Optimal preventive maintenance in a production inventory system

We consider a production inventory system that produces a single product type, and inventory is maintained according to an (S, s) policy. Exogenous demand for the product arrives according to a random process. Unsatisfied demands are not back ordered. Such a make-to-stock production inventory policy is found very commonly in discrete part manufacturing industry, e.g., automotive spare parts manufacturing. It is assumed that the demand arrival process is Poisson. Also, the unit production time, the time between failures, and the repair and maintenance times are assumed to have general probability distributions. We conjecture that, for any such system, the down time due to failures can be reduced through preventive maintenance resulting in possible increase in the system performance. We develop a mathematical model of the system, and derive expressions for several performance measures. One such measure (cost benefit) is used as the basis for optimal determination of the maintenance parameters. The model application is explained via detailed study of 21 variants of a numerical example problem. The optimal maintenance policies (obtained using a numerical search technique) vary widely depending on the problem parameters. Plots of the cost benefit versus the system characteristic parameters (such as, demand arrival rate, failure rate, production rate, etc.) reveal the parameter sensitivities. The results show that the actual values of the failure and maintenance costs, and their ratio are significant in determining the sensitivities of the system parameters.     

Hierarchical production control for a flow shop with dynamic setup changes and random machine breakdowns

In this paper, we study a manufacturing system consisting of two machines separated by two intermediate buffers, and capable of producing two different products. Each product requires a constant processing time on each of the machines. Each machine requires a constant non-negligible setup change time from one product to the other. The demand rate for each product is considered to be piecewise constant. Each machine undergoes failure and repair. The time-to-failure and time-to-repair are exponentially distributed random variables. The setup change and processing operations are resumable. We model our system as a continuous time, continuous flow process. An optimal control problem is formulated for the system to minimize the total expected discounted cost over an infinite horizon. To determine the optimal control policy structure, a discrete version of the problem is solved numerically using a dynamic programming formulation with a piecewise linear penalty function. A real-time control algorithm is then developed with the objective of maintaining low work-in-process inventory and keeping the production close to the demand. The algorithm uses a hierarchical control structure to generate the loading times for each product on each machine in real time and to respond to random disruptions in the system. The system is simulated using this algorithm to study its performance. The performance of the algorithm is also compared to alternative policies.     

Scheduling policies,batch sizes,and manufacturing lead times

In this paper we examine the impact of scheduling policies on batch sizing decisions in a multi-item production system. We also investigate the joint effect of scheduling policies and batch sizing decisions on production lead times. In particular we compare the performance of a first-come-first-served (FCFS) policy with that of a group scheduling (GS) policy and study the effect of each on the optimal batch size. We show that a GS policy can lead to significant performance gains, as measured by reduced lead times and higher production rates, relative to the FCFS policy, and characterize conditions under which these gains are realized. We also study the impact of the GS policy on other system operating parameters. In particular we find that using a GS policy eliminates the need for batching, preserves system capacity despite the presence of setups, and accommodates higher product mix variety. These results are shown to be very different from those obtained for the FCFS policy and to have important implications for the management and control of multi-item production facilities.     

Yield management with downward substitution and uncertainty demand in semiconductor manufacturing

Motivated by the high yield variability in the semiconductor industry where the quality of the end products is uncertain and is graded into one of several quality levels according to performance before being shipped. We consider a dynamic multi-period yield management problem of a two-stage make-to-stock system faced by a semiconductor manufacturing firm. In the first stage, the firm invests in raw material before any actual demand is known, and produces multiple types of products with random yield rates because of the presence of randomness in the process. In the second stage, products are classified into different classes by quality, and allocated in a number of sequential periods. Demand is also random and can be classified into multiple classes corresponding to product levels. Demands can be upgraded when one type of product has been depleted. This paper presents a multi-period, multi-product, downward substitution model to determine the optimal production input and allocation of the different products to satisfy demands. The production and allocation problem is modelled as a stochastic dynamic program in which the objective is to maximise the profit of the firm. We show that the simple one step upgrade substitution policy is optimal, and the objective function is concave in production input. An iterative algorithm is designed to find the optimal production input and numerical experiments are used to illustrate its effectiveness.     

POLICY ITERATION DYNAMIC PROGRAMMING APPLIED TO RESERVOIRS CONTROL

The paper is concerned with methods for operating reservoir systems in an optimal fashion. Although the value iteration technique is computationally good in determining a minimum total operating cost it can be difficult to isolate the associated optimal policy. When the optimal policy is under specific consideration it is sometimes useful to use a policy iteration technique despite its poorer computational performance. This paper demonstrates how a policy iteration technique can be applied to the reservoir operation problem. An example of a two-reservoir system is presented which contrasts the value-and policy-iteration techniques and demonstrates the advantages and disadvantages of each.     

