Weekly scheduling in the service industry: an application to mail processing and distribution centers

This paper addresses the midterm planning problem that arises at various service facilities staffed by full-time and part-time employees. In response to updated demand forecasts, expected leave, training assignments, and other contingencies, weekly adjustments are often required to better match available personnel with demand over the planning horizon. Unlike manufacturing where uniform 8-hour shifts are the rule, service organizations may experience several busy periods during the day that do not fit a standard shift. In such cases, supervisors must adjust employee schedules by assigning overtime, increasing the number of part-time hours, and calling in temporary workers. The situation is complicated by union contracts, labor rules, and company policies. To find solutions that can be implemented in a real-world environment, a two-phase approach was developed. In the first phase, the adjustment problem is formulated as a large-scale integer program and solved with a commercial code for those cases in which demand increases are limited to no more than 10% above the baseline. For the more general case, a new target-based heuristic was designed with the goal of finding good feasible solutions. In the second phase, the shift schedules are post-processed to provide daily assignments for each worker. An analysis of the problem arising in the first phase is presented for an application involving weekly scheduling at a mail processing and distribution center. The results indicate that high quality solutions can be obtained within a matter of minutes.     

Replanning working time under annualised working hours

Using annualised hours (i.e., distributing working hours irregularly over a year) grants a company the flexibility needed to meet the seasonal nature of demand. Since annualised hours can lead to a worsening of the staff's working conditions, many laws and collective bargaining agreements contain constraints that affect the distribution of working time. In the past few years, efforts have been made to develop methods for optimally solving planning problems involving annualised working hours. However, to our knowledge, the problem of replanning work time with annualised working hours has not been addressed in the literature. Herein, we explore different ways of achieving said replanning, using mixed-integer linear programming models. Two main objectives are considered: the cost of the new plan and the stability of the scheduling of workers’ working time. Solving the models for various scenarios yields the quantitative information that is needed to replan an annualised hours system.     

Optimal selection of application loading on cloud services

There is a need for identifying computing power hours and storage utilisation along with total cost optimisation. The present paper focuses on optimal selection of application loading process on the cloud services considering relevant factors. Using this model, small companies that plan to develop applications and use cloud services may determine cost and optimal selection of service by taking into account its own as well as provider’s perspectives into consideration. The paper consists of four stages. First stage deals with the estimation of required computing power hours in the planned duration. Second stage relates to the calculation of storage capacity. Third stage corresponds to the formation of multi objective goal programme to prioritise computing power hours and storage utilisation requirements of applications and optimise total cost of usage. Finally, fourth stage deals with the mixed integer non-linear programming to minimise total cost considering other variable factors. For small application developers who cannot afford in-house IT infrastructure, we find an optimal framework for allocating number of applications on cloud services such as Infrastructure as a Service and Platform as a Service. For ease in planning, the user company can quickly decide corresponding number of applications at appropriate services, and at the same time can reduce overall usage cost. With the help of proposed method, the service provider may keep a suitable inventory of cores to provide backup computing power and storage capacity. This adds value to developers also, as company can plan for their operations corresponding to the business growth.     

LABORATORY STUDIES OF REPETITIVE WORK. II : PROGRESS REPORT ON RESULTS FROM TWO SUBJECTS

This experiment is the first or a series undertaken to test proposals put forward earlier by the first author that in repetitive work (i) output would be higher and variability less if breaks were given at the end of an actite period (period of optimum performance) rather than at the point when output decreased; (ii) the end of an actile period would be indicated by the onset of irregularity in performance which could be determined by the incidence longcycle times in unpaced work and an increase in the number of missed cycles in paced work; and (iii) the length of an actile period will depend on the demand made by the job and upon the capacity of the worker to meet the demand (her actility)

Results from two subjects tested for a period of 3 1/ 2 months suggest that proposal (i) is correct. A condition in which two breaks were given at limes indicated by an increase in long times in unpaced performance gave a significantly better output and lower variance than a condition in which one break was given at a time indicated by a fall in output. Both subjects had relatively fewer misses in the paced condition when three breaks were given than when working continuously

The technique for obtaining long times in unpaced work which formed part of (ii) was found to be practical and a simpler method was devised. The results obtained seem to confirm that the method has validity. No definite conclusions can be drawn on paced work

There is some tentative confirmation of (iii); in the paced condition the actile period seems to have been 1 hour compared with 1 1/4hours in the unpaced condition. Further, the better worker gave her best unpaced performance when rest was given after 1 1/4 hours whereas the less good worker did best when rest was given after 1 hour.     

