An algorithm for production planning in a flexible production system

In this paper, we consider the problem of determining the production rate, production batch size, and production sequence when production rate, setup cost, and unit processing cost are sequence-dependent. Using a standard lot sizing model with backorder, a tabu search algorithm for solving this problem is proposed. The algorithm is tested on some random test problems and its performance is compared with random sequencing. Computational results show that the proposed algorithm is very efficient.     

An integrated vendor–buyer inventory model with backorder price discount and effective investment to reduce ordering cost

The single-vendor single-buyer integrated production inventory system has been an object of study for a long time, but little is known about the effect of investing in reducing ordering cost on the integrated inventory models with backorder price discount and variable lead time. The purpose of this article is to investigate in the continuous review model with backorder price discount and variable lead time to effectively increase investment and to reduce the joint expected annual total cost. The integrated strategy discussed here is one in which the buyer orders a quantity, then the vendor produces n times order quantity in each production cycle, in order to reduce setup cost. In addition, the buyer offers backorder price discounts to the customers that may motivate the customers’ desire for backorders, and buyer ordering cost can be reduced through effective investment. An integrated inventory model is established to find the optimal solutions of order quantity, ordering cost, backorder price discount, lead time, and the number of shipments from the vendor to the buyer in one production run, so that the joint expected annual total cost incurred has the minimum value. Furthermore, numerical examples are used to demonstrate the benefits of the model.     

Trade credit financing in the vendor–buyer inventory system with ordering cost reduction,transportation cost and backorder price discount when the received quantity is uncertain

Previous ordering cost reduction vendor–buyer inventory models with backorder price discount usually assumed that the buyer must pay to the vendor for the ordered items as soon as the items are received, the received quantity is same as the ordered quantity and the transportation cost is independent of the shipment lot-size. In practice, however, the vendor is willing to offer the buyer a certain credit period without interest to promote market competition as well as the buyer's quantity received may not match with the ordered quantity due to unavailability of the raw material, worker's strike, human errors in counting, transcribing, etc. Furthermore, the discounts are offered for the transportation cost of large ordered quantities. This paper derives a single-vendor single-buyer supply chain model for the ordering cost reduction inventory system with backorder price discount, taking into consideration the effect of transportation cost discount and the condition of permissible delay in payments include the case where the buyer's received quantity does not necessarily match the quantity requisitioned. We take the transportation cost as a function of the shipment lot-size and it is taken to be in an all-unit-discount cost format. Thus we incorporate transportation cost explicitly into the model and develop optimal solution procedures for solving the proposed inventory problem. Numerical example and sensitivity analyses are given to demonstrate the applications and performance of the proposed methodology.     

Production/inventory systems with a stochastic production rate under a continuous review policy

A single production facility is dedicated to producing one product with completed units going directly into inventory. The unit production time is a random variable. The demand for the product is given by a Poisson process and is supplied directly from inventory when available, or is backordered until it is produced by the production facility. Relevant costs are a linear inventory holding cost, a linear backorder cost, and a fixed setup cost for initiating a production run. The objective is to find a control policy that minimizes the expected cost per time unit.The problem may be modeled as an M/G/1 queueing system, for which the optimal decision policy is a two-critical-number policy. Cost expressions are derived as functions of the policy parameters, and based on convexity properties of these cost expressions, an efficient search procedure is proposed for finding the optimal policy. Computational test results demonstrating the efficiency of the search procedure and the behavior of the optimal policy are presented.     

Grouping in decomposition method for multi-item capacitated lot-sizing problem with immediate lost sales and joint and item-dependent setup cost

This article examines a dynamic and discrete multi-item capacitated lot-sizing problem in a completely deterministic production or procurement environment with limited production/procurement capacity where lost sales (the loss of customer demand) are permitted. There is no inventory space capacity and the production activity incurs a fixed charge linear cost function. Similarly, the inventory holding cost and the cost of lost demand are both associated with a linear no-fixed charge function. For the sake of simplicity, a unit of each item is assumed to consume one unit of production/procurement capacity. We analyse a different version of setup costs incurred by a production or procurement activity in a given period of the planning horizon. In this version, called the joint and item-dependent setup cost, an additional item-dependent setup cost is incurred separately for each produced or ordered item on top of the joint setup cost.     

