Operations Research


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OR, Production Planning & Control, PERT/CPM

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Operations Research

  1. 1. Operations Research Production Planning & Control PERT/CPM Netwark Diagram Manisha Maheshwari Introduction to the Case Study 1
  2. 2. This case study is about a crude oil manufacturing company which has several operating units .These units process the crude oil that is pumped through and transform it into multitude of hydrocarbon products. The unit runs 24 hours a day ,7 days a week. However it needs to be shut down for maintenance at some point of time for cleaning and other maintenance purpose. One such unit is Distillation unit (DU5)in Aston which can operate continuously for 3.5 years without any major equipment breakdowns and excessive loss of efficiency. Therefore DU5 is shutdown every 3.5years for cleaning ,inspection and repairs. However, its shutdown severely affects all others operating units. This time of shut down is critical and the length of the shut down should be minimum to limit production loss. The Maintenance of DU5 is carried out in two phases 1st is opening and cleaning the unit and the 2nd phase is finding and repairing damages. Shale uses PERT as a planning & controlling tool to minimize shutdown time. 1
  3. 3. Discuss Production Planning & Control and its importance Production Planning & Control Production is a process whereby raw material is converted into semi finished products and thereby adds to the value of utility of products, which can be measured as the difference between the value of inputs and value of outputs. Production function encompasses the activities of procurement, allocation and utilization of resources. The main objective of production function is to produce the goods and services demanded by the customers in the most efficient and economical way. Therefore efficient management of the production function is of utmost importance in order to achieve this objective. Production system is a system whose function is to convert a set of inputs into a set of desired outputs. Production management involves the managerial decisions regarding design of the product and design of the production system i.e. determination of production processes and production planning and control. Once the entrepreneur has taken the decisions regarding the product design and production processes and system, his next task is to take steps for production planning and control, as this function is essentially required for efficient and economical production. Planning and control involve generally the organization and planning of manufacturing process. Especially it consists of the planning of routing, scheduling, dispatching inspection, and coordination, control of materials, methods machines, tools and operating times. The ultimate objective is the organization of the supply and movement of materials and labor, machines utilization and related activities, in order to bring about the desired manufacturing results in terms of quality, quantity, time and place. Production planning without production control is like a bank without a bank manager, planning initiates action while control is an adjusting process, providing corrective measures for planned development. Production control regulates and stimulates the orderly how of materials in the manufacturing process from the The large & complex project of any organization involve number of interrelated activities with limited resources such as men, machine, material, money & time. It is not possible for management to make & execute on optimum schedule based on organizational capacities intuition. It is always an lookout for some methods & techniques which may help in planning & controlling the project. The need for such methods have lead into the development of network analysis. 1
  4. 4. STEPS OF PRODUCTION PLANNING AND CONTROL Production Planning and Control (PPC) is a process that comprises the performance of some critical; functions on either side, viz., planning as well as control. Production planning: Production planning may be defined as the technique of foreseeing every step in a long series of separate operations, each step to be taken at the right time and in the right place and each operation to be performed in maximum efficiency. It helps entrepreneur to work out the quantity of material manpower, machine and money requires for producing predetermined level of output in given period of time. Production control: Production control is the process of planning production in advance of operations, establishing the extract route of each individual item part or assembly, setting, starting and finishing for each important item, assembly or the finishing production and releasing the necessary orders as well as initiating the necessary follow-up to have the smooth function of the enterprise. PPC Process Production Planning Planning: Planning is the technique of foreseeing every step in a long series of separate operations, each step to be taken at the right time and in the right place and each operation to be performed in maximum efficiency. It helps entrepreneur to work out the quantity of material manpower, machine and money requires for producing predetermined level of output in given period of time. 1
