An optimization model for the design of a capacitated multi-product reverse logistics network with uncertainty

In this work the design of a reverse distribution network is studied. Most of the proposed models on the subject are case based and, for that reason, they lack generality. In this paper we try to overcome this limitation and a generalized model is proposed. It contemplates the design of a generic reverse logistics network where capacity limits, multi-product management and uncertainty on product demands and returns are considered. A mixed integer formulation is developed which is solved using standard B&B techniques. The model is applied to an illustrative case.     

A new VRPPD model and a hybrid heuristic solution approach for e-tailing

We analyze a business model for e-supermarkets to enable multi-product sourcing capacity through co-opetition (collaborative competition). The logistics aspect of our approach is to design and execute a network system where “premium” goods are acquired from vendors at multiple locations in the supply network and delivered to customers. Our specific goals are to: (i) investigate the role of premium product offerings in creating critical mass and profit; (ii) develop a model for the multiple-pickup single-delivery vehicle routing problem in the presence of multiple vendors; and (iii) propose a hybrid solution approach. To solve the problem introduced in this paper, we develop a hybrid metaheuristic approach that uses a Genetic Algorithm for vendor selection and allocation, and a modified savings algorithm for the capacitated VRP with multiple pickup, single delivery and time windows (CVRPMPDTW). The proposed Genetic Algorithm guides the search for optimal vendor pickup location decisions, and for each generated solution in the genetic population, a corresponding CVRPMPDTW is solved using the savings algorithm. We validate our solution approach against published VRPTW solutions and also test our algorithm with Solomon instances modified for CVRPMPDTW.     

Supply chain network downsizing with product line pruning using a new demand substitution

This paper presents an optimization model for downsizing a multi-product supply chain facing bankruptcy risk, where multi-functional production facilities are shared for producing a group of substitutable products. In order to determine the potential demand after discontinuation of certain product types, the proposed mixed integer programming model incorporates a new general formulation of demand substitution, which allows arbitrary demand diversion and arbitrary replacement rates between products under investigation. The new substitution formulation enables considering uneven substitutions for supply chain network design and therefore it extends currently used substitution approaches. A series of systematically generated downsizing cases confirm the validity of the here proposed approach, and illustrate how downsized chains can successfully adopt to the new circumstances.     

Production planning via scenario modelling

Several Linear Programming (LP) and Mixed Integer Programming (MIP) models for the production and capacity planning problems with uncertainty in demand are proposed. In contrast to traditional mathematical programming approaches, we use scenarios to characterize the uncertainty in demand. Solutions are obtained for each scenario and then these individual scenario solutions are aggregated to yield a nonanticipative or implementable policy. Such an approach makes it possible to model nonstationarity in demand as well as a variety of recourse decision types. Two scenario-based models for formalizing implementable policies are presented. The first model is a LP model for multi-product, multi-period, single-level production planning to determine the production volume and product inventory for each period, such that the expected cost of holding inventory and lost demand is minimized. The second model is a MIP model for multi-product, multi-period, single-level production planning to help in sourcing decisions for raw materials supply. Although these formulations lead to very large scale mathematical programming problems, our computational experience with LP models for real-life instances is very encouraging.     

两个约束条件下允许外购的多产品报童问题

研究在资源和预算约束条件下允许外购的多产品报童问题.为解决因资源有限而引起的缺货问题,允许外购,外购的最大可得到量是给定的.建立了在非零延迟时间外购情况下以求总体花费最小值为目标函数的的优化模型,分析了模型的结构特征,结合最优化理论,利用可行方向方法对模型进行了求解.数值结果表明了模型的合理性和算法的有效性.     

Production planning with uncertainty in the quality of raw materials: a case in sawmills

Motivated by sawmill production planning, this paper investigates multi-period, multi-product (MPMP) production planning in a manufacturing environment with non-homogeneous raw materials, and consequently random process yields. A two-stage stochastic program with recourse is proposed to address the problem. The random yields are modelled as scenarios with stationary probability distributions during the planning horizon. The solution methodology is based on the sample average approximation (SAA) scheme. The stochastic sawmill production planning model is validated through the Monte Carlo simulation. The computational results for a real medium capacity sawmill highlight the significance of using the stochastic model as a viable tool for production planning instead of the mean-value deterministic model, which is a traditional production planning tool in many sawmills.     

