DETERMINISTIC APPROXIMATIONS FOR INVENTORY MANAGEMENT AT SERVICE FACILITIES

We consider the problem of finding optimal inventory policies for a service facility where the demand for inventory occurs during the provision of service (e.g., fixing a car in a repair shop). The paper formulates a model where both the demand and service rates are assumed to be constant and deterministic. Consequently a queue forms only during stockouts. In the first of two models analyzed, the service rate is assumed to be fixed and cannot be controlled by the service facility. The ability to use this simple, deterministic model to approximate systems with probabilistic arrival and/or service distributions is also analyzed. The second model relaxes the assumption of a fixed service rate. Optimal inventory policies are derived under linear costs over ordering, inventory holding, customer waiting, and the service rate.     

Location and allocation of service units on a congested network

We consider the problem of locating facilities and allocating servers on a congested network (LASCN). Demands for service that originate from the nodes are assumed to be Poisson distributed and the servers provide a service time that is exponentially distributed. The objective is to minimize the total cost of the system which includes a fixed installation cost, a variable server cost, a cost associated with travel time and a cost associated with the waiting time in the facility for all the customers. The problem is formulated using non-linear programming and subsequently analyzed. Results for exact and approximate solution approaches are reported. We also show that we can modify the approaches to solve the LASCN with constraints limiting both the travel time to the servers and the waiting time of customers.     

On a Two Facility Scheduling Problem with Sequence Dependent Processing Time

This paper is concerned with a problem involving two processing facilities where it is assumed that the two facilities are to process operations of a particular project or job. Some of the operations can only be performed by one of the facilities, some by the other, and the remaining operations, by either facility. Further, it is assumed that the processing times for all operations are sequence dependent as well as processor dependent. An algorithm is proposed which obtains minimum or near minimum completion time of all operations. Suitable computational experience is provided.     

A large-scale hybrid simulated annealing algorithm for cyclic facility layout problems

The cyclic facility layout problem (CFLP) is a special case of the dynamic facility layout problem (DFLP) in which there are several production periods and the production cycle repeats itself by going to the first period after the last one because of the seasonal nature of products. In this article, a mixed integer programming formulation is developed for the CFLP. In the DFLP literature, department shapes are assumed to be given or fixed. However, this assumption does not hold in the case of the CFLP because the facility size is limited and the area requirements of the departments change significantly throughout the planning horizon. Therefore, department dimensions and sizes are considered as decision variables in the CFLP. A large-scale hybrid simulated annealing algorithm (LS-HSA) is proposed to solve the formulated problem and shown to be effective and versatile as it can be applied to various facility layout problems.     

The Uncapacitated Facility Location Problem With Primary and Secondary Facility Requirements

We consider the problem of locating uncapacitated facilities among a set of potential sites to minimize cost of serving a number of demand points each requiring service from two different facilities. This problem has many potential applications. One such application is location of emergency service facilities where it is desirable to have a primary and back-up service facility wthin a certain distance from every district An efficient solution procedure is developed. This procedure is tested on a number of problems and computational results are reported. It is compared to a state of the art commercial linear/integer programming package and found to be around two orders of magnitude faster than this package. It is also compared to a state of the art special purpose agorithm for the simple uncapacitated facility location problem to investigate the computational implications of introducing secondary service requirements. The model is used to illustrate the effect of considering secondary service on the spatial characteristics of the optimal set of locations. The model is further demonstrated on a “real life” example with 625 demand points and 30 potential facility locations.     

Locating capacitated facilities to maximize captured demand

We consider the problem of locating a set of facilities on a network to maximize the expected number of captured demand when customer demands are stochastic and congestion exists at facilities. Customers travel to their closest facility to obtain service. If the facility is full (no more space in the waiting room), they attempt to obtain service from the next-closest facility not yet visited from its current position on the network. A customer is lost either when the closest facility is located too far away or all facilities have been visited. After formulating the model, we propose two heuristic procedures. We combine the heuristics with an iterative calibration scheme to estimate the expected demand rate faced by the facilities: this is required for evaluating objective function values. Extensive computational results are presented.     

