The Effects of Learning on Optimal Lot Size Determination—Single Product Case

In this article the effects of learning on production lot sizing models are analyzed for the single product case. A general equation is developed for the average production time per unit, for producing the the annual demand in batches with some percentage of learning not retained between lots. Two models are developed, the first restricted to equal lot sizes and the second restricted to equal production intervals. A sample problem is solved to demonstrate the applications of learning to lot size determination.     

The impact of worker forgetting on production scheduling

Numerous articles suggest using the Japanese manufacturing strategy of minimizing inventories by producing small lot sizes. However, few studies actually have investigated the relative advantages or disadvantages of such a strategy. Worker productivity improvements during production of a batch (learning)and the loss of productivity improvements due to the breaks between batches (forgetting)both influence the optimal lot size for a product. The results of this study indicate that worker forgetting in a batch production environment can substantially increase optimal lot sizes. Since forgetting causes a type of setup cost by penalizing breaks in production, it is intuitive to expect an increase in optimal lot size for forgetting. This study confirms the expectation. What is interesting, however, is that only a small amount of forgetting is required to substantially increase the optimal lot size. The conditions under which lot sizes need to be significantly increased are discussed and illustrated. The results also suggest that special attention must be given to eliminate forgetting due to production disruption when using just-in-time scheduling techniques to reduce lot sizes. The use of automated processes in batch production may overcome the need for large lot sizes by negating the worker forgetting cost, which is a form of setup cost. Robotic technologies or flexible manufacturing systems are types of automated processes which can diminish the forgetting effect in a batch production mode, and therefore, allow efficient production of small lot sizes.     

A Heuristic for Multiple Lot Sizing For an Order Under Variable Yield

Consider a job shop which must completely fill a large make-to-order demand of a product where production yield is highly variable. After a production lot is completed, if the total output of satisfactory units is inadequate to satisfy the demand, then a new run (with associated setup cost) is made. When the output of good units exceeds the demand, then the excess units are scrapped (with possible salvage value). The optimal lot size minimizes the total of production, setup, holding, shortage, and scrap costs. A heuristic is developed based on the incremental cost of increasing the lot size by one unit. The computational ease and excellent cost performance of the heuristic favor its use in place of the mathematically optimal solution obtained by dynamic programming. Real world manufacturing applications and additional properties of the model are also discussed.     

A hybrid genetic algorithm for flowshop lot streaming with setups and variable sublots

Lot streaming is the process of splitting a given lot or job to allow the overlapping of successive operations in flowshops or multi-stage manufacturing systems to reduce manufacturing lead time. Recent literature shows that significant lead time improvement is possible if variable sublots, instead of equal or consistent sublots, are used when production setup time is considered. However, lot streaming problems with variable sublots are difficult to solve to optimality using off-shelf optimisation packages even for problems of small and experimental sizes. Thus, efficient solution procedures are needed for solving such problems for practical applications. In this paper, we develop a mathematical programming model and a hybrid genetic algorithm for solving n-job m-machine lot streaming problems with variable sublots considering setup times. The preliminary computational results are encouraging.     

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.     

The Effects of Learning on Optimal Lot Size Determination—Multiple Product Case

This article extends the analysis of an earlier paper by the authors for a single product to lot size determination for manufacturing cycles of multiple products. The effects of production breaks, learning interactions due to commonality of tasks and different learning rates for products are considered in the formulation of an equation for the average production time per unit. The equation is applied to an equal lot size per product model. An analysis of a model restricted to equal production intervals per product per cycle is also presented. A sample problem is solved to demonstrate the application of the effects of learning to multiple product lot size determination.     

Finite capacity scheduling method for MRP with lot size restrictions

Materials requirements planning (MRP) is a widely used production scheduling technique in the manufacturing industry. Based on the projected demand and the corresponding product structure, MRP prescribes the periodic production quantities for every end-item, subassembly and component. The goal of MRP is to reduce the inventory cost while simultaneously ensuring that dependent demand relationships are met. In its basic form, the dependent demand explosion used by MRP to schedule production does not consider the availability of resources, consequently the schedule is often capacity infeasible. The MRP progressive capacity analyser (PCA) procedure in which finite capacity planning and lot sizing are performed concurrently with the MRP bill of material (BOM) explosion process is introduced. The PCA procedure is executed in four steps. It models the lot size multiple restriction and can be easily modified for other lot sizing rules. This method has been validated and tested for sensitivity to fluctuations in demand patterns and lot sizes. It has also been compared and shown to outperform a popular methodology used in practice.     