An approximate dynamic programming approach for a product distribution problem

This paper proposes an approximate dynamic programming-based method for optimizing the distribution operations of a company manufacturing a certain product in numerous plants and distributing it to different regional markets for sale. The production at each plant and in each time period follows a nonstationary stochastic process. The product can be stored at the plants or be shipped to a regional market to serve the random demand. The proposed solution method formulates the problem as a dynamic program and uses approximations of the value function. We develop a tractable procedure to compute the marginal worth of a unit of inventory at a production plant. This quantity is used to update the value function approximations in an iterative improvement scheme. We numerically show that our method yields high quality solutions.     

A Synthesis of Tactical Fleet Planning Models for the Car Rental Industry

Daily tactical planning of the vehicle fleet is critical for a car rental business. In this decision-making process planners have to address the conflicting concerns of field management, namely, assuring adequate vehicle availability to satisfy customer demand while maintaining a high degree of utilization for each car in the fleet; this is achieved by the appropriate fleet deployment among car rental locations. This work was inspired by a series of problems encountered by the decision-makers of a major US car rental company. We first present the formulation of the tactical fleet planning model. Based on its structure, we decompose the model into a fleet deployment model and a transportation model. We develop optimal conditions for both subproblems and then we present a heuristic to reduce the gap from optimality for the complete model. We further present the application of the entire solution methodology via a case analysis for the State of Florida. Finally, we develop three extensions to the fleet deployment model to capture the cost of unsatisfied demand and fleet surplus, the service level, and a general price-demand function. We provide optimal closed-form conditions for all the extensions.     

Base position planning of mobile manipulators for assembly tasks in construction environments

With good mobility and flexibility, mobile manipulators have shown broad applications in construction scenarios. Base position (BP) planning, which refers to the robot autonomously determining its working station in the environment, is an important technique for mobile manipulators when performing the construction assembly task, especially in a large-scale construction environment. However, the BP planning process is tedious and time-consuming for a human worker to carry out. Thus, to improve the efficiency of construction assembly tasks, a novel BP planning method is proposed in this paper, which can lead to appropriate BPs and minimize the number of BPs at the same time. Firstly, the feasible BP regions are generated based on the grid division and the variable workspace of the mobile manipulator. Then, the positioning uncertainties of the mobile manipulator are considered in calculating the preferred BP areas using clustering. Lastly, a set coverage optimization model is established to obtain the minimum number of BPs using an optimization algorithm according to the greedy principle. The simulated experiment based on a 9-degree of free (DoF) mobile manipulator has been performed. The results illustrated that the time for BP planning was significantly reduced and the number of BPs was reduced by 63.41% compared to existing manual planning, which demonstrated the effectiveness of the proposed method. The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-022-00411-3     

A CAPACITY PLANNING MODEL FOR A MULTI-PRODUCT FACILITY

A deterministic capacity planning model for a multi-product facility is analyzed to determine (he sizes to be expanded (or disposed of) in each period so as to supply the known demand for N products on time and to minimize the total cost incurred over a finite planning horizon of T periods. The model assumes that each capacity unit of the facility simultaneously serves a prespecified number of demand units of each product, that costs considered include capacity expansion costs, capacity disposal costs, and excess (idle) capacity holding costs, and all the associated cost functions are nondecreasing and concave, and that backlogging is not allowed. The structure of an optimal solution is characterized and then used in developing an efficient dynamic programming algorithm that finds optimal capacity planning policies. The required computational effort is a polynomial function of N and T.     