Base-stock control for single-product tandem make-to-stock systems

In this paper, we consider a multiple-stage tandem production/inventory system producing a single product. Processing time at each stage is assumed to have a general stationary processing time distribution. The cost of holding work-in-process (WIP) inventory is different at each stage. Therefore, decisions on when to release work to the system as well as when to transfer WIP from one stage to another need to be made. We formulate this problem of release/production control as a Markov decision process. However, the optimal policy is rather complex, making its implementation impracticable in practice. We therefore investigate the performance of simple base stock policies. Our approach aggregates several stages into one and uses a simple approximation to compute 'approximately optimal' base stock levels. We present the results of a simulation study that tests the performance of our approximation in estimating the best base stock levels, and the performance of base stock policies as compared with the optimal policy.     

A cyclic policy for the loading of multiple products on a vehicle with different compartment sizes

In this paper, we address a multi-product loading problem in which a vehicle (a truck or a ship) is used to transfer multiple products. The product demands are different but stationary over time. The vehicle consists of compartments of different sizes and each compartment can contain only one product type during each shipment. No shortages are permitted, and we assume that the inventory holding cost is significantly lower than the delivery cost. The objective is to minimize the setup rate, that is, the number of deliveries per time unit. A cyclic policy is shown to be optimal, and a heuristic algorithm is developed to determine the cycle length as well as the assignments of products to the compartments during each of the requisite number of shipments made during that cycle. A comparison of the solutions obtained by the proposed algorithm with the optimal solutions (or a bound) indicate that the algorithm provides solutions with optimal setup rates in most of the problem instances considered and, when not optimal, the setup rates of these solutions are close to optimal values.     

Optimal reconfiguration policy to react to product changes

The increasing frequency of product and process modifications may significantly undermine the profitability of those production systems that are designed only on the basis of the current product requirements and eventually on the expectations of future variations of the market volumes. Indeed, the product typically evolves during its life cycle, by changing its technological characteristics and therefore its requirements on the production system. As a consequence, the production system may be forced to run in an inefficient and costly manner because it is no longer consistent with the modified product. This paper describes the reconfiguration problem of production systems and proposes the optimal reconfiguration policy to react to product changes, on uniformly distributed market demand and uniformly distributed technological requirements. A numerical case based on a real problem supports the applicability of the proposed reconfiguration policy.     

Satisfying customer preferences via mass customization and mass production

Two operational formats namely mass customization and mass production can be implemented to satisfy customer preference-based demand. The mass customization system consists of two stages: the initial build-to-stock phase and the final customize-to-order phase. The mass production system has a single stage: building products with pre-determined specifications to stock. In each case, the company makes decisions on the number of initial product variants, product specifications, production quantities and product pricing. Under a uniform customer preference distribution, the optimal number of base-product variants resembles the well known economic order quantity solution, and the optimal product specifications are equally spaced. We characterize three possible benefits of mass customization: (i) the gained surplus from offering each customer her ideal product; (ii) extra revenue from price discrimination; and (iii) reduced costs due to risk pooling under stochastic demand.     

Optimal pricing policy for a deteriorating product by dynamic tracking control

We study the optimal selling price of a deteriorating product under a deterministic situation in a finite time horizon where the time horizon is either known or unknown. Inventory holding cost is expressed as a quadratic function of the current inventory level. Given a known time horizon, we develop a model by considering the deterioration dynamics of the product, and show its equivalence to a generalised optimal control problem of a linear quadratic form, i.e. an optimal dynamic tracking problem with constraints on the control variable. An optimal pricing policy is derived based on the maximum value principle. The control policy takes a state feedback form; it exhibits a closed-loop relationship between the optimal selling price (control variable) and the optimal inventory level (state variable). Given an unknown time horizon, an optimal pricing policy is derived through a similar approach when the initial inventory level meets certain conditions. Numerical situations are conducted to illustrate the effectiveness of the derived price control policies. Some interesting managerial insights are discussed.     