Quasi-optimal integrated production, inventory and maintenance policies for a single-vendor single-buyer system with imperfect production process

In this paper we deal with the integrated supply chain management problem in the context of a single vendor-single buyer system for which the production unit is assumed to randomly shift from an in-control to an out-of-control state. At the end of each production cycle, a corrective or preventive maintenance action is performed, depending on the state of the production unit, and a new setup is carried out. Two different integrated production, shipment and maintenance strategies are proposed to satisfy the buyer’s demand at minimum total cost. The first one suggests that the buyer orders batches of size nQ and the vendor produces nQ and makes equal shipments of size Q. The second policy proposes that to satisfy the same ordered quantity, the vendor produces separately smaller batches of size Q, n times. The total integrated average cost per time unit corresponding to each strategy is considered as the performance criterion allowing choosing the best policy for any given situation.     

An optimal policy for a single-vendor and a single-buyer integrated system with setup cost reduction and process-quality improvement

The single-vendor single-buyer integrated production inventory system has been an object of study for a long time, but little is known about the effect of investing in reducing setup cost reduction and process-quality improvement for an integrated inventory system in which the products are sold with free minimal repair warranty. The purpose of this article is to minimise the integrated cost by optimising simultaneously the number of shipments and the shipment quantity, the setup cost, and the process quality. An efficient algorithm procedure is proposed for determining the optimal decision variables. A numerical example is presented to illustrate the results of the proposed models graphically. Sensitivity analysis of the model with respect to key parameters of the system is carried out. The paper shows that the proposed integrated model can result in significant savings in the integrated cost.     

基于果蝇优化算法的多工位装配序列规划

为同时解决产品装配序列规划和多工位分配问题,提出一种面向复杂产品的基于果蝇优化算法的多工位装配序列规划方法。首先,基于果蝇优化算法设计了针对求解序列的编码体系;其次,采用多子种群并行搜索模式,重新设计了果蝇优化算法的搜索过程;然后,为了综合考虑多工位上相关装配操作成本的影响,提出了新的适应度函数表达式,并将适应度函数与优先序列矩阵结合起来对进化过程进行引导,实现了对产品装配序列和工位分配顺序的优化;最后,以飞机起落架为例,验证了所提方法在解决多目标优化问题方面的有效性。     

Multi-objective optimization of hybrid backorder inventory model

This paper addresses inventory problem for the products that are sold in monopolistic and captive markets experiencing hybrid backorder (i.e., fixed backorder and time-weighted backorder). The problem with stochastic demand is studied first by developing single objective (cost) inventory model. Computational results of a numerical problem show the effectiveness of hybrid backorder inventory model over fixed backorder inventory model. The model is later extended to multi-objective inventory model. Three objectives of multi-objective inventory model are the minimization of total cost, minimization of stockout units and minimization of the frequency of stockout. A multi-objective particle swarm optimization (MOPSO) algorithm is used to solve the inventory model and generate Pareto curves. The Pareto curves obtained for hybrid backorder inventory model are compared with the existing Pareto curves that are based on fixed backorder. The results show a substantial reduction in stockout units and frequency of stockout with a marginal rise in cost with proposed hybrid backorder inventory system in comparison to existing fixed backorder inventory system. Sensitivity analysis is done to study the robustness of total cost, order quantity, and safety stock factor with the change in holding cost. In the end, the performance of the MOPSO algorithm is compared with the multi-objective genetic algorithm (MOGA). The metrics that are used for the performance measurement of the algorithms are error ratio, spacing and maximum spread.     

Evolutionary algorithm for advanced process planning and scheduling in a multi-plant

Integration of process planning and scheduling is one of the most important functions to support flexible planning in a multi-plant. The planning and scheduling are actually interrelated and should be solved simultaneously. In this paper, we propose an advanced process planning and scheduling model for the multi-plant. The objective of the model is to decide the schedules for minimizing makespan and operation sequences with machine selections considering precedence constraints, flexible sequences, and alternative machines. The problem is formulated as a mathematical model, and an evolutionary algorithm is developed to solve the model. Numerous experiments are carried out to demonstrate the efficiency of the proposed approach.     

