An integrated system solution for supply chain optimization in the chemical process industry

This paper considers a complex scheduling problem in the chemical process industry involving batch production. The application described comprises a network of production plants with interdependent production schedules, multi-stage production at multi-purpose facilities, and chain production. The paper addresses three distinct aspects: (i) a scheduling solution obtained from a genetic algorithm based optimizer, (ii) a mechanism for collaborative planning among the involved plants, and (iii) a tool for manual updates and schedule changes. The tailor made optimization algorithm simultaneously considers alternative production paths and facility selection as well as product and resource specific parameters such as batch sizes, and setup and cleanup times. The collaborative planning concept allows all the plants to work simultaneously as partners in a supply chain resulting in higher transparency, greater flexibility, and reduced response time as a whole. The user interface supports monitoring production schedules graphically and provides custom-built utilities for manual changes to the production schedule, investigation of various what-if scenarios, and marketing queries. RID="*" ID="*" The authors would like to thank Hans-Otto Günther and Roland Heilmann for helpful comments on draft versions of this paper.     

Set-up and production planning in hybrid manufacturing–remanufacturing systems with large returns

Hybrid systems that use both raw materials and returned products in the production process are considered. The system contains one facility, and undergoes set-ups each time it switches between two production modes. In particular, we address systems engaged mainly in remanufacturing and having a large percentage of return. This situation is encountered in companies with mature remanufacturing channels. The targeted application area is comprised of hybrid systems that uses leasing as a business model with manufacturing serving to attenuate return uncertainty. To evaluate the system performance, we take into account manufacturing and remanufacturing costs, holding costs in serviceable and return inventories, backlog and set-up costs. Our analysis of hybrid systems with high return levels reveals features that are peculiar to such systems and that differentiate them from systems with lower return rates. We first present analytical solutions for optimal production and set-up schedule, and determine the possible cycle shapes for reliable systems. Optimal policies contain intervals of manufacturing and remanufacturing at maximal rate, and intervals of on-demand and on-return remanufacturing. Failure-prone systems are studied next, using the formalism of stochastic dynamic programming. Optimal policies give rise to the trajectories converging to the patterns similar to the analytically calculated cycles.     

The effect of supply and demand uncertainties on the optimal production and sales plans for new products

When introducing a new product, firms face a hierarchy of decisions at the strategic and operational levels including capacity sizing, time to market or starting sales, initial inventory required by the product’s release time and production management in response to changes in the demand (hereafter referred to as production-sales policies). The goal of this paper was to show the importance of considering both supply and demand uncertainties in the determination of the production-sales policy which has been overlooked in the existing literature. More specifically, we test two main hypotheses: (1) ignoring supply and demand uncertainties may lead to potentially incorrect decisions; and, (2) the decision could be different if risk is used as the primary performance measure instead of the commonly used expected (mean) profit. We perform extensive experimentation with a Monte Carlo simulation model of the stochastic supply-restricted new product diffusion and use different statistical procedures, namely, the Welch’s t-test and a nonparametric double-bootstrap method to compare the average and percentiles of the profit for different policies, respectively. The results indicate that the correctness of the two hypotheses depends on the diffusion speed, consumers’ backlogging behaviour, production capacity, price and variable production and inventory costs. The findings also have important implications for managers regarding market entry time, parameter estimation, production strategy and the implementation of the proposed model.     

A Stackelberg-Nash model for new product design

Existing conjoint approaches to optimal new product design have focused on the Nash equilibrium concept to model competitive reactions. Whereas these approaches have treated all competing firms equally as Nash players, one firm may have an advantage over its rivals, e.g., more pre-experience on competitors’ behavior and/or a first-mover advantage. This paper proposes a Stackelberg-Nash (leader-followers) model which can accomodate such information for decision making. The optimal product design problem is formulated from the perspective of a profit-maximizing new entrant (the leader) who wants to launch a brand onto an existing product market and acts with foresight by anticipating price-design reactions of the incumbent firms (the Nash followers). In the absence of closed-form solutions, we use a sequential iterative procedure to compute a Stackelberg-Nash equilibrium and to establish its uniqueness. The new conjoint model is illustrated under several competitive scenarios and price, design and profit implications are compared to a simple Nash equilibrium model. We find that a Stackelberg leader strategy may not only yield a much higher profit for the new entrant than a Nash strategy, but may also lead to strong profit asymmetries between competitors with still higher profits for the incumbent firms. In other words, the incumbent firms may also benefit strongly from a new entrant choosing a Stackelberg leader strategy.     