Flexible work-in-process production system in supply chain management under quality improvement

For a complex product production, any flexible manufacturing system with a work-in-process inventory is recommended for a supply chain management (SCM) system. Building a flexible manufacturing system increases the total cost of the supply chain; for this reason, a discrete investment is important. For flexible production systems, production rate within a finite specific interval of production rate as work-in-process inventory is calculated. The aim of the supply chain is to reduce the total cost when demand during the lead time is a random variable with a normal distribution. A crashing cost is utilised to reduce the duration of lead time within the supply chain system. A model is proposed to obtain the optimal flexible production rate with the reduced total cost of the supply chain. A classical optimisation technique is employed to obtain the closed-form and quasi-closed-form solutions of the decision variables. An improved algorithm is designed to obtain the global minimum cost of SCM under the framework of a flexible production system. An illustrative numerical example and sensitivity analysis are given to test the model. A numerical study proves that this model obtains the minimum cost with the optimal decision variables.     

Two-stage hybrid flow shop batching and lot streaming with variable sublots and sequence-dependent setups

A paint manufacturing firm's customers typically place orders for two or more products simultaneously. Each product belongs to a family that denotes batching compatibility during manufacturing. Further, products can be split into several sublots to allow overlapping production in a two-stage hybrid flow shop wherein various identical, capacitated machines operate in parallel at each stage. We present a mixed-integer linear program (MILP) for this integrated batching and lot streaming problem with variable sublots, incompatible job families, and sequence-dependent setup times. The model determines the number and size of sublots for each product and the production sequencing for each sublot such that the total weighted completion time is minimised. To promote practical implementation, we develop and evaluate heuristics to efficiently solve this problem.     

Accounting for idle capacity cost in the scheduling of economic lot sizes

This paper considers the issue of idle capacity cost in determining economic lot sizes. Two mathematical models are developed for the economic lot scheduling problem (ELSP). In Model I, the ELSP with fixed production rates is formulated under both the common cycle and time-varying lot sizes approaches. The associated constrained optimization problem in the time-varying lot sizes approach is reduced to solving a parametric quadratic programming problem. In Model II, the modified ELSP (or MELSP) is treated with variable production rates and unit production cost of each item as a function of its production rate. An upper bound and a lower bound on the MELSP are derived. Lot-sizing decisions of the proposed models are obtained and their dependencies on the idle capacity cost are examined with numerical examples.     

Optimization of multistage production systems with variable production times and costs

Introducing a concept of ‘ production speed ’ as a decision variable, a production model with variable (speed-dependent) production time and cost for producing a product item was constructed. Optimization analysis was mode on a single-item, multistage production system in an attempt to determine the optimal production speeds for all stages and the optimal cycle time. For a case of multiple-item production, an optimal job sequence and the optimal production speeds for all jobs were analysed, such that the total flow time was minimized as a primary objective and, in addition, the total production cost was minimized as a secondary objective.     

Lot size approximation based on minimising total delay in a shop with multi-assembly products

Minimising the total delay in the procurement of materials is one of the most important objectives in the production management of a manufacturing shop with multi-assembly products. This criterion is affected by the lot sizes of the materials used in the assembly of final products. Therefore, the optimum production lot size of products should be determined to minimise the total delay. In this paper, four types of delay, namely priority, processing, staging and requirements delay are formulated based on a multi-product MRP (MP-MRP) graph activity. To optimise lot sizes and minimise total delay (TD), the lead time and due date of products are considered. Artificial neural network (ANN) and regression methods are then applied to obtain the nonlinear function of TD versus the lot sizes of products. The delay-based lot size approximation (DBLSA) algorithm is proposed for obtaining the approximated lot size of products. Results obtained for a 2P-MRP case study show the effectiveness of the solutions obtained by the proposed algorithm.     

Economic lot sizing for an imperfect production system subject to random breakdowns

This article considers an economic manufacturing quantity model for an imperfect production process that is subject to random machine breakdowns. The product is manufactured intermittently in batches to meet a constant demand. During a production run, the system is assumed to deteriorate over time. As a result, a fixed proportion of items produced are defective. The system is also subject to random breakdowns. A no-resumption inventory control policy is adopted. Under this policy, the production run is aborted when a breakdown occurs. Production will be resumed only when all on-hand inventories are depleted. Corrective maintenance is carried out immediately after a breakdown. The time-to-shift and the time-to-breakdown are two random variables following different exponential distributions. The objective is to find an optimal production lot size that minimizes the expected (long-run) total cost per unit time. Several models are investigated and a numerical approach is developed to obtain an optimal production lot size.     

Pure and mixed strategies for the EOQ repair and waste disposal problem

In this paper the analysis of the EOQ repair and waste disposal model with variable setup numbers for production and repair within some collection time interval is continued. The cost analysis is now extended to the extreme waste disposal rates and it is shown that the pure (bang-bang) policy of either no waste disposal (total repair) or no repair (total waste disposal) dominates the strategy of mixing waste disposal and repair. Moreover, the different behavior of the minimum cost, of the optimal setup numbers, lot sizes and collection intervals for small and large waste disposal rates is discussed.     

