e., 600 demand centers and 600 possible locations.     

Normative Models for Some Warehouse Sizing Problems

The problem examined is the determination of the optimum size for a warehouse used to store products over a finite planning horizon. Both fixed and changeable warehouse size problems are treated under conditions of deterministic and probabilistic storage demand. The latter is formulated as a linear programming problem and transformed via duality theory into an equivalent network flow problem for efficient solution. Costs considered are those due to warehouse construction, storage of products within the facility, and storage demand not satisfied by storage in the warehouse.     

The G-group heuristic to solve the multi-product,sequencing, lot sizing and scheduling problem in flow shops

This paper presents a new heuristic to solve the problem of making sequencing, lot sizing and scheduling decisions for a number of products manufactured in a flow shop environment, so as to minimize the sum of setup and inventory holding costs while a given demand is fulfilled without backlogging. The proposed solution method first determines sequencing decisions then lot sizing and scheduling decisions are simultaneously determined. This heuristic, called the G-group method, divides the set of products into G groups and requires that products belonging to the same group have the same cycle time. Also, the cycle time of each group is restricted to be an integer multiple of a basic period. For each basic period of the global cycle, the products to be produced during this period and the production sequence to be used are chosen. Then, a non-linear program is solved to determine lot sizes and to construct a feasible production schedule. To evaluate its performance, the G-group method was compared to four other methods. Numerical results show that the proposed heuristic outperforms all these methods.     

Strategic inventory deployment in the steel industry

Integrated Steel Manufacturers (ISMs) perform all of the steps necessary to convert iron ore into finished products. As a result they are characterized by high capital expenditures and long cycle times. The custom nature of finished products and significant demand uncertainty explains why ISMs typically produce to order. However, recent increased competition from low cost mini-mills is causing some ISMs to compete by serving the needs of higher-paying customers who want exotic products, and faster and reliable deliveries. Consequently, ISMs are exploring the option of satisfying a portion of their demand by converting strategically placed semi-finished inventory into finished products, which helps to reduce both the time between order receipt and order dispatch, and its variability. In this study we propose a two-stage stochastic integer programming model that can be used to choose the semi-finished products that should be made to stock, and their target inventory levels. Properties of this model are exploited to develop a fast heuristic applicable to large-scale instances of the problem encountered in industry. Numerical experiments are used to validate the heuristic, and examples based on data from a particular ISM are used to illustrate important managerial insights.     

Product recovery optimization in closed-loop supply chain to improve sustainability in manufacturing

When business practices shift from a traditional open supply chain to a closed loop instead, the environmental and societal issues are efficiently integrated in business development. However, even an efficiently integrated shift introduces a number of trade-offs due to the contradictory goals that emerge from that business’s economical, environmental and social dimensions. In this paper, we propose a multi-objective mixed integer mathematical problem for a generic closed-loop supply chain (CLSC) network to rationalise how a system’s product recovery helps to improve manufacturing sustainability. The CLSC network proposed in this study consists of a hybrid manufacturing facility, warehouse, distribution centres, collection centres and a hybrid recovery facility (HRF). The proposed model determines the best location for the HRF and optimal flow of products, recovered parts and material in the network while it simultaneously maximises profit, saves activity costs, helps to decrease the harmful effects of the manufacturing process and makes a positive impact on societal development. To validate the model, a numerical illustration with the help of a case study from an electrical manufacturing industry is offered. The results authenticate the approach of the model towards the fulfilment of various environmental regulations. A sensitivity analysis, completed on demand, and the return rate also assists decision-makers to manage their decisions with a broader insight towards manufacturing sustainability.     