Optimisation of multi-stage JIT production-pricing decision: centralised and decentralised models and algorithms

This research studies the optimal decision for product pricing, production lot sizing in a multi-stage serial just-in-time production system with kanban-controlled policy. A decentralised decision model and a centralised decision model of this problem are formulated as a mixed-integer nonlinear programming problem. In order to solve the models, three algorithms are developed. The first one is an approximate procedure which solves the decentralised decision model; the second one is a proximate optimal procedure using two-phase search technique that solves the centralised decision model, and the third one is an approximate method using meta-heuristic technique which is used for both decentralised and centralised models. Numerical example shows that centralised decision can obtain higher economic benefit with lower cost and higher revenue and profit. Meanwhile, when demand is more price sensitive, centralised decision can achieve significant profit enhancement. Computational results attribute to different characteristics of the problem and solution superiority.     

Production and subcontracting control for an unreliable manufacturing system with setups

This paper deals with the problem of joint production, setup and subcontracting control of unreliable manufacturing systems producing two product types. The production requires setups each time it switches from one product type to another. Subcontracting is an integral part of the decision-making process due to limited production capacity in existing facility. The objective is to propose an effective control policy for the considered system which simultaneously manages production, setup and subcontracting activities. The complexity of the problem lies in the interaction between internal manufacturing decisions and subcontracting that outsource a part of the production, in a dynamic and stochastic environment. An experimental optimisation approach is adopted to determine the optimal control parameters which minimise the average total cost. Extensive sensitivity analyses are performed to illustrate the robustness and the usefulness of the adopted approach. An in-depth study comparing five control policies across a wide range of system parameters is also conducted. Extended cases closer to reality are also investigated considering elements such as the preventive maintenance and the production of non-conforming products. The best control policy in terms of economic performance is then obtained. Valuable insights providing a better understanding of interactions involving production, setup, and subcontracting are discussed.     

Dynamic rationing and ordering policies for multiple demand classes

In this paper, we study the dynamic rationing problem for multiple demand classes with Poisson demands. We first consider a multi-period problem with zero lead time and show that the optimal rationing and ordering policies are, respectively, the dynamic rationing policy and the base stock policy. We then extend this model to a non-zero lead time and show that there is no simple optimal structure for this extended problem. A myopic policy and a lower bound are proposed. The numerical results show that the dynamic rationing policy outperforms the static rationing policy and its performance is very close to the optimal policy under a wide range of operating conditions.     

Product family platform selection using a Pareto front of maximum commonality and strategic modularity

Product family design offers a cost-effective solution for providing a variety of products to meet the needs of diverse markets. At the beginning of product family design, designers must decide what can be shared among the product variants in a family. Optimal design formulations have been developed by researchers to find one optimal component sharing solution based on commonality, cost or technical performance of a product family. However, these optimization methods may not be able to apply in consumer product design because some metrics (e.g., visual appeal and ergonomics) of a consumer product cannot be formulized. In this paper, we suggest a tradeoff between commonality and the quality of the modular architecture in product family platform selection. We introduce a method for designers to identify multiple component sharing options that lie along a Pareto front of maximum commonality and strategic modularity. The component sharing options along the Pareto front can be evaluated, compared, and further modified. We demonstrate the method using a case study of product family platform selection of high-end and low-end impact drivers and electric drills. In the case study, the quality of the modular architecture is evaluated using a design structure matrix (DSM) for each of product variants. Three architectures along the Pareto front with maximum commonality, optimal modularity, and a balanced solution of the two metrics are highlighted and further examined to validate the effectiveness of our method.     

Base-stock control for single-product tandem make-to-stock systems

In this paper, we consider a multiple-stage tandem production/inventory system producing a single product. Processing time at each stage is assumed to have a general stationary processing time distribution. The cost of holding work-in-process (WIP) inventory is different at each stage. Therefore, decisions on when to release work to the system as well as when to transfer WIP from one stage to another need to be made. We formulate this problem of release/production control as a Markov decision process. However, the optimal policy is rather complex, making its implementation impracticable in practice. We therefore investigate the performance of simple base stock policies. Our approach aggregates several stages into one and uses a simple approximation to compute approximately optimal base stock levels. We present the results of a simulation study that tests the performance of our approximation in estimating the best base stock levels, and the performance of base stock policies as compared with the optimal policy.     

Analysis of supply contracts with total minimum commitment

In this paper we analyze a supply contract for a single product that specifies that the cumulative orders placed by a buyer, over a finite horizon, be at least as large as a (contracted upon) given quantity. We assume that the demand for the product is uncertain, and the buyer places orders periodically. We derive the optimal purchase policy for the buyer for a given total minimum quantity commitment and a discounted price. We show that the policy is characterized by the order-up-to levels of the corresponding finite horizon and a single-period standard newsboy problem with no commitment but with discounted price. We show that this policy can be computed easily. We can use this to evaluate any discount schedule characterized by a set of (price discount, minimum commitment) pairs.     