ATO通用策略在费用分担模型的应用

以由一个零部件供应商和一个产品组装制造商组成的ATO两级供应链为对象,研究零部件供应商和组装产品制造商共同投资缩短零部件供应提前期以缩短产品交货期的相关模型.在此情况下,主要从成品组装制造商的角度建立相关成本模型,以总运作成本最小化为目标求解零配件供应提前期和订货批量两个决策变量,通过比较三种产品结构的结果考察了通用件和制造商费用分担份额对产品交货提前期及总运作成本的影响.算例分析表明,采用通用件有助于减少制造商的总运作成本,并在制造商费用分担额度较大时,有利于缩短产品交货提前期.     

New integrated model to estimate the manufacturing cost and production system performance at the conceptual design stage of helicopter blade assembly

This paper describes a new integrated model development to estimate the manufacturing cost and production system performance at the conceptual design stage. A fully automated conceptual framework for design for manufacturing (DFM) has been developed. An integrated product process design concept using activity based costing is applied in this paper. The new integrated model consists of four sub-modules: the geometric parameters generation module, processing time estimation module, activity based costing (ABC) module and production system performance module. All of the input-output data flows of developed modules are fully integrated for automated manufacturing cost analysis and production system performance. A developed integrated model is very useful for designers or integrated product development team to make a decision for evaluating the design alternatives and trade-offs between design and manufacturing phases at the conceptual design stage. A case study for a composite helicopter rotor blade is included.     

The capacitated lot sizing problem with setup carry-over

Although there is a significant amount of literature on the capacitated lot sizing problem, there has been insufficient consideration of planning problems in which it is possible for a lot size, or production run, to continue over consecutive time periods without incurring multiple setups. While there are papers that consider this feature, they typically restrict production to at most one product in each period. We present a set of mixed integer linear programs for the capacitated lot sizing problem that incorporate setup carry-over without restricting the number of products produced in each time period. Efficient reformulations are developed for finding optimal solutions, and a Lagrangian decomposition heuristic is provided that quickly generates near-optimal solutions. The computational results demonstrate that incorporating setup carry-over has a significant effect on both cost and lot sizes.     

Setup cost reduction in an inventory model with finite-range stochastic lead times

Traditionally, upon solution, independent demand inventory models result in the determination of a closed form for the economic lot size. Generally, this is obtained from the result that holding costs and setup costs are constant and equal at the optimum. However, the experience of the Japanese indicates that this need not be the case. Specifically, setup cost may be reduced by investing in reduced setup times resulting in smaller lot sizes and increased flexibility. Various authors have investigated the impact of such investment on classical lot sizing formulas which has resulted in the derivation of modified relationships. A common assumption of this research has been that demand and lead time are deterministic. This paper extends this previous work by considering the more realistic case of investing in decreasing setup costs where lead time is stochastic. Closed form relationships for optimal lot size, optimal setup cost, optimal total cost, etc. are derived. Numerical results are presented for cases where lead times follow uniform and normal distributions. Sensitivity analysis is performed to indicate under what conditions investment is warranted.     

Manufacturing lot-sizing,procurement and delivery schedules over a finite planning horizon

In this study, an integrated manufacturing system for technology-related companies whose products are experiencing continuous price decrease during the life cycle is studied for optimal procurement, production and delivery schedules over a finite planning horizon. The model considers the inventory cost both at manufacturing and at delivery from supplier. Since the price is continuously decreasing, a manufacturing firm delivers the finished goods in small quantities frequently. Frequent deliveries in small lots are effective to reduce the total cost of the supply chain. The key for high-tech industries is to reduce the inventory holding time since the component prices are continuously decreasing, and this can only be achieved by implementing an efficient supply chain. Therefore, the main purpose of this paper is to develop an integrated inventory model for high-tech industries in JIT environment under continuous price decrease over finite planning horizon while effectively and successfully accomplishing supply chain integration so that the total cost of the system is minimal. An efficient algorithm is developed to determine the optimal or near-optimal lot sizes for raw material procurement, and manufacturing batch under a finite planning horizon. Finally, the solution technique developed for the model is illustrated with numerical examples.     

Just-in-time purchasing: an integrated inventory model involving deterministic variable lead time and quality improvement investment

Nowadays supply chain management is a popular practice in manufacturing systems, and just-in-time (JIT) production plays a crucial role in supply chain environments. Companies are using JIT production to gain and maintain a competitive advantage. The characteristics of JIT systems are consistent high quality, small lot sizes, frequent delivery, short lead time, and close supplier ties. This paper presents an integrated inventory model to minimize the sum of the ordering/setup cost, holding cost, quality improvement investment and crashing cost by simultaneously optimizing the order quantity, lead time, process quality and number of deliveries while the probability distribution of the lead time demand is normal. This integrated inventory model is useful particularly for JIT inventory systems where the vendor and the purchaser form a strategic alliance for profit sharing.