A forward and reverse logistics shipment planning model

Many supply chains contain both forward and reverse logistics flows where forwarders are often asked to manage forward and reverse logistics activities in a cost-efficient manner. Reverse logistics jobs are different from forward logistics jobs, apart from the physical movement directions, and they have different logistics service requirements that usually require special facility setups. The choice of reverse logistics centres is also an important cost saving factor in a supply chain network. We consider cost saving activities through combining transportation activities and logistics activities in forward and reverse logistics jobs. A mixed 0–1 LP model is proposed to solve the shipment planning problem and the choice of reverse logistics centre. Managerial issues in implementation are discussed in an illustrative case.     

A new continuous model for multiple re-entrant manufacturing systems

The semiconductor manufacturing systems that involve a large number of products and many steps can be modeled through conservation laws for a continuous density variable on production processes. In this paper, the basic partial differential equation (PDE) models for single-product re-entrant manufacturing systems are proposed first. However, through the validation of numerical examples, the basic continuous models do not perform well for single-product re-entrant systems. Then, a new state equation that takes into account the re-entrant degree of a product is introduced to improve the basic continuous models. The applicability of the modified continuous model is illustrated through numerical examples. The influence of the influx variation on the outflux is also discussed. With the changes of influx, the outflux has a reverse phenomenon. Based on the new state equation, the continuous model for multi-product re-entrant systems with different priorities is established, and an example is provided to illustrate the applicability of the new continuous model.     

Jointly pricing and ordering for a multi-product multi-constraint newsvendor problem with supplier quantity discounts

We present an extension to the multi-product newsvendor problem by incorporating the retailer’s pricing decision as well as considering supplier quantity discount. The objective is to maximize the expected profit of the retailer through jointly determining the ordering quantities and selling prices for the products, subject to multiple capacity constraints. We formulate the problem as a Generalized Disjunctive Programming (GDP) model and develop a Lagrangian heuristic approach for its solution. Randomly produced instances involving up to 1000 products are used to test the proposed approach. Computational results show that the Lagrangian heuristic approach can present very good solutions to all instances in reasonable time.     

Capacity planning with congestion effects

Important operational performance measures for a successful firm include not only price and quality, but also fast and on time delivery of customer orders. Capacity is a key issue in determining the lead time from customer order to delivery. However, capacity planning models seldom consider the impact of capacity levels on lead time performance. An important characteristic of this paper is the incorporation of congestion effects and their impact on lead time in making capacity acquisition decisions. It is especially important in a make-to-order environment, where customer orders arrive randomly and lead to high variability and congestion. This work was motivated by our observations of such tradeoffs at firms in several industries. We present a model to make equipment choice decisions in a multi-product, multi-machine, and single-stage production environment with congestion effects. The model is a nonlinear integer program. We present a heuristic solution procedure for this problem, which is based on a lower bound for the formulation that can be solved efficiently. The computational study shows that the solution procedure is quite effective in solving industry size problems. We illustrate the application of the model using data from a chemical-testing laboratory. We also discuss various extensions of the model.     

Service level robustness in stochastic production planning under random machine breakdowns

In this paper, we consider a multi-period, multi-product production planning problem where the production rate and the customer service level are random variables due to machine breakdowns. In order to determine robust production plans, constraints are introduced in the stochastic capacitated lot-sizing problem to ensure that a pre-specified customer service level is met with high probability. The probability of meeting a service level is evaluated by using the first passage time theory of a Wiener process to a boundary. A two-step optimization approach is proposed to solve the developed model. In the first step, the mean-value deterministic model is solved. Then, a method is proposed in the second step to improve the probability of meeting service level. The resulting approach has the advantage of not being a scenario-based one. It is shown that substantial improvements in service level robustness are often possible with minimal increases in expected cost.     