Multi-objective cell formation and production planning in dynamic virtual cellular manufacturing systems

This article presents a fuzzy goal programming-based approach for solving a multi-objective mathematical model of cell formation problem and production planning in a dynamic virtual cellular manufacturing system. In a dynamic environment, the product mix and part demand change over a planning horizon decomposed into several time periods. Thus, the cell formation done for one period may be no longer efficient for subsequent periods and hence reconfiguration of cells is required. Due to the variation of demand and necessity of reconfiguration of cells, the virtual cellular manufacturing (VCM) concept has been proposed by researchers to utilise the benefits of cellular manufacturing without reconfiguration charges. In a VCM system, machines, parts and workers are temporarily grouped for one period during which machines and workers of a group dedicatedly serve the parts of that group. The only difference of VCM with a real CM is that machines of the same group are not necessarily brought to a physical proximity in VCM. The virtual cells are created periodically depending on changes in demand volumes and mix, as new parts accumulate during a planning horizon. The major advantage of the proposed model is the consideration of demand and part mix variation over a multi-period planning horizon with worker flexibility. The aim is to minimise holding cost, backorder cost and exceptional elements in a cubic space of machine–part–worker incidence matrix. To illustrate the applicability of the proposed model, an example has been solved and computational results are presented.     

Combined strategic and operational planning – an MILP success story in chemical industry

We describe and solve a real world problem in chemical industry which combines operational planning with strategic aspects. In our simultaneous strategic & operational planning (SSDOP) approach we develop a model based on mixed-integer linear (MILP) optimization and apply it to a real-world problem; the approach seems to be applicable in many other situations provided that people in production planning, process development, strategic and financial planning departments cooperate. The problem is related to the supply chain management of a multi-site production network in which production units are subject to purchase, opening or shut-down decisions leading to an MILP model based on a time-indexed formulation. Besides the framework of the SSDOP approach and consistent net present value calculations, this model includes two additional special and original features: a detailed nonlinear price structure for the raw material purchase model, and a detailed discussion of transport times with respect to the time discretization scheme involving a probability concept. In a maximizing net profit scenario the client reports cost saving of several millions US$. The strategic feature present in the model is analyzed in a consistent framework based on the operational planning model, and vice versa. The demand driven operational planning part links consistently to and influences the strategic. Since the results (strategic desicions or designs) have consequences for many years, and depend on demand forecast, raw material availability, and expected costs or sales prices, resp., a careful sensitivity analysis is necessary showing how stable the decisions might be wit h respect to these input data.     

A Two-Stage Planning Model for Power Scheduling in a Hydro-Thermal System Under Uncertainty

A two-stage stochastic programming model for the short- or mid-term cost-optimal electric power production planning is developed. We consider the power generation in a hydro-thermal generation system under uncertainty in demand (or load) and prices for fuel and delivery contracts. The model involves a large number of mixed-integer (stochastic) decision variables and constraints linking time periods and operating power units. A stochastic Lagrangian relaxation scheme is designed by assigning (stochastic) multipliers to all constraints that couple power units. It is assumed that the stochastic load and price processes are given (or approximated) by a finite number of realizations (scenarios). Solving the dual by a bundle subgradient method leads to a successive decomposition into stochastic single unit subproblems. The stochastic thermal and hydro subproblems are solved by a stochastic dynamic programming technique and by a specific descent algorithm, respectively. A Lagrangian heuristics that provides approximate solutions for the primal problem is developed. Numerical results are presented for realistic data from a German power utility and for numbers of scenarios ranging from 5 to 100 and a time horizon of 168 hours. The sizes of the corresponding optimization problems go up to 400.000 binary and 650.000 continuous variables, and more than 1.300.000 constraints.     

Simulation and performance evaluation of partially and fully integrated sales and operations planning

This article presents rolling horizon simulation models and performance analysis of partially and fully integrated sales and operations planning (S&OP) against traditional decoupled planning in a multi-site make-to-order (MTO) based manufacturing supply chain. Three simulation models are developed illustrating, respectively, the fully integrated S&OP model, which integrates cross-functional planning of sales, production, distribution, and procurement centrally; the partially integrated S&OP model, in which the joint sales and production planning is performed centrally while distribution and procurement are planned separately at each site; and the decoupled planning model, in which sales planning is carried out centrally while production, distribution, and procurement are planned separately and locally. A solution procedure is provided for each model so that a more realistic planning process can be simulated. Performances of rolling horizon simulation models are evaluated against those of the fixed horizon deterministic models. The results demonstrate that while deterministic models are important for theoretical studies, they are insufficient for decision support and performance evaluations in a real business environment. A rolling horizon simulation model is required to provide more realistic solutions. The effects of demand uncertainties and forecast inaccuracies are incorporated in the evaluation. The study is carried out based on a real industrial case of a Canadian-based oriented strand board (OSB) manufacturing company.     

