Optimal production and pricing policies in a combined make-to-order/make-to-stock system

In this paper, we consider a production system which is capable to produce two types of products. The first type of products is make-to-order, while the second type is make-to-stock whose demand is satisfied by the on-hand inventory. The demand arrival rates of both types of products are price-sensitive. The excess demand that cannot be satisfied immediately is either backlogged or lost. The system costs include the holding costs of product inventories and shortage costs of unsatisfied demand. The objective is to maximise the total discounted profit over an infinite planning horizon by coordinating the production process and pricing decisions. By analysing the properties of objective functions, we characterise the optimal control policy by two switch curves and the optimal price is also given for different ordering and inventory levels. We also explore the monotonicity of both switch curves which will reduce the computation effort. Numerical experiments are conducted to demonstrate the use of the switch curves in managing the production system and illustrate that compared with the static pricing policy, the optimal integrated price and inventory control policy can result in a significant profit improvement in the make-to-order/make-to-stock system that is much higher than in a single-product system.     

Dynamic admission control for two customer classes with stochastic demands and strict due dates

We study a dynamic capacity allocation problem with admission control decisions of a company that caters for two demand classes with random arrivals, capacity requirements and strict due dates. We formulate the problem as a Markov decision process (MDP) in order to find the optimal admission control policy that maximises the expected profit of the company. Such a formulation suffers a state-space explosion. Moreover, it involves an additional dimension arising from the multiple possible order sizes that customers can request which further increases the complexity of the problem. To reduce the cardinality of possible policies, and, thus, the computational requirements, we propose a threshold-based policy. We formulate an MDP to generate such a policy. To deal with the curse of dimensionality, we develop threshold-based approximate algorithms based on the state-reduction heuristics with aggregation proposed previously. Our results reveal that for the majority of instances considered the optimal policy has a threshold structure. We then demonstrate the superiority of the proposed threshold-based approximate algorithms over two benchmark policies in terms of the generated profits and the robustness of the solutions to changes in operational conditions. Finally, we show that our proposed policies are also robust to changes in actual demand from its estimation.     

Single CNC machine scheduling with controllable processing times and multiple due dates

In this study, we solve the single CNC machine scheduling problem with controllable processing times. Our objective is to maximize the total profit that is composed of the revenue generated by the set of scheduled jobs minus the sum of total weighted earliness and weighted tardiness, tooling and machining costs. Customers offer multiple due dates to the manufacturer, each coming with a distinct price for the order that is decreasing as the date gets later, and the manufacturer has the flexibility to accept or reject the orders. We propose a number of ranking rules and scheduling algorithms that we employ in a four-stage heuristic algorithm that determines the processing times for each job and a final schedule for the accepted jobs simultaneously, to maximize the overall profit.     

Order acceptance and scheduling policies for a make-to-order environment with family-dependent lead and batch setup times

In many make-to-order production situations with batch setup times, customer orders are grouped into family-dependent batches to limit the loss of capacity due to setups. These batches, however, cannot be too large, since the make-to-order character requires that orders have to be produced in time. This trade-off between setup time efficiency and due-date adherence creates a challenging scheduling problem referred to in the literature as the Customised Stochastic Lot Scheduling Problem. Typically, suppliers reduce the complexity of the production problem by quoting lead times that are equal for all customer families. This choice, however, is in many cases too restrictive. In this paper, we show quantitatively by means of Markov decision processes (MDPs) that using family-dependent lead times can result in a significant gain in profit as compared with using standard lead times. We develop a simple heuristic acceptance/scheduling policy, and demonstrate that this heuristic performs very well compared with the optimal policy of the MDP for a wide range of parameters.     

Optimal Production Control in Stochastic Manufacturing Systems with Degenerate Demand

The paper studies the production inventory problem of minimizing the expected discounted present value of production cost control in manufacturing systems with degenerate stochastic demand. We have developed the optimal inventory production control problem by deriving the dynamics of the inventory-demand ratio that evolves according to a stochastic neoclassical differential equation through Ito’s Lemma. We have also established the Riccati based solution of the reduced (one-dimensional) HJB equation corresponding to production inventory control problem through the technique of dynamic programming principle. Finally, the optimal control is shown to exist from the optimality conditions in the HJB equation.     