A stochastic bi-objective location model for strategic reverse logistics

In this paper we propose a comprehensive model for reverse logistics planning where many real-world features are considered such as the existence of several facility echelons, multiple commodities, choice of technology and stochasticity associated with transportation costs and waste generation. Moreover, we adopt a bi-objective model for the problem. First, the cost for building and operating the network is to be minimized. Second, the obnoxious effect caused by the reverse network facilities is also to be minimized. A two-stage stochastic bi-objective mixed-integer programming formulation is proposed, in which the strategic decisions are considered in the first stage and the tactical/operational decisions in the second one. A set of different scenarios is considered, and the extensive form of the deterministic equivalent problem is presented. This model is tested with a case study based on some data from the Spanish province of Cordoba. Nondominated solutions are obtained by combining the two different objectives and by using a general solver.     

An interactive fuzzy goal programming approach for multi-period multi-product production planning problem

This study addresses an interactive multiple fuzzy goal programming (FGP) approach to the multi-period multi-product (MPMP) production planning problem in an imprecise environment. The proposed model attempts to simultaneously minimize total production costs, rates of changes in labor levels, and maximizing machine utilization, while considering individual production routes of parts, inventory levels, labor levels, machine capacity, warehouse space, and the time value of money. Piecewise linear membership functions are utilized to represent decision maker’s (DM’s) overall satisfaction levels. A numerical example demonstrates the feasibility of applying the proposed model to the MPMP problem. Furthermore, the proposed interactive approach facilitates the DM with a systematic framework of decision making process which enables DM to modify the search direction to reach the most satisfactory results during solving process.     

Speculative production and anticipative reservation of reactive capacity by a multi-product newsvendor

In this paper the optimal sourcing decisions of a multi-product newsvendor prior to the selling season of the products are studied. To satisfy the uncertain demands, the newsvendor can either utilize speculative production, or anticipatively reserve capacity. During the selling season when demand has become known, the newsvendor can utilize its reserved capacity and reactively satisfy demand uncovered by its speculative production. For the case where capacity for speculative production may be limited, but potential reservation of reactive capacity is unlimited two capacity reservation settings are analyzed and compared. In the first one capacity for each product has to be reserved separately, while in the second setting one joint capacity reservation for all products is permitted which can then be allocated to the different products optimally during the selling season. For the case of separate individual reservations the optimal strategies are analytically derived and structural insights concerning their existence are presented. As the model allowing for joint reservation can not be tackled analytically in general an approximation based on an LP formulation is used. Through a numerical example insights on the value of the increased flexibility induced by joint reservation, the cost-premium acceptable for joint reservation and the relative levels of capacity reservation in the two settings are given.     

Reverse logistics network design for product recovery and remanufacturing

Due to environmental concerns, reverse logistics now is becoming an important strategy to increase customer satisfaction. This research develops a generic mixed integer nonlinear programming model (MINLP) for reverse logistics network design. This is a multi-echelon reverse logistics model. It maximizes total profit by handling products returned for repair, remanufacturing, recycling, reuse, or incineration/landfill. A hybrid genetic algorithm (GA) is proposed to solve the problem. The designed model is validated and tested by using a real-life example of recycling bulk waste in Taoyuan City, Taiwan. Sensitivity analyses are conducted on various parameters to illustrate the capabilities of the proposed model. Post-optimality analysis and comparison show that the proposed model performs better than current reverse logistic operations and the proposed hybrid GA demonstrates the efficiency of solving the complex reverse logistics problem.     

Analysis of a two-stage telecommunication supply chain with technology dependent demand

We analyze a two-stage telecommunication supply chain consisting of one operator and one vendor under a multiple period setting. The operator faces a stochastic market demand which depends on technology investment level. The decision variables for the operator are the initial technology investment level and the capacity of the network for each period. The capacity that the operator installs in one period also remains available in subsequent periods. The operator can increase or decrease the available capacity at each period. For this model, an algorithm to find the centralized optimal solution is proposed. A profit sharing contract where firms share both the revenue and operating costs generated throughout the periods along with initial technology investment is suggested. Also a coordinating quantity discount contract where the discount on the price depends on the total installed capacity is designed. The case where the vendor decides on the technology investment level and the operator decides on the capacity of the network is also analyzed and it is shown that this game has a unique Nash equilibrium.     

