A web-based methodology for product design evaluation and optimisation

The authors have developed a methodology that takes advantages of the World Wide Web to analyse and develop optimal new product designs. This paper describes the methodology and illustrates its application to a case study involving the design of an actual Web site where music CDs are sold. The proposed methodology has the following features: (a) it is based on a design inspired by conjoint analysis; (b) it involves unobtrusive electronic measurement of the actual behavior of Web users who remain undisturbed by experimental factors; and (c) it utilises an integer programming approach to seek optimal Web site configurations. The methodology uses limited dependent variable methods to develop response models that provide the basis for the development of objective functions for an optimisation model. The optimisation model can consider either single or multiple objective functions by using a Pareto optimum approach.     

A joint optimisation model for inventory replenishment,product assortment,shelf space and display area allocation decisions

In this paper, we propose an optimisation model to determine the product assortment, inventory replenishment, display area and shelf space allocation decisions that jointly maximize the retailer’s profit under shelf space and backroom storage constraints. The variety of products to be displayed in the retail store, their display locations within the store, their ordering quantities, and the allocated shelf space in each display area are considered as decision variables to be determined by the proposed integrated model. In the model formulation, we include the inventory investment costs, which are proportional to the average inventory, and storage and display costs as components of the inventory costs and make a clear distinction between showroom and backroom inventories. We also consider the effect of the display area location on the item demand. The developed model is a mixed integer non-linear program that we solved using LINGO software. Numerical examples are used to illustrate the developed model.     

Consolidation of customer orders into truckloads at a large manufacturer

We describe the development and operation of an interactive system based on a mathematical optimisation model which is used by a major US manufacturer to consolidate customer orders into truckloads. Dozens of users employ the system daily for planning delivery of orders from manufacturing plants to customers by truckload carriers, saving numerous hours of the users' time and reducing transportation costs.     

An Integrated Inventory Model for a Single Product System

In this paper, an inventory model is given which unifies the inventory problem of raw materials and the finished product for a single product manufacturing system. The product is manufactured in batches and the raw materials are obtained from outside suppliers. The objective is to minimize the total variable costs of the system.     

Cost-oriented assembly line balancing: Model formulations,solution difficulty,upper and lower bounds

This paper deals with cost-oriented assembly line balancing. First we focus on the special objective function and a formal problem statement. Then we concentrate on general model formulations that can be solved by standard optimisation tools and introduce several improvements to existent models. These models are designed for either general branch-and-bound techniques with LP-relaxation or general implicit enumeration techniques. Further we discuss the solution difficulty of the problem and show that the “maximally-loaded-station-rule” has to be replaced by the “two-stations-rule”. Compared to the time-oriented version, this causes an enormous increase in solution difficulty. We introduce improved and new bounds for the number of stations and for the relevant costs per product unit. These are used in the general model formulations as well as in specially designed optimisation methods. Finally we give a brief overview of these specially designed methods that are discussed in detail in Amen (2000a,b, 2001).     

Coordinated control of distribution supply chains in the presence of fuzzy customer demand

This paper considers a single product inventory control in a Distribution Supply Chain (DSC). The DSC operates in the presence of uncertainty in customer demands. The demands are described by imprecise linguistic expressions that are modelled by discrete fuzzy sets. Inventories at each facility within the DSC are replenished by applying periodic review policies with optimal order up-to-quantities. Fuzzy customer demands imply fuzziness in inventory positions at the end of review intervals and in incurred relevant costs per unit time interval. The determination of the minimum of defuzzified total cost of the DSC is a complex problem which is solved by applying decomposition; the original problem is decomposed into a number of simpler independent optimisation subproblems, where each retailer and the warehouse determine their optimum periodic reviews and order up-to-quantities. An iterative coordination mechanism is proposed for changing the review periods and order up-to-quantities for each retailer and the warehouse in such a way that all parties within the DSC are satisfied with respect to total incurred costs per unit time interval. Coordination is performed by introducing fuzzy constraints on review periods and fuzzy tolerances on retailers and warehouse costs in local optimisation subproblems.     

Optimisation of integrated reverse logistics networks with different product recovery routes

The awareness of importance of product recovery has grown swiftly in the past few decades. This paper focuses on a problem of inventory control and production planning optimisation of a generic type of an integrated Reverse Logistics (RL) network which consists of a traditional forward production route, two alternative recovery routes, including repair and remanufacturing and a disposal route. It is assumed that demand and return quantities are uncertain. A quality level is assigned to each of the returned products. Due to uncertainty in the return quantity, quantity of returned products of a certain quality level is uncertain too. The uncertainties are modelled using fuzzy trapezoidal numbers. Quality thresholds are used to segregate the returned products into repair, remanufacturing or disposal routes. A two phase fuzzy mixed integer optimisation algorithm is developed to provide a solution to the inventory control and production planning problem. In Phase 1, uncertainties in quantity of product returns and quality of returns are considered to calculate the quantities to be sent to different recovery routes. These outputs are inputs into Phase 2 which generates decisions on component procurement, production, repair and disassembly. Finally, numerical experiments and sensitivity analysis are carried out to better understand the effects of quality of returns and RL network parameters on the network performance. These parameters include quantity of returned products, unit repair costs, unit production cost, setup costs and unit disposal cost.     