Optimal burn-in time and warranty length under fully renewing combination free replacement and pro-rata warranty

Warranty is an important factor of marketing products; however, warranty always involves additional costs to the seller and these costs usually depend on product reliability. Burn-in is considered as a part of the production process in which the manufactured products are operated under accelerated stresses for a short time period before their release and has been applied as a way for enhancing product reliability. In the present paper, a cost model is developed to determine the optimal burn-in time and warranty length for non-repairable products under the fully renewing combination free replacement and pro-rata warranty (FRW/PRW) policy. Denoting w as the warranty length of the product, under the FRW/PRW policy, the seller agrees to replace the product that fails prior to the time point w′, where w′<w, from the time of purchase with a new product at no cost to the buyer; meanwhile, any failure in the time interval from w′ to w results in a pro-rata replacement, i.e., any product is replaced with a new item at pro-rata cost to the buyer. Numerical examples are provided given that the failure time of the product follows either the mixed exponential distribution or the mixed Weibull distribution and four warranty policies are examined. Based on the results of analysis, it is noted that the fully renewing combination FRW/PRW is always better than the fully renewing policy in terms of cost.     

Tool replacement for production with a low fraction of defectives

In manufacturing industry, the tool replacement cost is, in many cases, a significant portion of the production cost. Early tool replacement increases the production cost. Overdue tool replacement, however, results in poor production quality. Accordingly, improving production quality while maintaining a low production cost is essential. The index C_pk is regarded as a yield-based index. For a fixed C_pk value, the production yield and fraction of defectives can be calculated. In this paper, we present an analytical approach using C_pk to determine the optimal tool replacement time. An accurate process capability must be calculated, particularly when the data contain assignable cause variation. Tool wear is a dominant and inseparable component in many machining processes (a systematic assignable cause), and ordinary capability measures become inaccurate because process data are contaminated by the assignable cause variation. Considering process capability changes dynamically, an estimator of C_pk is investigated. The closed form of the exact sampling distribution is derived. An effective tool management procedure for determining the optimal tool replacement time is presented for processes with a low fraction of defectives. For illustrative purposes, an application example involving tool wear is presented.     

Development of a product design and supply-chain fulfillment system for discontinuous innovation

Given the lengthy product development lifecycle process, high cost, and low success rate, many firms avoid considering discontinuous innovation strategies, in spite of their increase in frequency and importance in many markets. Even with advances in automation and technology, many of the techniques being utilised in product development are relatively unchanged, and the definition of discontinuous innovation itself lacks a structural component. To address this problem, the authors developed a methodology for generative customisation to implement discontinuous innovation. Using the emerging technologies of generative design and agent-based modelling, the authors developed a methodology to create product inventions and measure product innovations using a complex adaptive system (CAS) model. This appears to be the first model that represents a complex adaptive system environment to measure the success of discontinuous innovation in the development of a market equilibrium agent model.     

An investigation of multiproduct,multimachine production scheduling and inventory control of a flow-shop system

Unlike most of the previous studies of the multiproduct, multimachine systems, hero an attempt is made to consider the man-machine overtime and idleness costs together with the usual inventory-related costs (the set-up costs, carrying costs, and back-logging costs). The major assumptions of the model include: (a) demand for each product is captive and constant; (b) single or multiple facility work centres may be employed: (c) the total manufacturing operations of any single product must be completed before another product can be started; (d) all the manufacturing facilities are set up simultaneously for each of the products and its production can be started only after all the machines are ready. The annual total variable cost function is found to be very complex. Therefore, a recursive algorithm is required to solve this function for the values of optimal produetion-cycle-thnes of the individual products, T_j ^*,s . As the facilities are assumed to produce only one product at a time, these cycle time values need to be fitted into a production schedule so that there is no conflict between any two products on any of the machines and so that any modification in the values of T_j ^*,s result in the least increase of the system's total annual variable costs. Such total annual variable costs, computed with the help of this model and its alogrithm for 15 different situations, are compared with those provided by two other known models. Each time this model performs significantly better than the other two.     