A stochastic production planning model under uncertain seasonal demand and market growth

This paper proposes a stochastic production planning model for an international enclosure manufacturing company with seasonal demand and market growth uncertainty. The company purchases material and subassembly from overseas and long lead times have been observed. To prevent excess inventory and stockout, the company is required to forecast its demand and project its purchasing decisions and production load to its key suppliers in an effort to reduce risks for both parties. To assist purchasing and production decisions, a two-stage stochastic production planning model that explicitly includes uncertainty is developed with the goal of minimising the total production, inventory, and overtime costs under all scenarios. The model is solved using real data from the company and results have demonstrated the effectiveness of the model compared with various deterministic models. Parametric analyses are performed to derive managerial insights related to issues such as overtime usage, inventory holding costs and the proper selection of scenarios under pessimist, neutral, and optimist outlooks. The model has been implemented and an annual saving of more than $400,000 in inventory cost has been achieved.     

Dynamic planned safety stocks in supply networks

Safety stocks are commonly used in inventory management for tactically planning against uncertainty in demand and/or supply. The usual approach is to plan a single safety stock value for the entire planning horizon. More advanced methods allow for dynamically updating this value. We introduce a new line of research in inventory management: the notion of planning time-phased safety stocks. We assert that planning a time-phased set of safety stocks over a planning horizon makes sense because larger safety stocks are appropriate in times of greater uncertainty while lower safety stocks are more appropriate when demand and/or supply are more predictable. Projecting a vector of safety stock values is necessary to assure upstream members in the supply network have advanced warning of changes. We perform an empirical study of U.S. industry, which demonstrates that significant savings can be achieved by employing dynamic planned safety stocks, confirming recent case study reports. We provide a simple optimisation model for the problem of minimising inventory given a vector of safety stock targets. We propose a computationally efficient solution procedure and demonstrate its implementation in an MRP/ERP system. We then illustrate an MRP/ERP planning system feature, which employs a dynamic planned safety stock module that supports a production planner by showing the inventory implications of safety stock plans.     

Optimal maintenance—replacement policy under imperfect maintenance

During a given planning period, in order to have the system working at or below a fixed failure rate, it may be necessary to replace the system to minimize the expected total cost. Preventive maintenance (PM) or replacement should be performed whenever the system reaches the maximum failure rate. This paper formulates a cost model and a branching algorithm to determine the number of PM interventions to be performed between each replacement and the number of such replacements during the planning period to minimize the expected total cost. Adjustment of the failure rate for the system degradation after each PM intervention and inflationary trends in cost factors are also incorporated. Numerical illustration and computational times have been presented.     

Inventory relocation for overlapping disaster settings in humanitarian operations

The number and scale of humanitarian operations has significantly increased during the past decades due to the rising number of humanitarian emergencies and natural disasters worldwide. Therefore, the development of appropriate planning methods for optimization of the respective supply chains is constantly growing in importance. A specific problem in the context of humanitarian operations is the supply of relief items to the affected areas after the occurrence of a sudden change in demand or supply, for example, due to an epidemic or to unexpected shortages, during an ongoing humanitarian action. When such overlapping disasters occur, goods must be relocated to existing depots in a way which enables rapid supply to regions with new and urgent demand. At the same time, ongoing operations have to continue, i.e., the other regions should not suffer from shortages, and possible future emergencies must be taken into account. This is a planning situation under uncertainty as it is not known in advance if and where a disruption—and hence additional demand—will occur. In this paper, an optimization model for such situations is developed based on penalty costs for non-satisfied demand. A rolling horizon approach for solving the model is presented, and it is shown that taking into account the possibility of future disruptions can help to balance inventories and to reduce total non-served demand.     

A robust optimisation model for aggregate and detailed planning of a multi-site procurement-production-distribution system

The planning problem in the context of a multi-site procurement-production-distribution system (MSPPDS) considered in this paper is motivated from a real life case of a multinational consumer goods company. A robust optimisation model considering model robustness and solution robustness in the objective function is developed for integrated planning in three dimensions. Detailed production, procurement and distribution plans are integrated; countrywide aggregate production plan is integrated with a detailed plan. Similarly the detailed production plans from the previous planning cycle are integrated with current production plans. Constraints on storage space, production capacity and the time lag between procurement, production and distribution activities are captured in the model. Procurement and production plans are treated as ‘here-and-now’ decisions and the distribution plans are treated as ‘wait-and-see’ decisions to be implemented based on the realised demand scenario. The model is illustrated using an example problem and also successfully applied to the data of a consumer goods company involving 104,000 variables (with 832 integer variables) and 21,000 constraints.     