Capacitated replenishment and disposal planning for multiple products with resalable returns

We consider a replenishment and disposal planning problem (RDPP) that arises in settings where customer returns are in as-good-as-new condition. These returns can be placed into inventory to satisfy future demand or can be disposed of, in case they lead to excess inventory. Our focus is on a multi-product setting with dynamic demands and returns over a finite planning horizon with explicit replenishment and disposal capacities. The problem is to determine the timing of replenishment and disposal setups, along with the associated quantities for the products, so as to minimize the total costs of replenishment, disposal, and inventory holding throughout the planning horizon. We examine two variants of the RDPP of interest both of which are specifically motivated by a spare part kitting application. In one variant, the replenishment capacity is shared among multiple products while the disposal capacity is product specific. In the other variant, both the replenishment and disposal capacities are shared among the products. We propose a Lagrangian Relaxation approach that relies on the relaxation of the capacity constraints and develop a smoothing heuristic that uses the solution of the Lagrangian problem to obtain near-optimal solutions. Our computational results demonstrate that the proposed approach is very effective in obtaining high-quality solutions with a reasonable computational effort.     

Generalized minimal cost flow problem in fuzzy nature: An application in bus network planning problem

The aim of minimal cost flow problem (MCFP) in fuzzy nature, which is denoted with FMCFP, is to find the least cost of the shipment of a commodity through a capacitated network in order to satisfy imprecise concepts in supply or demand of network nodes and capacity or cost of network links. Fuzzy supply–demand may arise in real problems, where incomplete statistical data or simulation results are used. Also, variation in the cost or capacity of links is commonly happening. In the present paper, after defining a total order on LR type fuzzy numbers, three models are studied; MCFP with fuzzy costs, MCFP with fuzzy supply–demand and a combination of two cases. For the first model, scaling negative cycle cancelling algorithm, which is a polynomial time algorithm, is proposed. For the second model, “nominal flow” is introduced which provides an efficient scheme for finding fuzzy flow. For the third model, we present an exact and some heuristic methods. Numerical examples are illustrated to demonstrate the efficiency of the proposed schemes. Finally, an application of this viewpoint in bus network planning problem is provided.     

联合订货下基于ø-散度的多产品库存鲁棒优化模型

针对多产品联合库存决策问题,在市场需求不确定条件下,建立了考虑联合订货成本的多产品库存鲁棒优化模型。针对不确定市场需求,采用一系列未知概率的离散情景进行描述,给出了基于最小最大准则的鲁棒对应模型,并证明了(s,S)库存策略的最优性。进一步,在仅知多产品市场需求历史数据基础上,采用基于ø-散度的数据驱动方法构建了满足一定置信度要求的关于未知需求概率分布的不确定集。在此基础上,为获得(s,S)库存策略的相关参数,运用拉格朗日对偶方法将所建模型等价转化为易于求解的数学规划问题。最后,通过数值计算分析了Kullback-Leibler散度和Cressie-Read散度以及不同的置信水平下的多产品库存绩效,并将其与真实分布下应用鲁棒库存策略得到的库存绩效进行对比。结果表明,需求分布信息的缺失虽然会导致一定的库存绩效损失,但损失值很小,表明基于文中方法得到的库存策略能够有效抑制需求不确定性扰动,具有良好的鲁棒性。     

Hybrid simulated annealing and MIP-based heuristics for stochastic lot-sizing and scheduling problem in capacitated multi-stage production system

This paper addresses lot sizing and scheduling problem of a flow shop system with capacity constraints, sequence-dependent setups, uncertain processing times and uncertain multi-product and multi-period demand. The evolution of the uncertain parameters is modeled by means of probability distributions and chance-constrained programming (CCP) theory. A new mixed-integer programming (MIP) model with big bucket time approach is proposed to formulate the problem. Due to the complexity of problem, two MIP-based heuristics with rolling horizon framework named non-permutation heuristic (NPH) and permutation heuristic (PH) have been performed to solve this model. Also, a hybrid meta-heuristic based on a combination of simulated annealing, firefly algorithm and proposed heuristic for scheduling is developed to solve the problem. Additionally, Taguchi method is conducted to calibrate the parameters of the meta-heuristic and select the optimal levels of the algorithm’s performance influential factors. Computational results on a set of randomly generated instances show the efficiency of the hybrid meta-heuristic against exact solution algorithm and heuristics.