Bi-objective facility expansion and relayout considering monuments

In this paper, the unequal area facility expansion and relayout problem is studied. The facility relayout problem is important since both manufacturing and service entities must modify their layouts over time when their operational characteristics change. A bi-objective approach is proposed to solve the relayout problem for cases of both a fixed facility area and an expanded facility area. Material handling costs and relayout costs are minimized using a tabu search meta-heuristic optimizer. This heuristic randomly alternates the objective function between the two objectives of the problem in each step and, by doing so, eliminates the difficulty of weighting and scaling the two objectives. The approach is flexible in handling various aspects of the problem such as stationary portions of departments (i.e., monuments), addition of new departments, and changes in existing department and facility areas. Computational experiments show that the bi-objective tabu search approach is effective and tractable. The use of the Pareto front of designs is demonstrated by showing a few approaches to analyzing the trade-offs between initial costs (relayout cost) and ongoing expenses (material handling costs).     

Optimization Models for Scheduling of Jobs

This work is motivated by a particular scheduling problem that is faced by logistics centers that perform aircraft maintenance and modification. Here we concentrate on a single facility (hangar) which is equipped with several work stations (bays). Specifically, a number of jobs have already been scheduled for processing at the facility; the starting times, durations, and work station assignments for these jobs are assumed to be known. We are interested in how best to schedule a number of new jobs that the facility will be processing in the near future. We first develop a mixed integer quadratic programming model (MIQP) for this problem. Since the exact solution of this MIQP formulation is time consuming, we develop a heuristic procedure, based on existing bin packing techniques. This heuristic is further enhanced by application of certain local optimality conditions.     

Optimal and Heuristic Facility Phase-out Strategies

This paper presents an efficient branch and bound algorithm and near optimal heuristic algorithms for solving the problem of withdrawing inventory and/or service facilities for a good or service whose overall demand is declining over time. In particular, this paper models the problem faced by a manager who must consider closing up to M initially open and operating support facilities as demand shifts and declines over a T period planning horizon. The criterion is minimization of total estimated discounted costs. The costs considered are the variable operating cost at each facility, the transportation costs between facilities and demand centers, and the costs to operate and close each facility. Computational results are presented for both the optimum finding and heuristic algorithms.     

Optimal control of servers in front and back rooms with correlated work

In this article we deal with the problem of optimal server allocation between the front and the back room of a service facility (for all states of the system) when the work in the back room is generated by the service provided in the front room. The servers are cross-trained and can switch between front room and back room tasks without any loss of productivity. We also determine the optimal number of servers required to meet certain service levels. Our service criteria is that both the mean number of customers waiting for service in the front room and the mean number of jobs (work) accumulated are bounded from above. We model the problem as a Markov decision problem and use linear programming to solve it.     

An integrated materials handling model for machine location in existing facilities

A machine location criterion is proposed for situations where machines must be located in existing facilities to manufacture new products. The location criterion is based on a measure of materials handling service. It is applicable when an existing, automated materials handling system is fully integrated within an existing manufacturing facility. The service level is measured by the expected rate of unsuccessful load transfers associated with a fixed production schedule, handling system, and assignment of machines to locations in a facility. An analytical model focused on the interfaces of automated materials handling systems is formulated to predict the corresponding service level associated with alternative machine locations in an existing facility. The model is illustrated through a sample problem which demonstrates how the specific operating characteristics of a typical automated materials handling system can be modelled to predict handling performance for alternative machine locations.     