Joint optimisation of production rate and preventive maintenance in machining systems

This paper studies an integrated control strategy of production and maintenance for a machining system which produces a single type of product to meet the constant demand. Different from previous research, we assume in this study that during the production, the production rate not only influences the life of cutting tool, but also the reliability of the machine. Both the replacement of cutting tool and the preventive maintenance (PM) of machine are considered in this paper. The machine is preventively maintained at the Nth tool replacement or correctively repaired at the machine failure, whichever occurs first. PM and corrective repair may cause shortage which can be reduced by controlling inventory. There are two decision variables p and N, where p denotes the production rate and N denotes the number of cutting tool replacement before the PM is performed. An integrated model is developed to simultaneously determine the optimal production rate and PM policy that minimise the total expected cost per unit item produced. Finally, an illustrative example and sensitivity analysis are given to demonstrate the proposed model.     

Two-critical-number control policy for a stochastic production inventory system with partial backlogging

This paper deals with a production–inventory control model with partial backlogging, in which a reflected Brownian motion governs the inventory level variation. We consider a single storage facility with infinite capacity and assume that shortages are allowed and the total amount of stock-out is a mixture of backordering and lost sales. In addition, the production facility is controlled by a two-parameter (m, M) policy, which switches the production rate when the inventory level reaches the threshold values. The aim is to determine the optimal control parameters m and M by minimising the long-run total expected cost of the system. Some results are illustrated using numerical examples. A sensitivity analysis of the optimal solution with respect to major parameters is also carried out.     

A CAPACITY PLANNING MODEL FOR A MULTI-PRODUCT FACILITY

A deterministic capacity planning model for a multi-product facility is analyzed to determine (he sizes to be expanded (or disposed of) in each period so as to supply the known demand for N products on time and to minimize the total cost incurred over a finite planning horizon of T periods. The model assumes that each capacity unit of the facility simultaneously serves a prespecified number of demand units of each product, that costs considered include capacity expansion costs, capacity disposal costs, and excess (idle) capacity holding costs, and all the associated cost functions are nondecreasing and concave, and that backlogging is not allowed. The structure of an optimal solution is characterized and then used in developing an efficient dynamic programming algorithm that finds optimal capacity planning policies. The required computational effort is a polynomial function of N and T.     

Strategic configuration of flexible electronics assembly facilities facing stochastic requirements

Flexible configuration of manufacturing facilities is a key strategy for efficiently improving market responsiveness and market share in the face of uncertain future product demand. Flexible facility configurations can produce an efficient production system that allows higher capacity utilization given uncertainty in product demand and mix. The aim of this paper is to consider the alternative choices of flexible equipment available at the strategic planning level and to make decisions about the facility design and configuration that best suits the specific needs of the manufacturing system under consideration. A chance constrained mixed integer programming model for strategic configuration and capacity planning of flexible multiple-stage production facilities under time-varying production requirements is introduced in this paper. It is an integrated model that determines the number of assembly lines required, the flexible automation levels required in each line, capacity levels, and product assignments/reassignments for a multiple-stage production system, considering the stochastic nature of the demand. A two-step heuristic based on genetic algorithms is proposed and tested. Experimental results indicate that the two-step heuristic performs well in terms of both computation speed and solution accuracy.     

On a branch-and-bound approach for a Huff-like Stackelberg location problem

Modelling the location decision of two competing firms that intend to build a new facility in a planar market can be done by a Huff-like Stackelberg location problem. In a Huff-like model, the market share captured by a firm is given by a gravity model determined by distance calculations to facilities. In a Stackelberg model, the leader is the firm that locates first and takes into account the actions of the competing chain (follower) locating a new facility after the leader. The follower problem is known to be a hard global optimisation problem. The leader problem is even harder, since the leader has to decide on location given the optimal action of the follower. So far, in literature only heuristic approaches have been tested to solve the leader problem. Our research question is to solve the leader problem rigorously in the sense of having a guarantee on the reached accuracy. To answer this question, we develop a branch-and-bound approach. Essentially, the bounding is based on the zero sum concept: what is gain for one chain is loss for the other. We also discuss several ways of creating bounds for the underlying (follower) sub-problems, and show their performance for numerical cases. This work has been supported by the Ministry of Education and Science of Spain through grant SEJ2005/06273/ECON. M. Elena Sáz was supported by a junior research grant of Mansholt Graduate School (Wageningen Universiteit).     