A network prototype for integrated production-distribution planning with non-multi-functional plants

This paper proposes a two-echelon network prototype for integrated production and distribution planning where non-multi-functional plants supply multiple types of products with limited quantities to the customers via capacitated warehouses. Four variations of the prototype, formulated as individual mixed integer programming models, are solved using the branch and bound algorithms by numerical experiments to examine the cost implications of production-distribution strategies involving single-sourcing constraints on different levels of the supply chain. Further discussions on the practicality and versatility of the proposed prototype (i.e. its ability to consider different facility locations, specialised capabilities of individual plants, safety stock levels and demand characteristics) illustrate the usefulness of the prototype to industry practitioners when making strategic and/or tactical decisions.     

Service parts logistics: a benchmark analysis

This paper summarizes the results of a benchmark study focusing on after-sales service logistics systems for technologically complex high-value products, i.e., in the computer industry. Current industrial practices and trends in service logistics operations are reported on. Specific data on costs, revenues, service measures, control policies, and distribution strategies were collected and used to define best practice performance. Analysis methodologies to support cross-sectional comparisons and causal factors are discussed.     

Scheduling multistage hybrid flowshops with multiprocessor tasks by an effective heuristic

This study considers the scheduling problem of multistage hybrid flowshops with multiprocessor tasks, which is a core topic for numerous industrial applications. An effective and efficient heuristic, namely the heuristic of multistage hybrid flowshops (HMHF) is proposed to solve this problem. To verify the developed heuristic, computational experiments are conducted on a well-known benchmark problem set. The results are compared with 10 constructive heuristics and a tabu search (TS) based meta-heuristic from the relevant literature. These computational results show that the proposed HMHF heuristic is highly effective when compared to these algorithms for this problem on the same benchmark instances.     

Genetic algorithm optimisation of an integrated aggregate production–distribution plan in supply chains

A production plan concerns the allocation of resources of the company to meet the demand forecast over a certain planning horizon and a distribution plan involves the management of warehouse storage assignments, transport routings and inventory management issues. A production–distribution plan integrates the decisions in production, transport and warehousing as well as inventory management. The overall performance of a supply-chain is influenced significantly by the decisions taken in its production–distribution plan and hence one key issue in the performance evaluation of a supply chain is the modelling and optimisation of the production–distribution plan considering its actual complexity. Based on the integration of Aggregate Production Plan and Distribution Plan, this article develops a mixed integer non-linear formulation for a two-echelon supply network (i.e. a production-distribution network) considering the real-world variables and constraints. Genetic Algorithm (GA), known as a robust technique for solving complex problems, is employed for the optimisation of the developed mathematical model due to its ability to effectively deal with a large number of parameters. To demonstrate the applicability of the methodology, a real-life case study will be finally studied incorporating the production of different types of products in several manufacturing plants and the distribution of finished products from plants to a number of end-users via multiple direct/indirect transport routes.     

A genetic algorithm for dynamic inbound ordering and outbound dispatching problem with delivery time windows

This article considers an inbound ordering and outbound dispatching problem for a single product in a third-party warehouse, where the demands are dynamic over a discrete and finite time horizon, and moreover, each demand has a time window in which it must be satisfied. Replenishing orders are shipped in containers and the freight cost is proportional to the number of containers used. The problem is classified into two cases, i.e. non-split demand case and split demand case, and a mathematical model for each case is presented. An in-depth analysis of the models shows that they are very complicated and difficult to find optimal solutions as the problem size becomes large. Therefore, genetic algorithm (GA) based heuristic approaches are designed to solve the problems in a reasonable time. To validate and evaluate the algorithms, finally, some computational experiments are conducted.     