A Profit-maximizing Plant-loading Model with Demand Fill-rate Constraints

This paper discusses a new formulation of a class of plant product-mix loading problems which are characterized by capacitated production facilities, demand fill-rate requirements, fixed facility costs, concave variable production costs and an integrated network structure which encompasses inbound supply and outbound distribution flows. In particular, we are interested in assigning product lines and volumes to a set of capacitated plants under the demand fill-rate constraints. Fixed costs are incurred when a product line is assigned to a plant. The variable production-cost function also exhibits concavity with respect to each product-line volume. Thus both scale economies and plant focus effect are considered explicitly in the model. The model also can be used to determine which market to serve in order to best allocate the firm's resources. The problem formulation leads to a concave mixed-integer mathematical programme. Given the state of the art of non-linear programming techniques, it is often not possible to find global optima for reasonably sized problems. We develop an optimization algorithm within the framework of Benders' decomposition for the case of a piecewise linear concave cost function. Our algorithm generates optimal solutions efficiently.     

Optimal process control policies under a time-varying cost structure

Quality experts have recognized two types of quality costs resulting from failure of control; namely, internal and external failure costs of control. Explicitly considering the difference between internal and external failure costs in designing statistical process control procedures is especially important in today’s business environment because (1) inventory holding time is strategically kept very short because of the just-in-time philosophy, and (2) product values decrease at a very fast rate over time because of advances in technology and keen competition. In this paper, we develop a process control model under a time-varying cost structure, based on internal and external failure costs. Using the model, we also study the process control policies when the value of the product may decrease over time. We consider two forms of product perishability. The first is an exponential product value drop, and the second is a fixed life product life.     

The effect of lifetime buys on warranty repair operations

Lifetime buys are a common practice in the electronics and telecommunication industries. Under this practice, manufacturers procure their repair parts inventory in one order to support the spare part needs of a product for the duration of its warranty repair period. In this paper, we consider a repair operation in which defective items under warranty are returned to a manufacturer who either repairs these items using its spare parts inventory or replaces each defective unit with a new product. We show how fixed repair capability costs, variable repair costs, inventory holding costs, and replacement costs affect a firm's optimal repair and replacement decisions. The model is used to gain insights for products from a major mobile device manufacturer in the United States.     

A Lagrangian relaxation approach to multi-period inventory/distribution planning

We consider a multi-period inventory/distribution planning problem (MPIDP) in a one-warehouse multiretailer distribution system where a fleet of heterogeneous vehicles delivers products from a warehouse to several retailers. The objective of the MPIDP is to minimise transportation costs for product delivery and inventory holding costs at retailers over the planning horizon. In this research, the problem is formulated as a mixed integer linear programme and solved by a Lagrangian relaxation approach. A subgradient optimisation method is employed to obtain lower bounds. We develop a Lagrangian heuristic algorithm to find a good feasible solution of the MPIDP. Computational experiments on randomly generated test problems showed that the suggested algorithm gave relatively good solutions in a reasonable amount of computation time.     

Operations research games: A survey

This paper surveys the research area of cooperative games associated with several types of operations research problems in which various decision makers (players) are involved. Cooperating players not only face a joint optimisation problem in trying, e.g., to minimise total joint costs, but also face an additional allocation problem in how to distribute these joint costs back to the individual players. This interplay between optimisation and allocation is the main subject of the area of operations research games. It is surveyed on the basis of a distinction between the nature of the underlying optimisation problem: connection, routing, scheduling, production and inventory.     

An efficient model formulation for level of repair analysis

Given a product design and a repair network, a level of repair analysis (lora) determines for each component in the product (1) whether it should be discarded or repaired upon failure and (2) at which echelon in the repair network to do this. The objective of the lora is to minimize the total (variable and fixed) costs. We propose an ip model that generalizes the existing models, based on cases that we have seen in practice. Analysis of our model reveals that the integrality constraints on a large number of binary variables can be relaxed without yielding a fractional solution. As a result, we are able to solve problem instances of a realistic size in a couple of seconds on average. Furthermore, we suggest some improvements to the lora analysis in the current literature.     