Joint determination of order quantity and reorder point of continuous review model under quantity and freight rate discounts

The increased emphasis on transportation costs has enhanced the need to develop models with transportation consideration explicitly. However, in stochastic inventory models, the transportation cost is considered implicitly as part of fixed ordering cost and thus is assumed to be independent of the size of the shipment. As such, the effect of the transportation and purchasing costs are not adequately reflected in final planning decisions. In this paper, transportation and purchasing considerations are integrated with continuous review inventory model. The objective is to view the system as an integrated whole and determine the lot size and reorder point which minimize the expected total cost per unit time. In addition, procedures are developed to solve the proposed models. Numerical experiments are also performed to explore the effect of key parameters on lot size, reorder point and expected total cost. The new models have a significant impact on lot size, reorder point and expected total cost. Savings up to 17.15% of the expected total cost are realized when using the proposed models.     

A dynamic two-segment partial backorder control of (r,Q) inventory system

Inventory management involves determination of shortage policy. It specifies the conditions for losing or backordering a demand. Alternative policies include pure backorder, pure lost sales, and partial backorder (using a single backorder control limit). When the backorder-cost is time dependent it makes sense to modify the backorder-limit over time. Thus, a new form of partial backorder policy (PB2) with two-segment backorder control limits is introduced. The traditional policies mentioned above, are special cases of PB2. Hence, we provide a unified framework for studying different policies that deal with shortage. The PB2 problem is formulated and solved as a discrete time, stochastic constrained control problem. Its performance is numerically compared with the simpler alternative policies. In some cases its cost savings, versus the best of PB and PL, exceeds 15%, and 7% versus a single backorder limit policy. The economical advantage is significant over a wide range of the problem parameters.Scope and purposeThis paper develops an expanded framework for modeling shortages in inventory management. It recognizes that optimal backordering strategy may change over time during an “out-of-stock” period. The paper is motivated by experience in the chemical industry in which, the cost of backordering is highly time related. Inventory managers, in this industry, consider to lose sales initially (once they run out of stock) and begin to backorder demand later as they approach the replenishment time. A two-segment partial backorder (r,Q) model is introduced and solved. Pure backorder (PB), pure lost sales (PL), and partial backorder (using a single backorder limit), are all special cases of the proposed model. The problem is formulated and solved as a discrete time, stochastic constrained control problem. Its performance is numerically compared with the simpler alternative policies. In some cases its cost savings, versus the best of PB and PL, exceeds 15%, and 7% versus a single backorder limit policy. The economical advantage is significant over a wide range of the problem parameters. The partial backorder policy we propose is not only different from those in the literature, but it provides new control flexibility.     

Analytic network process and multi-period goal programming integration in purchasing decisions

This paper presents a multi-period inventory lot sizing scenario, where there is single product and multiple suppliers. By considering multi-period planning horizon, an integrated approach of Archimedean Goal Programming (AGP) and Analytic Network Process (ANP) is suggested. This integrated approach proposes a two-stage mathematical model to evaluate the suppliers and to determine their periodic shipment allocations given a number of tangible and intangible criteria. In the evaluation stage, the suppliers are evaluated according to 14 criteria that are involved in four control hierarchies; benefit, opportunity, cost and risk (BOCR). In the shipment stage, a multi objective mixed integer linear programming (MOMILP) model is described to solve the order allocation problem. This MOMILP model is suggested to achieve target values of periodic goals: budget, aggregate quality, total value of purchasing (TVP) and demand over the planning horizon, without exceeding vendor production capacities. This multi-period model is solved by using AGP. Finally some computational experiments are conducted to test the performance of the proposed method.     

Production planning and worker training in dynamic manufacturing systems

Production planning is a vital activity in any manufacturing system, and naturally implies assigning the available resources to the required operations. This paper develops and analyzes a comprehensive mathematical model for dynamic manufacturing systems. The proposed model integrates production planning and worker training considering machine and worker time availability, operation sequence and multi-period planning horizon. The objective is to minimize machine maintenance and overhead, system reconfiguration, backorder and inventory holding, training and salary of worker costs. Computational results are presented to verify the proposed model.     

Stochastic (Q, r) inventory model with customer reneging

This paper presents a stochastic inventory model for situations in which, during a stockout period, unsatisfied demands are initially backordered but may renege (leave) probabilistically at the rate ρ to be filled elsewhere. The model is suggested by the customers' different reactions to a stockout condition: some patient customers wait until their demand is satisfied, while other impatient or urgent customers cannot wait long and have to fill their demand from another source. The cost of a backorder is assumed to be proportional to the length of time for which the backorder exists, and a fixed penalty cost is incurred per unit of lost demand. Based on a heuristic treatment of a lot-size reorder-point policy, a mathematical model representing the average annual cost of operating the inventory system is developed. The optimal operating policy variables minimizing the average annual cost can be calculated iteratively. At the extremes when ρ = 0 and ρ = ξ, the model presented reduces to the usual backorders and lost sales case, respectively.     