Batch sizing with controllable production rates in a multi-stage production system

In this paper, a comprehensive model is presented for cell formation and layout design in cellular manufacturing systems (CMS). The proposed model incorporates an extensive coverage of important operational features and especially layout design aspects to determine optimal cell configuration and Intra and Inter-cell layout in CMS. Hence, proposed integrated approach attempts to design intra and inter-cell layout and material handling flow path structure simultaneously. We examine the great potential benefits of providing these features consist of routing flexibility, operation sequence, machine capacity, considering number of cells as a decision variable, un-equal dimension of machines, free machines and cells orientation, and considering pickup and drop off station for each cell. In order to show the effects and important of integrated design in the CMS, two approaches, sequentially and integrated, have been investigated and demonstrate the integrated approach improve the quality of obtained solution. The proposed model is a mixed integer non-linear programme. Linearisation procedures are proposed to transfer it into a linearised mixed integer programming formulation. Computational results are presented with the linearised formulation. We presented several enhancements in terms of valid inequalities and extensions to the proposed model in order to improve its computational performance. Finally, concluding remarks are provided.     

Lot-sizing in a multi-stage flow line production system with energy consideration

In this paper, a single-item capacitated lot-sizing problem in a flow-shop system with energy consideration is studied. The planning horizon is defined by a set of periods where each one is characterised by a length, an allowed maximal power, an electricity price, a power price and a demand. The objective is to determine the quantities to be produced by each machine at each period while minimising the production cost in terms of electrical, inventory, set-up and power required costs. For medium- and large-scale problems, lot-sizing problems are hard to solve. Therefore, in this study, two heuristics are developed to solve this problem in a reasonable time. To evaluate the performances of these heuristics, computational experiments are presented and numerical results are discussed and analysed.     

Route selection and flow control in a multi-stage manufacturing system with heterogeneous machines within stages

With increasing market competition and the need to serve diverse market segments, many companies are responding to customer needs by manufacturing parts in small batches. Unless properly planned, batch production can lead to high material handling time. In this paper, a methodology for selecting the best routeing for a batch in a multi-stage production system with material handling considerations is presented. Each stage consists of multiple, functionally identical machines that have non-identical characteristics. The model determines the optimal routeing for the batch and generates the number of parts to handle or transport at a time as a unit load between machines in order to minimize total batch manufacturing time. The result from the model provides the optimal routeing (i.e., the machine to use at each production stage) and the number of parts to move at a time as a sub-lot. The solution procedure developed is easy to use and can be incorporated as a daily shop management tool.     

Optimal stocking strategies for inventory mechanism with a stochastic short-term price discount and partial backordering

Price discount is an important research topic in the field of inventory management. The existing research on this topic mainly considers fixed price discount, but ignores the situation in which stochastic short-term price discount may be involved. In this paper, we study an inventory problem considering stochastic short-term price discount and partial backordering. To address this problem, we propose an optimal replenishment and stocking model to maximise the retailers' profit. After that, a cost–benefit analysis-based heuristic method for solving the developed model is presented by considering two scenarios depending on whether a replenishment point belongs to a discount period or not. Furthermore, an algorithm is provided to elicit an optimal ordering policy from multiple solutions derived from the given heuristic solution method. Finally, a real case is offered to demonstrate the application of the proposed model, followed by a sensitivity analysis. The results indicate that a retailer can identify the optimal replenishment policy with the aim of achieving maximal profit in situations where stochastic short-term price discount and partial backordering are considered for certain inventory problems at hand. In addition, sensitivity analysis illustrates a fact that different values of the introduced parameters may influence the optimal replenishment policy.     

Optimal policies of a two-echelon serial inventory system with general limited capacities

We study optimal policies of capacitated two-echelon serial inventory systems under periodic review. For a system with smaller downstream capacity, we fully characterise the optimal policy as a further modified echelon base stock policy using an intuitive backward induction. The key lies in the magnitude relation between the initial upstream stock level and the downstream capacity. For a system with smaller upstream capacity, we demonstrate that the optimal policy is of a more complex structure where there can be at most four/five target levels up to which the upstream/downstream echelon tries to produce/order. The numbers of levels and their values depend on the length of remaining horizons and the amount of initial upstream inventories. We also specify these potential target levels and then suggest a way to simplify the search of optimal solutions.     