Periodic product distribution from multi-depots under limited supplies

Physical distribution is one of the key functions in logistics systems, involving the flow of products from manufacturing plants or distribution centers through the transportation network to consumers. It is a very costly function, especially for the distribution industries. While maintaining the desired customer service levels, an effort is made in this paper to improve distribution strategies and reduce the distribution cost for the multi-product, multi-depot periodic distribution problem. In industry practice, depots typically operate independently and solely within their own territories. However, it may be beneficial to allow those depots to operate interdependently, particularly when the product supplies are limited at some depots. In such cases, the distributors may satisfy customers' requests by delivering products from other depots that hold more supplies. In particular, the impact of interdependent operations among depots, which has not previously been addressed in the context of industrial applications, is investigated in this research. A mixed-integer linear programming model is formulated to represent the multi-product, multi-depot periodic distribution problem. Three tabu search heuristics with different long-term memory applications are developed to solve the problem. The performance of the heuristics is evaluated by comparing the solutions obtained with the optimal solutions or lower bounds from the regular branch-and-bound method as well as a fast technique to find a lower bound that is developed in this research. The heuristics provide optimal/good quality solutions in a much shorter time. A randomized complete block design is applied to test the performance of the heuristics on various problem structures. The experimental results show that the tabu search heuristic that incorporates the use of a long-term memory in the diversification process outperforms the other heuristics. The heuristic is further applied to investigate the impact of interdependent operations among depots. The results reveal that interdependent operations among depots provide significant savings in costs over independent operations among depots, especially for large-size problems.     

On the optimal lot-sizing and scheduling problem in serial-type supply chain system using a time-varying lot-sizing policy

In this paper, we solve the optimal sequencing, lot-sizing and scheduling decisions for several products manufactured through several firms in a serial-type supply chain so as to minimise the sum of setup and inventory holding costs while meeting given demand from customers. We propose a three-phase heuristic to solve this NP-hard problem using a time-varying lot- sizing approach. First, based on the theoretical results, we obtain candidate sets of the production frequencies and cycle time using a junction-point heuristic. Next, we determine the production sequences for each firm using a bin-packing method. Finally, we obtain the production times of the products for each firm in the supply chain system by iteratively solving a set of linear simultaneous equations which were derived from the constraints. Then, we choose the best solution among the candidate solutions. Based on the numerical experiments, we show that the proposed three-phase heuristic efficiently obtains feasible solutions with excellent quality which is much better than the upper-bound solutions from the common cycle approach.     

A cutting plane approach for the single-product assembly system design problem

This paper evaluates a new branch-and-cut approach, establishing a computational benchmark for the single-product, assembly system design (SPASD) problem. Our approach, which includes a heuristic, preprocessing, and two cutgenerating methods, outperformed OSL in solving a set of 102 instances of the SPASD problem. The approach is robust; test problems show that it can be applied to variations of the generic SPASD problem that we encountered in industry.     

Bicriteria sequencing for just-in-time mixed-model assembly lines

Under a Just-In-Time (JIT) pull system the sequencing of products requires the satisfaction of two main goals: (1) keeping a constant rate of usage of parts, and (2) smoothing the workload at work stations to avoid line stoppages. By using a practical observation related to JIT delivery systems we propose a two-step approach, where in the first step we consider only goal (1) by applying a benchmark heuristic. In the second step we focus on goal (2), by investigating the effectiveness of a spacing-constraint based approach, commonly used in the automotive industry, in comparison with a more general time-based one. We designed and conducted a simulation experiment based on the practical situation of final assembly lines and we found that the benchmark heuristic represents an appropriate choice for step one (based on a new performance measure that represents a lower bound on variation in parts utilization). For the second step, related to workload smoothing, the spacing-constraint based method presents better achievement than the time-based one.     

An improved version of the production switching heuristic for the aggregate production planning problem

The production switching heuristic (PSH) is recognized as an effective solution method for the aggregate production planning problem in industries where production is limited to discrete levels. However, we find that the PSH is not sufficiently responsive to demand fluctuation and tends to make belated decisions. This shortcoming stems mainly from the switching mechanism. This paper proposes an improved version of the PSH. The heuristic uses an improved switching mechanism which can be shown to dominate the PSH. The effectiveness of the proposed heuristic is investigated with several well known problems including the paint factory problem. The results are compared with those of the linear decision rule and the linear programming model as well as the PSH.