Production rate control of an unreliable manufacturing cell with adjustable capacity

This article addresses the production control problem of an adjustable capacity unreliable manufacturing cell responding to a single product type demand. The manufacturing cell is composed of an unreliable machine, called the ‘central machine’. Due to availability fluctuations, the central machine may fall short of meeting the long-term demand rate. In order to quickly adjust the production capacity and thus meet the demand, a reserve machine is called upon in support if the finished product inventory level drops below a specific threshold. Such a machine involves higher production costs compared with the central one. This article aims to determine the optimal production control policy for the involved machines in order to minimise production, inventory and backlog costs over an infinite horizon. This article proposes a continuous dynamic programming formulation of the problem and adopted a numerical scheme to solve the optimality conditions equations. The optimal production policy is shown to be described by a state dependent hedging point policy (SDHPP). To determine the optimal control policy parameters, an experimental approach based on design of experiments, simulation modelling, and response surface methodology is proposed. Several sensitivity analyses have been carried out and have shown the robust behaviour of the developed policy facing expected variations of the system parameters. The results also show that the proposed SDHPP policy outperforms classical stand-by and parallel machines based control policies. The usefulness of the proposed approach is outlined for more complex situations where the system must deal with non-exponential failure and repair time distributions.     

Control of a manufacturing system with random product yield and downward substitutability

We consider a manufacturing system where the quality of the end product is uncertain and is graded into one of several quality levels after production. We assume stochastic demand for each quality level, stochastic production times, and random quality yields. We also assume downward substitutability (i.e., customers who require a given product will be satisfied by a higher quality product at the same price). The firm produces to stock and has the option to refuse satisfying customers even when it has items in stock. We formulate this problem as a Markov Decision Process in the context of a simple M/M/1 make-to-stock queue with multiple customer classes to gain insight into the following questions: (i) how does the firm decide when to produce more units (i.e., what is the optimal production policy?) and (ii) how does the firm decide when to accept/reject orders and when to satisfy customers demanding lower quality products using higher quality products? In the case of two product classes, we completely characterize the structure of the optimal production and acceptance/substitution policies. However, the structure of the optimal policy is complicated and we therefore develop a simple heuristic policy for any number of classes which performs very well. We finally extend our heuristic to the system where production occurs in batches of size of larger than one, the system where there is a setup cost for initiating production, and the case where processing time distribution is Erlang.     

Factors affecting opportunity of worksharing as a dynamic line balancing mechanism

We consider the problem of optimal worksharing between two adjacent workers each of whom processes a fixed task in addition to their shared task(s). We use a Markov Decision Process (MDP) model to compute optimal policies and provide a benchmark for evaluating threshold policy heuristics. Our approach differs from previous studies of dynamic line balancing in that we focus on system architecture factors that affect the performance improvement opportunity possible through worksharing relative to a traditional static worker allocations, as well as practical heuristics for worksharing. We find that three such factors are significant whether we use an optimal or a heuristic control policy: ability to preempt the shared task, granularity of the shared task and overall variability of the task times. Understanding the role of these factors in a given production environment provides a means for determining where and how worksharing can have significant logistical benefits.     

Switchgear component commonality design based on trade-off analysis among inventory level,delivery lead-time and product performance

The shortening of product delivery lead-times can usually be achieved by keeping high-level components in inventory, however in small-volume production systems, maintaining such inventories is often a costly as well as a risky business strategy. If the risk of maintaining unsold inventory can be decreased, even small-volume manufacturers may be able to justify holding more significant quantities of versatile inventory. This paper discusses a component commonality effect to breakthrough the trade-off relationship between inventory levels and delivery lead-times for such small-volume production systems. By using the same component in different products, inventory maintenance costs can be dramatically reduced, but component commonality design problems are inherently complex, since excessive module commonality may lead to lower product performances, and there are trade-off relationships between product performance and cost reductions obtained through component commonality. In this paper, such a design problem is formulated as a multiobjective component commonality design optimisation problem considering inventory level, delivery lead-time and product performance, and the optimal solutions are obtained as a Pareto optimal solution set. Detailed procedures concerning the proposed design method, including inventory simulation, are discussed and developed for a switchgear design problem. Finally, an example switchgear design problem is solved to illustrate that optimal use of component commonalities across different modules can significantly reduce inventory costs, while also shortening product delivery lead-times.