Capacity planning of serial and batch machines with capability constraints for wafer fabrication plants

Capacity planning is crucial to the investment and performance of wafer fabs. This research proposes a practical procedure to calculate the required number of machines with serial and batch processing characteristics, respectively. Several formulae are first presented. Five heuristic algorithms are then proposed to determine the lower bound, the upper bound, and the near-optimal of the number of machines of the type with capability constraint. Data from real foundry fabs are used in a case study to determine the required number of 64 types of equipment and to evaluate the performance of the proposed procedure. The algorithm using the best ratio of production efficiency and equipment cost to select the machine type with capability constraint results in the least required number of machines, the highest machine utilisation, and the lowest equipment investment. An AutoSched AP simulation model is used to evaluate if a wafer fab using the calculated number of machines of each type can result in a preset monthly output rate. Simulation results indicate that the proposed procedure can quickly and accurately calculate the required number of machines leading to the required monthly production target. Fab managers can use this tool to conduct what-if analysis for equipment investment alternatives.     

Robust production control policy for a multiple machines and multiple product-types manufacturing system with inventory inaccuracy

Inventory inaccuracy often exists in manufacturing systems, which has great negative impact on the performance of production control, e.g. very high work-in-process holding cost or backlog penalty. To hedge against inventory inaccuracy, the robust production control problems will be investigated for a multiple machines and multiple product-types manufacturing system with uncertain production capacity. The objective of our problem is to minimise the average production cost. To solve this problem, a robust production control policy is developed, which is insensitive to the inventory record errors, and whose robustness is better than the traditional hedging point policy for optimal production control. Finally, numerical experiments are conducted to examine the performance of the proposed robust production control policy against inventory inaccuracy. Based on the experimental results, the conditions of applying the proposed policy are also obtained.     

Impact of the alignment between the strategic and operational levels of a manufacturing enterprise

In today's economic environment, manufacturing organisations compete against each other as part of supply chains (SC). As both the SC strategic level and production floor operational level are interdependent, a misalignment between them has a deep impact on the performance of the manufacturing organisation. For this reason, in this paper we develop an analytical expression of the impact such misalignment has on the manufacturing organisation performance, specifically, its demand fulfillment ability. The usefulness of the analytical expression is illustrated via the development, for the case of a local furniture company, of a system dynamics (SD) simulation model. The SD simulation model is tested under different operational conditions, so the case study company can derive conclusions regarding actions to improve its demand fulfillment ability.     

Comparison of order-fulfilment performance in MTO and MTS systems with an inventory cost budget constraint

The make-to-order or make-to-stock decision is an important issue faced by firms in many industries. In the existing literature, optimisation models comparing the cost of making product to stock versus making it to order have been widely developed. Motivated by the problem faced by a machinery company, we examine the issue from a different perspective and formulate service-maximisation models with inventory cost budget constraints. We compare and analyse order-fulfilment performance measures for the two different production control systems. The goal is to identify the key influencing factors and devise a production strategy that maximises service performance subject to resource constraint. We show that the MTO production control system is preferred in the production system with low component values and long component processing times and high value and short lead time in the final assembly stage; while the MTS production control system is applicable to the production system with high component values and short component processing times and little value and long lead time in the final assembly stage.     

Optimal manufacturing policy in a reverse logistic system with dependent stochastic returns and limited capacities

The stochastic models of systems with reverse logistics usually assume that the quantity of products returned is independent of sales. This hypothesis is obviously not true and can lead to suboptimal production policies. In this paper a new sales-dependent returns model is described. In this model, the returns depend on the useful life of the products sold and on the probability of an end-of-life product being returned. A Markov decision problem is formulated in order to obtain the optimal manufacturing policy. A numerical example is provided to illustrate the use of the defined model. An approximated Markov decision model is defined where the optimal policy is easily obtained. The optimal policies of the original and the approximated models are compared.     