  5. 5. Routing: Under this, the operations, their path and sequence are established. To perform these operations the proper class of machines and personnel required are also worked out. The main aim of routing is to determine the best and cheapest sequence of operations and to ensure that this sequence is strictly followed. In small enterprises, this job is usually done by entrepreneur himself in a rather adhoc manner. Scheduling: It means working out of time that should be required to perform each operation and also the time necessary to perform the entire series as routed, making allowances for all factors concerned. It mainly concerns with time element and priorities of a job. Loading: The next step is the execution of the schedule plan as per the route chalked out it includes the assignment of the work to the operators at their machines or work places. So loading determines who will do the work as routing determines where and scheduling determines when it shall be done. The usefulness of their technique lies in the fact that they compare what has been done and what ought to have been done. Production control Dispatching: Dispatching involves issue of production orders for starting the operations. Necessary authority and conformation is given for: 1. Movement of materials to different workstations. 2. Movement of tools and fixtures necessary for each operation. 3. Beginning of work on each operation. 4. Recording of time and cost involved in each operation. 5. Movement of work from one operation to another in accordance with the route sheet. 6. Inspecting or supervision of work Dispatching is an important step as it translates production plans into production. Follow up: Every production programme involves determination of the progress of work, removing bottlenecks in the flow of work and ensuring that the productive operations are taking place in accordance with the plans. It spots delays or deviations from the production plans. It helps to reveal detects in routing and scheduling, misunderstanding of orders and instruction, under loading or overloading of work etc. All problems or deviations are investigated and remedial measures are undertaken to ensure the completion of work by the planned date. Inspection: This is mainly to ensure the quality of goods. It can be required as effective agency of production control. Corrective measures: Corrective action may involve any of those activities of adjusting the route, rescheduling of work changing the workloads, repairs and maintenance of machinery or equipment, control over inventories of the cause of deviation is the poor performance of the employees. Certain personnel decisions like training, transfer, demotion etc. may have to be taken. Alternate methods may be suggested to handle peak loads. Importance & Benefits Production planning and control can facilitate the entrepreneurs in the 1
  6. 6. following ways (1) Optimum Utilization of Capacity: With the help of Production Planning and Control [PPC] the entrepreneur can schedule his tasks and production runs and thereby ensure that his productive capacity does not remain idle and there is no undue queuing up of tasks via proper allocation of tasks to the production facilities. No order goes unattended and no machine remains idle. (2) Inventory control: Proper PPC will help the entrepreneur to resort to just- in- time systems and thereby reduce the overall inventory. It will enable him to ensure that the right supplies are available at the right time. (3) Economy in production time: PPC will help the entrepreneur to reduce the cycle time and increase the turnover via proper scheduling. (4) Ensure quality: A good PPC will provide for adherence to the quality standards so that quality of output is ensured. To sum up we may say that PPC is of immense value to the entrepreneur in capacity utilization and inventory control. More importantly it improves his response time and quality. As such effective PPC contributes to time, quality and cost parameters of entrepreneurial success. Discuss Operations Research & its Significance Operations Research 1
  7. 7. Operations research (O.R.) is the discipline of applying advanced analytical methods to help make better decisions. By using techniques such as mathematical modeling to analyze complex situations, operations research gives executives the power to make more effective decisions and build more productive systems based on:  More complete data  Consideration of all available options  Careful predictions of outcomes and estimates of risk  The latest decision tools and techniques O.R. is unique. It's best of breed, employing highly developed methods practiced by specially trained professionals. It’s powerful, using advanced tools and technologies to provide analytical power that no ordinary software or spreadsheet can deliver out of the box. And it’s tailored to you, because an O.R. professional offers you the ability to define your specific challenge in ways that make the most of your data and uncover your most beneficial options. To achieve these results, O.R. professionals draw upon the latest analytical technologies, including:  Simulation Giving you the ability to try out approaches and test ideas for improvement  Optimization Narrowing your choices to the very best when there are virtually innumerable feasible options and comparing them is difficult  Probability and Statistics Helping you measure risk, mine data to find valuable connections and insights, test conclusions, and make reliable forecasts Few definition of O.R  “O.R. is the art of giving bad answers to problems which otherwise have worse answers”--T. L. Satty.  “O.R. is the scientific method of providing executive departments with the quantitative basis for decision under their control.”--P. M. Morse and G. E. Kimball  “O.R. is a scientific approach to problems solving for executive management.”-- H. M. Wanger Significant features of O.R. 1. Decision-Making:- Primarily, O.R. is addressed to managerial decision- making or problem-solving. A major premise of O.R is that decision-making, irrespective of the situation involved, can be considered as general systematic process. 2. Scientific Approach:- O.R employs scientific methods for the purpose of solving problems. It is a formalized process of reasoning. 3. Objective:- O.R. attempts to locate the best or optimal solution to the problem under consideration. For this purpose, it is necessary that a measure of effectiveness is defined which is based on the goals of the organization. This 1