Workforce planning and allocation for mid-volume truck manufacturing: A case study

A case study for the short-term workforce planning and allocation for labour-intensive transfer lines is addressed. Trucks are assembled on a serial line, and they show large differences in the processing times at each station. These differences are due to the assembling options provided to the customers. Given the assignment of operations to stations, we have to find a loading sequence for the products, a worker allocation and a floater time allocation to minimize the whole labour costs at the line. We develop a solution approach for this problem and, in particular, discuss the necessities and implications by considering a rolling planning horizon. Especially, when planning for a number of subsequent shifts, we have to model the time interdependencies carefully. The results of the numerical studies show that relevant savings can be achieved by using an advanced planning system.     

A robust optimization approach to enhancing reliability in production planning under non-compliance risks

Certain regulated industries are monitored by inspections that ensure adherence (compliance) to regulations. These inspections can often be with very short notice and can focus on particular aspects of the business. Failing such inspections can bring great losses to a company; thus, evaluating the risks of failure against various inspection strategies can help it ensure a robust operation. In this paper, we investigate a game-theoretic setup of a production planning problem under uncertainty in which a company is exposed to the risk of failing authoritative inspections due to non-compliance with enforced regulations. In the proposed decision model, the inspection agency is considered an adversary to the company whose production sites are subject to inspections. The outcome of an inspection is uncertain and is modeled as a Bernoulli-distributed random variable whose parameter is the mean of non-compliance probabilities of products produced at the inspected site and, therefore, is a function of production decisions. If a site fails an inspection, then all its products are deemed adulterated and cannot be used, jeopardizing the reliability of the company in satisfying customers’ demand. In the proposed framework, we address two sources of uncertainty facing the company. First, through the adversarial setting, we address the uncertainty arising from the inspection process as the company does not know a priori which sites the agency will choose to inspect. Second, we address data uncertainty via robust optimization. We model products’ non-compliance probabilities as uncertain parameters belonging to polyhedral uncertainty sets and maximize the worst-case expected profit over these sets. We derive tractable and compact formulations in the form of a mixed integer program that can be solved efficiently via readily available standard software. Furthermore, we give theoretical insights into the structure of optimal solutions and worst-case uncertainties. The proposed approach offers the flexibility of matching solutions to the level of conservatism of the decision maker via two intuitive parameters: the anticipated number of sites to be inspected, and the number of products at each site that are anticipated to be at their worst-case non-compliance level. Varying these parameters when solving for the optimal products allocation provides different risk-return tradeoffs and thus selecting them is an essential part of decision makers’ strategy. We believe that the robust approach holds much potential in enhancing reliability in production planning and other similar frameworks in which the probability of random events depends on decision variables and in which the uncertainty of parameters is prevalent and difficult to handle.     

Development and application of a worker assignment model to evaluate a lean manufacturing cell

In lean manufacturing environments, cross-training is often used to achieve multi-skilling in order to increase flexibility in meeting fluctuating demand, to create a shared sense of responsibility, and to balance workload between cross-trained workers. This paper presents a model that assigns workers to tasks within a lean manufacturing cell while minimizing net present cost. In determining how to assign workers to tasks, the model addresses production requirements to meet customer demand, skill depth requirements for tasks, varying quality levels based on skill depth, and job rotation to retain skills for a cross-trained workforce. The model generates an assignment of workers to tasks and determines the training necessary for workers to meet skill requirements for tasks and customer demand. While the model can be used in a number of ways, in this paper it is used to generate a worker assignment schedule for cross-trained workers in a dedicated lean manufacturing cell in an electronics assembly plant and to evaluate the effect of increased cross-training on the cell. The resulting worker assignment schedules for the current state and several alternative scenarios for the cell are evaluated using cost results from the optimization model and from a simulation model to assess additional performance metrics. These results demonstrate the usefulness of the worker assignment model and indicate that moderate increases from current cross-training levels are not beneficial for this cell.