Optimal manufacturing and delivery schedules in a supply chain system of deteriorating items

The market is changing from minute to minute nowadays. Increasing cooperation and pursuing of the optimal interest of the integrated supply chain system become more effective than acting alone in the face of competition. In this research, an integrated inventory policy between a single producer and a multi-buyer is developed. The model extends the research of Lin and Lin (2007 Lin, C and Lin, YS. 2007. A cooperative inventory policy with deteriorating items for a two-echelon model. European Journal of Operational Research, 178(1): 92–111. [Crossref], [Web of Science ®] , [Google Scholar], A cooperative inventory policy with deteriorating items for a two-echelon model. European Journal of Operational Research, 178 (1), 92–111) by changing the single-buyer system to the multi-buyer system. This problem is solved under the assumptions of equal replenishments and production cycles. The producer and buyers collaboratively intend to decrease their joint total cost of operation. We consider the deterioration of items at all levels of producer, buyer and in-transport, and the backorders at buyer's level only. The algorithm to find the optimal solution is given, and Matlab and Maple software are used. A numerical example is also presented.     

Designing group layout of unequal-area facilities in a dynamic cellular manufacturing system with variability in number and shape of cells

This paper presents a new mixed-integer non-linear programming model for designing the group layout (GL) of unequal-area facilities in a cellular manufacturing system (CMS) under a dynamic environment. There are some features that make the presented model different from the previous studies. These include: (1) manufacturing cells with variable numbers and shapes, (2) machine depot keeping idle machines, (3) machines of unequal-areas, (4) manufacturing cells with rectangle regular shapes established on the continuous shop floor and (5) integration of cell formation and GL as interrelated decisions involved in the design of a CMS in a dynamic environment. The objective function is to minimises the total costs of intra- and inter-cell material handling, machine overhead, machine relocation, machine processing, purchasing machines and forming cells. Since the problem is NP-hard, an efficient simulated annealing (SA) algorithm is developed to solve the presented model. The performance of this model is illustrated by two numerical examples. It is then tested using several test problems with different sizes and settings to verify the computational efficiency of the developed algorithm in comparison to the classical genetic algorithm (GA). The obtained results show that the quality of the solutions obtained by SA is better than GA.     

Optimal decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging

Considering the characteristics of the stochastic shift of the machine state and the uncertainty of the product quality of production, in this paper, we develop an optimisation decision of economic production quantity model for an imperfect manufacturing system under hybrid maintenance policy with shortages and partial backlogging. We assume that the production process is imperfect stemming from the machine reliability and the probability of out-of-control, a hybrid maintenance policy combined of emergency maintenance and preventive maintenance is executed during each production run. Three decision models based on the scenarios of machine breakdown and repair time are developed. The optimal production quantity and maintenance inspection number during each production run are solved with minimising the expected average cost of the system. Numerical examples are used to demonstrate the effectiveness and feasibility of the model. Sensitivity analysis is conducted to analyse the impacts of key parameters on the optimal decision. Some implications related to the effective and economical execution of maintenance policy for practitioners are derived.     

基于模型不确定性的保险人最优投资再保险问题研究

研究了以破产概率最小化为目标的模糊厌恶型保险人的最优投资再保险问题。假设保险人可购买比例再保险,同时可投资于一个风险资产。保险人的盈余过程由扩散风险模型描述,风险资产的价格过程由常方差弹性 (CEV) 模型描述。根据动态规划原理建立了优化问题相应的 HJB 方程,针对特殊的弹性系数给出了保险人的最优鲁棒投资再保险策略的解析解。最后,通过数值模型分析了模型参数对最优投资-比例再保险策略和值函数的影响。研究发现保险人的模糊厌恶程度越高,其采取的投资再保险策略呈现出越保守的特点。     

Optimising installation (R,Q) policies in distribution networks with stochastic lead times: a comparative analysis of guaranteed- and stochastic service models

This paper studies two modelling approaches to the multi-echelon inventory optimisation problem in a distribution network with stochastic demands and lead times. It compares the performance of a novel guaranteed-service model (GSM), using an installation (R, Q) inventory control policy, with a stochastic service model (SSM) considering ordering, holding and flexibility costs. From both cycle service level and fill rate perspectives, our numerical analysis of the 1-warehouse 2-retailer network shows that cost difference between both models is driven by the internal service level at the warehouse. The GSM outperforms the SSM for over 80% of the simulated instances and realises an average total cost improvement of approximately 10%. This analysis goes against earlier results that showed a relatively low-cost difference between the two approaches, and demonstrates that it is worthwhile to evaluate competing models for multi-echelon inventory optimisation in real-world supply chains with batch ordering and variable lead times.