  8. 8. measure is then used as the basis to compare the alternative courses of action. 4. Inter- disciplinary Team Approach:- O.R. is interdisciplinary in nature & requires a team approach to a solution of the problem. Managerial problems have economic, physical, psychological, biological, sociological & engineering aspects. This requires a blend of people with expertise in the areas of mathematics, statistics, engineering, economics, management, computer science & so on 5. Digital Computer:- use of a digital computer has become an integral part of the O.R. approach to decision making. The computer may be required due to the complexity of the model, volume of data required & the computations to be made. Significance The Operations Research Value Proposition O.R. consistently delivers significant value – strategic to tactical, top-line to bottom- line – to the organizations and executives who use it. Organizations worldwide in business, the military, health care, and the public sector are realizing powerful benefits from O.R., including:  Business insight Providing quantitative and business insight into complex problems  Business performance Improving business performance by embedding model-driven intelligence into an organization’s information systems to improve decision making  Cost reduction Finding new opportunities to decrease cost or investment  Decision making Assessing the likely outcomes of decision alternatives and uncovering better alternatives  Forecasting Providing a better basis for more accurate forecasting and planning  Improved scheduling Efficiently scheduling staff, equipment, events, and more  Planning Applying quantitative techniques to support operations, tactical planning, and strategic planning  Pricing Dynamically pricing products and services  Productivity Helping organizations find ways to make processes and people more productive  Profits Increasing revenue or return on investment; increasing market share  Quality Improving quality as well as quantifying and balancing qualitative considerations  Recovery Gaining greater control and achieving turn-around  Resources Gaining greater utilization from limited equipment, facilities, money, and personnel  Risk Measuring risk quantitatively and uncovering factors critical to managing and reducing risk  Throughput Increasing speed or throughput and decreasing delays Answering the challenges you face today Organizations and the world in which they operate continue to become more 1
  9. 9. complex. Huge numbers of choices and relentless time pressures and margin pressures make the decisions you face more daunting and more difficult. Meanwhile, new enterprise applications and software are generating massive amounts of data – and it can seem like an overwhelming task to turn that data into insight and answers. But all that data and the availability of more and cheaper computing power are creating an important opportunity for decision makers – one O.R. is ideally designed to help you take advantage of. O.R. professionals thrive on challenges that involve large numbers of variables, complex systems, and significant risks. As a result, O.R. can help today’s executives with many of the specific challenges they face, such as:  Deciding where to invest capital in order to grow  Getting more value out of ERP, CRM, and other software systems  Figuring out the best way to run a call center  Locating a warehouse or depot to deliver materials over shorter distances at reduced cost  Forecasting sales for a new kind of product that has never been marketed before  Solving complex scheduling problems  Planning for a potential terrorist attack  Deciding when to discount, and how much  Getting more cycles out of manufacturing equipment  Optimizing a portfolio of investments, whether it contains financial securities or pharmaceutical product inventory  Deciding how large a budget to devote to Internet vs. traditional sales  Planting crops in the face of uncertainty about weather and consumer demand  Speeding up response time, whether selling a product or responding to a 911 call Techniques Employed The projects univentory variable activities employ PERT ( project evaluation review technique) whereas the project involving only deterministic activities are handled by CPM ( Critical path method) . Thus CPM is based on a single estimate of required. time to execute an activity. PERT system is based on the estimate of time required for executing the activity. We explain both the processes in detail. 1