Multi-commodity warehouse location and distribution planning with inventory consideration

We consider the problem of designing a distribution network for a logistics provider that acquires products from multiple facilities and then delivers those products to many retail outlets. Potential locations for consolidation facilities that combine shipments for cost reduction and service improvements are considered. The problem is formulated with direct shipment and consolidation opportunities. A novel mathematical model is derived to solve a complex facility location problem determining: (i) the location and capacity level of warehouses to open; (ii) the distribution route from each production facility to each retailer outlet; and (iii) the quantity of products stocked at each warehouse and retailer. A genetic algorithm and a specific problem heuristic are designed, tested and compared on several realistic scenarios.     

Economic lot scheduling problems incorporating a cost of using the production facility

This paper considers scheduling the production of several different items on a single machine with constrained capacity, commonly known as the economic lot scheduling problem (ELSP). Most traditional approaches for the ELSP consider the sum of the set-up cost and inventory holding cost and provide cyclic schedules that minimise this sum. In practice, there are not only costs for set-ups and inventory holding, but also costs for operating the production facility due to, for example, electricity, service, maintenance, tools, operators, etc, which depend on the number of hours the facility is operating per working day. In this paper, we modify the traditional cost function to include not only set-up and inventory holding cost but also a time variable cost for operating the production facility. The paper shows it is possible to adapt a previous heuristic procedure to this complemented cost. The model can help to determine cyclic schedules and the number of production hours per working day.     

MILP-based campaign scheduling in a specialty chemicals plant: a case study

Supply chain management in chemical process industry focuses on production planning and scheduling to reduce production cost and inventories and simultaneously increase the utilization of production capacities and the service level. These objectives and the specific characteristics of chemical production processes result in complex planning problems. To handle this complexity, advanced planning systems (APS) are implemented and often enhanced by tailor-made optimization algorithms. In this article, we focus on a real-world problem of production planning arising from a specialty chemicals plant. Formulations for finished products comprise several production and refinement processes which result in all types of material flows. Most processes cannot be operated on only one multi-purpose facility, but on a choice of different facilities. Due to sequence dependencies, several batches of identical processes are grouped together to form production campaigns. We describe a method for multicriteria optimization of short- and mid-term production campaign scheduling which is based on a time-continuous MILP formulation. In a preparatory step, deterministic algorithms calculate the structures of the formulations and solve the bills of material for each primary demand. The facility selection for each production campaign is done in a first MILP step. Optimized campaign scheduling is performed in a second step, which again is based on MILP. We show how this method can be successfully adapted to compute optimized schedules even for problem examples of real-world size, and we furthermore outline implementation issues including integration with an APS.     

基于服务剧场模型的社区文体设施服务设计研究

目的 通过服务设计思维与服务剧场模型来探究社区文体设施的服务接触,并提出社区文体设施的服务设计方向及改进策略。方法 以服务设计思维为出发点,采用服务剧场模型对社区文体设施服务中的利益相关者与服务接触进行梳理,并以此展开社会调研,归纳出当前文体设施的服务缺口;通过改进和完善服务接触,使服务流程更加完整、缜密,并进一步优化文体设施服务蓝图,提出设计思路。结论 社区文体公共设施服务的有效执行需要从更加全面、系统的服务设计视角出发,注重核心服务接触前期与核心服务接触后期的完整与连贯。通过整合利益相关者之间的沟通与协作、线上线下多渠道的信息传递,以及文体设施、活动空间、场地环境和周边配套设施的设立与规划,并以此构建新的服务蓝图与设计,从而为优化社区文体设施服务提供参考。     

Dynamic and static job allocation for multi-server systems

We consider the optimal assignment of groups of jobs to a fixed number of time periods over a finite horizon to minimize the total facility idling and job waiting costs. The capacity of the facility varies randomly in the sense that the time that each one of the multiple servers becomes available is random (servers arrive late). The service times are also random and are independent and identically distributed. With approximations, we formulate a dynamic optimization model for this problem. With a simple modification, we can apply this dynamic model to a static outpatient appointment problem. We propose two methods to compute the capacity distribution: (1) Poisson approximation and (2) simulation. While the Poisson approximation works well for exponential service times, the simulation scheme enables us to use the dynamic model without actually specifying the service time distribution. The performance measures of the schedules obtained with these two methods compare well with those of the optimal allocation obtained from (exhaustive) simulation. We also conduct numerical studies to investigate the dynamics between the idling and waiting costs ratio and the number of scheduling periods.     