A Stochastic Vehicle Routing Problem with Travel Time Uncertainty: Trade-Off Between Cost and Customer Service

On-time shipment delivery is critical for just-in-time production and quick response logistics. Due to uncertainties in travel and service times, on-time arrival probability of vehicles at customer locations can not be ensured. Therefore, on-time shipment delivery is a challenging job for carriers in congested road networks. In this paper, such on-time shipment delivery problems are formulated as a stochastic vehicle routing problem with soft time windows under travel and service time uncertainties. A new stochastic programming model is proposed to minimize carrier’s total cost, while guaranteeing a minimum on-time arrival probability at each customer location. The aim of this model is to find a good trade-off between carrier’s total cost and customer service level. To solve the proposed model, an iterated tabu search heuristic algorithm was developed, incorporating a route reduction mechanism. A discrete approximation method is proposed for generating arrival time distributions of vehicles in the presence of time windows. Several numerical examples were conducted to demonstrate the applicability of the proposed model and solution algorithm.     

Inventory model with partial backorders

This article presents a deterministic inventory model for situations in which, during the stockout period, a fraction j8 of the demand is backordered and the remaining fraction 1 — β is lost. By defining a time proportional backorder cost and a fixed penalty cost per unit lost, a convex objective function representing the average annual cost of operating the inventory system is obtained. The optimal operating policy variables are calculated directly. At the extremes β = 1 and β = 0 the model presented reduces to the usual backorders and lost sales case, respectively.     

An integrated production and inventory model for a system comprising an assembly supply chain and a distribution network

This study investigates the production and inventory problem for a system comprising an assembly supply chain and a distribution network. A uniform lot size is produced uninterruptedly with a single setup at each production stage. Equal-sized batch shipment policy is applied to the whole system and the number of batches can be varied. All retailers have agreed on a joint replenishment policy with a common replenishment cycle. The objective is to determine the optimal common replenishment cycle, the number of batches of each production stage and retailer, all of which minimises the integrated total cost. Moreover, a new concept is introduced; namely, critical replenishment cycle. The replenishment cycle division (RCD) and recursive tightening (RT) methods are then developed to obtain the optimal solutions to the subject problem. Two theorems are verified to ensure the solutions obtained by the RCD and RT methods reaching the global optimum. An example is presented to illustrate the procedures involved in the RCD and RT methods.     

Optimal determination of the process means,process tolerances,and resetting cycle for process planning under process shifting

A proper process planning can significantly improve a producer’s competitiveness in regard to delivering high-quality and low-cost products with short development-cycle time. Because of process shifting, the produced quality may change during a production run and lead to early product failures. Hence, to compensate for such process shifting, there is a need to determine the optimal resetting cycle before the next setup as well as the initial settings at the beginning of a production run. As the process tolerance is one of the key elements in the production process, determination of the process tolerance must also be considered. Due to the interdependence among decision variables, a model for process planning is proposed to simultaneously determine the initial setting, process tolerance, and resetting cycle, so that the average total cost, in a period of resetting cycle, which includes the setup cost, quality loss, failure cost and tolerance cost, is minimized under process-capability limits, functionality requirements, and conforming rate restrictions.     

Annual production budget in the beverage industry

Driven by a real-world application in the beverage industry, this paper provides a design of a new VNS variant to tackle the annual production budget problem. The problem consists of assigning and scheduling production lots in a multi-plant environment, where each plant has a set of filling lines that bottle and pack drinks. Plans also consider final product transfers between the plants. Our algorithm fixes setup variables for family of products and determines production, inventory and transfer decisions by solving a linear programming (LP) model. As we are dealing with very large problem instances, it is inefficient and unpractical to search the entire neighborhood of the incumbent solution at each iteration of the algorithm. We explore the sensitivity analysis of the LP to guide the partial neighborhood search. Dual-reoptimization is also used to speed-up the solution procedure. Tests with instances from our case study have shown that the algorithm can substantially improve the current business practice, and it is more competitive than state-of-the-art commercial solvers and other VNS variants.