  10. 10. USES of PERT/CPM 1. Construction of buildings, bridges, irrigation, project. 2. Budgets , auditing procedures 3. Missile developments. 4. Planning strategy. 5. Research & development. 6. Market penetration programme. 7. To find best traffic flow pattern in a large city. 8. Preparing univentory plans. PERT- Program Evaluation and Review Technique Complex projects require a series of activities, some of which must be performed sequentially and others that can be performed in parallel with other activities. This collection of series and parallel tasks can be modeled as a network. In 1957 the Critical Path Method (CPM) was developed as a network model for project management. CPM is a deterministic method that uses a fixed time estimate for each activity. While CPM is easy to understand and use, it does not consider the time variations that can have a great impact on the completion time of a complex project. The Program Evaluation and Review Technique (PERT) is a network model that allows for randomness in activity completion times. PERT was developed in the late 1950's for the U.S. Navy's Polaris project having thousands of contractors. It has the potential to reduce both the time and cost required to complete a project. The Network Diagram In a project, an activity is a task that must be performed and an event is a milestone marking the completion of one or more activities. Before an activity can begin, all of its predecessor activities must be completed. Project network models represent activities and milestones by arcs and nodes. The PERT chart may have multiple pages with many sub-tasks. The milestones generally are numbered so that the ending node of an activity has a higher number than the beginning node. Incrementing the numbers by 10 allows for new ones to be inserted without modifying the numbering of the entire diagram. Steps in the PERT Planning Process PERT planning involves the following steps: 1. Identify the specific activities and milestones. 2. Determine the proper sequence of the activities. 3. Construct a network diagram. 1
  11. 11. 4. Estimate the time required for each activity. 5. Determine the critical path. 6. Update the PERT chart as the project progresses. 1. Identify Activities and Milestones The activities are the tasks required to complete the project. The milestones are the events marking the beginning and end of one or more activities. It is helpful to list the tasks in a table that in later steps can be expanded to include information on sequence and duration. 2. Determine Activity Sequence This step may be combined with the activity identification step since the activity sequence is evident for some tasks. Other tasks may require more analysis to determine the exact order in which they must be performed. 3. Construct the Network Diagram Using the activity sequence information, a network diagram can be drawn showing the sequence of the serial and parallel activities. For the original activity-on-arc model, the activities are depicted by arrowed lines and milestones are depicted by circles or quot;bubblesquot;. If done manually, several drafts may be required to correctly portray the relationships among activities. Software packages simplify this step by automatically converting tabular activity information into a network diagram. 4. Estimate Activity Times Weeks are a commonly used unit of time for activity completion, but any consistent unit of time can be used. A distinguishing feature of PERT is its ability to deal with uncertainty in activity completion times. For each activity, the model usually includes three time estimates:  Optimistic time - generally the shortest time in which the activity can be completed. It is common practice to specify optimistic times to be three standard deviations from the mean so that there is approximately a 1% chance that the activity will be completed within the optimistic time.  Most likely time - the completion time having the highest probability. Note that this time is different from the expected time.  Pessimistic time - the longest time that an activity might require. Three standard deviations from the mean is commonly used for the pessimistic time. PERT assumes a beta probability distribution for the time estimates. For a beta distribution, the expected time for each activity can be approximated using the following weighted average: 1
  12. 12. Expected time = ( Optimistic + 4 x Most likely + Pessimistic ) / 6 This expected time may be displayed on the network diagram. To calculate the variance for each activity completion time, if three standard deviation times were selected for the optimistic and pessimistic times, then there are six standard deviations between them, so the variance is given by: [ ( Pessimistic - Optimistic ) / 6 ]2 5. Determine the Critical Path The critical path is determined by adding the times for the activities in each sequence and determining the longest path in the project. The critical path determines the total calendar time required for the project. If activities outside the critical path speed up or slow down (within limits), the total project time does not change. The amount of time that a non-critical path activity can be delayed without delaying the project is referred to as slack time. If the critical path is not immediately obvious, it may be helpful to determine the following four quantities for each activity:  ES - Earliest Start time  EF - Earliest Finish time  LS - Latest Start time  LF - Latest Finish time These times are calculated using the expected time for the relevant activities. The earliest start and finish times of each activity are determined by working forward through the network and determining the earliest time at which an activity can start and finish considering its predecessor activities. The latest start and finish times are the latest times that an activity can start and finish without delaying the project. LS and LF are found by working backward through the network. The difference in the