Supply chain network design with unreliable suppliers: a Lagrangian relaxation-based approach

This paper deals with the integrated facility location and supplier selection decisions for the design of supply chain network with reliable and unreliable suppliers. Two problems are addressed: (1) facility location/supplier selection; and (2) facility location/supplier reliability. We first consider the facility location and supplier selections problem where all the suppliers are reliable. The decisions concern the selection of suppliers, the location of distribution centres (DCs), the allocation of suppliers to DCs and the allocation of retailers to DCs. The objective is to minimise fixed DCs location costs, inventory and safety stock costs at the DCs and ordering costs and transportation costs across the network. The introduction of inventory costs and safety stock costs leads to a non-linear NP-hard optimisation problem. To solve this problem, a Lagrangian relaxation-based approach is developed. For the second problem, a two-period decision model is proposed in which selected suppliers are reliable in the first period and can fail in the second period. The corresponding facility location/supplier reliability problem is formulated as a non-linear stochastic programming problem. A Monte Carlo optimisation approach combining the sample average approximation scheme and the Lagrangian relaxation-based approach is proposed. Computational results are presented to evaluate the efficiency of the proposed approaches.     

Equipment scheduling at mail processing and distribution centers

Mail Processing and Distribution Centers (P&DCs) run 24 hours a day, 7 days a week and are staffed by a skilled complement of full-time, part-time, and temporary employees. A recurrent problem faced by facility managers involves the development of daily schedules for the automation equipment used to process the mail. The ultimate goal is to minimize the labor costs associated with running the facility while ensuring that all service standards are met. The focus of this paper is on the equipment scheduling aspect of the problem. In particular, we seek a weekly schedule that satisfies all operational, technological, and legal constraints of the system at a minimum cost. The problem is modeled as a large-scale mixed-integer linear program and solved sequentially using a three-stage methodology. In each stage, a separate criterion is optimized and the corresponding objective function value is used as a constraint in subsequent stages. To ease the computational burden, two major enhancements are developed. The first is a pre-processor designed to reduce the number of integer variables; the second is a heuristic that uses the linear programming solution as a target and attempts to find a feasible integer point as close to it as possible. The methodology is demonstrated with data obtained from the Dallas P&DC. The computations indicate that for letter operations alone the annual savings will be on the order of $1.6 million per facility when the system is implemented nationwide over the next 3 years.     

An improved algorithm for solving a multi-period facility location problem

An exact algorithm for the multi-period facility location problem is proposed that efficiently integrates mixed-integer and dynamic programming methods. Two simplification procedures are introduced to reduce the size of the general multi-period facility location problem substantially. Because the proposed algorithm utilizes dynamic programming to obtain the optimal sequence over the entire planning horizon, many near-optimal solutions also become available that are extremely useful for postoptimality analysis. The solution method is tested and compared with a well-known procedure on several problems with varying conditions. The comparisons appear very promising, and the required CPU times by the proposed method are substantially reduced.     

Cyclic lot scheduling with sequence-dependent set-ups: a heuristic for disassembly processes

The importance of material and product recovery is steadily increasing, mainly due to customer expectations and take-back obligations. Disassembly is a major operation in material and product recovery, since returned products are often disassembled to separate materials and components. The paper considers the problem of scheduling several items on a single disassembly facility. It develops a cyclic lot-scheduling heuristic for disassembly processes with sequence- dependent set-ups, resulting in disassembly frequencies for the items. Additionally, the way the problem is formulated allows calculation of the profitable use of the facility. The disassembly frequencies and the profitable use of the facility are used to create a cyclic schedule.