A combinatorial approach to a class of parallel-machine,continuous-time scheduling problems

The paper analyzes a manufacturing system with N non-identical, parallel machines continuously producing one product type in response to its demand. Inventory and backlog costs are incurred when tracking the demand results in inventory surpluses and shortages respectively. In addition, the production cost of a machine is incurred when the machine is not idle. The objective is to determine machine production rates so that the inventory, backlog, and production costs are minimized. For problems with demand defined as an arbitrary function of time, numerical methods are suggested to approximate an optimal solution. The complexity of the approximation methods is polynomial, while finding an exact optimal solution requires exponential time. In a case when production is to cope with a special form of a single-mode, K-level piece-wise constant demand, we prove, with the aid of the maximum principle, that the exact optimal solution can be found as a combination of analytical and combinatorial tools in O(KN ²( max {K,2N})²) time.     

Dynamic vs static pricing in a make-to-stock queue with partially controlled production

We consider a capacitated make-to-stock production system that offers a product to a market of price-sensitive users. The production process is partially controlled. On the one hand, the decision-maker controls the production of a single facility. On the other hand, an uncontrolled flow of items arrives at the stock. Such a situation occurs in several contexts; for example, when there is a return flow of products or a fixed delivery contract. We model the system as a make-to-stock queue with lost sales. We address the static pricing problem and the dynamic pricing problem with the objective of maximizing the average profit over an infinite horizon. For both problems, we characterize the optimal production and pricing policy. We also obtain analytical results for the static pricing problem. From numerical results, we show that dynamic pricing might be much more beneficial when the production is not totally controlled.      

Optimal self-scheduling and bidding strategy of a thermal unit subject to ramp constraints and price uncertainty

This study proposes methods for solving the optimal self-scheduling and bidding strategy of a thermal generating unit subject to ramp constraints and price uncertainty. In the first-half of the study, the authors propose a polynomial algorithm for deterministic self-scheduling for the generating company (GenCo) to optimally respond to day-ahead markets assuming market prices can be precisely forecasted. The authors then consider the GenCo bidding to real-time market in the second-half of the study. A multi-stage stochastic program is set up, where in the first stage the GenCo makes a decision as whether it should submit a bid or change an existing bid to the real-time market. In case that the GenCo participates in the first stage, the unit is dispatched by the market in the next stage. Then the process repeats. The authors propose a regressionbased method to approximate the recourse function and determine the optimal commitment and dispatch policy for the GenCo, which yields the optimal bidding strategy for the GenCo to participate the real-time spot market.     

A bivariate optimal replacement policy for a multistate repairable system

In this paper, a deteriorating simple repairable system with k+1 states, including k failure states and one working state, is studied. It is assumed that the system after repair is not “as good as new” and the deterioration of the system is stochastic. We consider a bivariate replacement policy, denoted by (T,N), in which the system is replaced when its working age has reached T or the number of failures it has experienced has reached N, whichever occurs first. The objective is to determine the optimal replacement policy (T,N)^* such that the long-run expected profit per unit time is maximized. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. We prove that the optimal policy (T,N)^* is better than the optimal policy N^* for a multistate simple repairable system. We also show that a general monotone process model for a multistate simple repairable system is equivalent to a geometric process model for a two-state simple repairable system in the sense that they have the same structure for the long-run expected profit (or cost) per unit time and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results.     

Financial and product market integration: Responses of Japanese firms

Abstract and Key Results

Optimal production plan for a multi-products manufacturing system with production rate dependent failure rate

This study deals with the problem of dependence between production and failure rates in the context of a multi-product manufacturing system. It provides an answer about how to produce (i.e. the production rates) and what to produce (i.e. which product) over a finite horizon of H periods of equal length. We consider a single randomly failing and repairable manufacturing system producing two products P_a and P_b . The product P_a is produced to supply the strategic demand d(k) of the principal customer via a buffer stock S over k periods (k?=?1,?2,?…?,?H). The second product P_b is produced to meet a secondary but very profitable demand. It is produced during a given interval at the end of each period k. We develop a genetic algorithm to determine simultaneously the optimal production rate of the first product during each period k and the optimal duration of the production interval of the second product, maximising the total expected profit.     

Fuzzy approach to the robust facility layout in uncertain production environments

The proposed method approaches the problem of the optimal facility layout using fuzzy theory. The optimal layout is a robust layout that minimizes the total material handling cost, when the product market demands are uncertain variables, which are defined as fuzzy numbers. Since each department has a limited production capacity, not all possible combinations, deriving from each product's market demand, are taken into account because some combination could exceed the overall department's productivity. Therefore, the optimal solution results by solving a 'constrained' fuzzy optimization problem, in which the fuzzy material handling costs corresponding to the layouts are evaluated, and a ranking method, which considers the grade of pessimism of the decision maker, is established to determine the optimal layout.