The use of optimisation for enhancing the development of a novel sustainable masonry unit

This paper examines whether it is possible to utilise optimisation techniques to enhance the efficiency of the experiment-based development of a new product. Conventionally, a laboratory-based experimental investigation requires to check all combinations of all independent parameters describing the product; hence the optimum levels of the tested parameters is obtained. As a result there may be many thousands of samples produced to optimise these parameters; this is a time consuming, costly and laborious process. Instead, it is suggested that an empirical model is established and validated using the results of the laboratory investigation making it suitable for optimisation.     

Capacity decisions for high-tech products with obsolescence

Modern high-tech products experience rapid obsolescence. Capacity investments must be recouped during the brief product lifecycle, during which prices fall continuously. We employ a multiplicative demand model that incorporates price declines due to both market heterogeneity and product obsolescence, and study a monopolistic firm’s capacity decision. We investigate profit concavity, and characterize the structure of the optimal capacity solution. Moreover, for products with negligible variable costs, we identify two distinct strategies for capacity choice demarcated by an obsolescence rate threshold that relates both to market factors and capacity costs. Finally, we empirically test the demand model by analyzing shipping and pricing data from the PC microprocessor market.     

An Investigation of Feedstuffs for Dairy Cattle on Liverton Farm

This paper is based on the winning entry in the Operational Research Competition for Schools 1979. It examines the winter feed costs for dairy cattle on a Devon farm. The present feed is investigated using computer assisted optimisation techniques. The paper then examines whether silage should be introduced; the possible savings and necessary capital costs are calculated. In conclusion it proposes that the present feed be reduced and silage introduced as the main constituent, giving an initial annual saving of £13,000. The proposals are being seriously considered by the farmer and may be implemented in the near future.     

A theoretical justification of the set covering greedy heuristic of Caprara et al.

Large scale set covering problems have often been approached by constructive greedy heuristics, and much research has been devoted to the design and evaluation of various greedy criteria for such heuristics. A criterion proposed by Caprara et al. (1999) is based on reduced costs with respect to the yet unfulfilled constraints, and the resulting greedy heuristic is reported to be superior to those based on original costs or ordinary reduced costs.We give a theoretical justification of the greedy criterion proposed by Caprara et al. by deriving it from a global optimality condition for general non-convex optimisation problems. It is shown that this criterion is in fact greedy with respect to incremental contributions to a quantity which at termination coincides with the deviation between a Lagrangian dual bound and the objective value of the feasible solution found.     

Modelling and optimisation for sustainable development policy assessment

Earlier work on sustainable development devised a policy assessment tool that was based on a static optimisation formulation. Key ingredients in sustainable development problems are the presence of random effects and the conflict between different objectives. To accommodate these, the earlier formulation was strongly stochastic and was posed in a multi-objective framework. The purpose of this paper is to consider the extension of the work to a formulation that deploys dynamic optimisation. In particular it is the aim here to use simulations based on a large scale model to derive dynamic rather than static representations, to integrate these into the optimisation scheme and to assess the benefits.     

A hybrid simulated annealing for solving an extended model of dynamic cellular manufacturing system

This paper develops a mixed-integer programming model to design the cellular manufacturing systems (CMSs) under dynamic environment. In dynamic environment, the product mix and part demand change under a multi-period planning horizon. Thus, the best designed cells for one period may not be efficient for subsequent periods and reconfiguration of cells is required. Reconfiguration may involve adding, removing or relocating machines; it may also involve a change in processing rout of part types from a period to another. The advantages of the proposed model are as follows: considering the batch inter/intra-cell material handling by assuming the sequence of operations, considering alternative process plans for part types, and considering machine replication. The main constraints are maximal cell size and machine time-capacity. The objective is to minimize the sum of the machine constant and variable costs, inter- and intra-cell material handling, and reconfiguration costs. An efficient hybrid meta-heuristic based on mean field annealing (MFA) and simulated annealing (SA) so-called MFA–SA is used to solve the proposed model. In this case, MFA technique is applied to generate a good initial solution for SA. The obtained results show that the quality of the solutions obtained by MFA–SA is better than classical SA, especially for large-sized problems.     

The capacitated distribution and waste disposal problem

We study the problem of the simultaneous design of a distribution network with plants and waste disposal units, and the coordination of product flows and waste flows within this network. The objective is to minimize the sum of fixed costs for opening plants and waste disposal units, and variable costs related to product and waste flows. The problem is complicated by (i) capacity constraints on plants and waste disposal units, (ii) service requirements (i.e. production must cover total demand) and (iii) waste, arising from production, to be disposed of at waste disposal units. We discuss alternative mathematical model formulations for the two-level distribution and waste disposal problem with capacity constraints. Lower bounding and upper bounding procedures are analyzed. The bounds are shown to be quite effective when embedded in a standard branch and bound algorithm. Finally, the results of a computational study are reported.