latest and earliest finish of each activity is that activity's slack. The critical path then is the path through the network in which none of the activities have slack. The variance in the project completion time can be calculated by summing the variances in the completion times of the activities in the critical path. Given this variance, one can calculate the probability that the project will be completed by a certain date assuming a normal probability distribution for the critical path. The normal distribution assumption holds if the number of activities in the path is large enough for the central limit theorem to be applied. Since the critical path determines the completion date of the project, the project can be accelerated by adding the resources required to decrease the time for the activities in the critical path. Such a shortening of the project sometimes is referred to as project crashing. 1
  13. 13. 6. Update as Project Progresses Make adjustments in the PERT chart as the project progresses. As the project unfolds, the estimated times can be replaced with actual times. In cases where there are delays, additional resources may be needed to stay on schedule and the PERT chart may be modified to reflect the new situation. Benefits of PERT PERT is useful because it provides the following information:  Expected project completion time.  Probability of completion before a specified date.  The critical path activities that directly impact the completion time.  The activities that have slack time and that can lend resources to critical path activities.  Activity start and end dates. Limitations The following are some of PERT's weaknesses:  The activity time estimates are somewhat subjective and depend on judgment. In cases where there is little experience in performing an activity, the numbers may be only a guess. In other cases, if the person or group performing the activity estimates the time there may be bias in the estimate.  Even if the activity times are well-estimated, PERT assumes a beta distribution for these time estimates, but the actual distribution may be different.  Even if the beta distribution assumption holds, PERT assumes that the probability distribution of the project completion time is the same as the that of the critical path. Because other paths can become the critical path if their associated activities are delayed, PERT consistently underestimates the expected project completion time. CPM - Critical Path Method In 1957, DuPont developed a project management method designed to address the challenge of shutting down chemical plants for maintenance and then restarting the plants once the maintenance had been completed. Given the complexity of the process, they developed the Critical Path Method (CPM) for managing such projects. CPM provides the following benefits:  Provides a graphical view of the project. 1
  14. 14.  Predicts the time required to complete the project.  Shows which activities are critical to maintaining the schedule and which are not. CPM models the activities and events of a project as a network. Activities are depicted as nodes on the network and events that signify the beginning or ending of activities are depicted as arcs or lines between the nodes. Steps in CPM Project Planning 1. Specify the individual activities. 2. Determine the sequence of those activities. 3. Draw a network diagram. 4. Estimate the completion time for each activity. 5. Identify the critical path (longest path through the network) 6. Update the CPM diagram as the project progresses. 1. Specify the Individual Activities From the work breakdown structure, a listing can be made of all the activities in the project. This listing can be used as the basis for adding sequence and duration information in later steps. 2. Determine the Sequence of the Activities Some activities are dependent on the completion of others. A listing of the immediate predecessors of each activity is useful for constructing the CPM network diagram. 3. Draw the Network Diagram Once the activities and their sequencing have been defined, the CPM diagram can be drawn. CPM originally was developed as an activity on node (AON) network, but some project planners prefer to specify the activities on the arcs. 4. Estimate Activity Completion Time The time required to complete each activity can be estimated using past experience or the estimates of knowledgeable persons. CPM is a deterministic model that does not take into account variation in the completion time, so only one number is used for an activity's time estimate. 5. Identify the Critical Path The critical path is the longest-duration path through the network. The significance of the critical path is that the activities that lie on it cannot be delayed without delaying the project. Because of its impact on the entire project, critical path analysis is an important aspect of project planning. The critical path can be identified by determining the following four parameters for each activity: 1
  15. 15.  ES - earliest start time: the earliest time at which the activity can start given that its precedent activities must be completed first.  EF - earliest finish time, equal to the earliest start time for the activity plus the time required to complete the activity.  LF - latest finish time: the latest time at which the activity can be completed without delaying the project.  LS - latest start time, equal to the latest finish time minus the time required to complete the activity. The slack time for an activity is the time between its earliest and latest start time, or between its earliest and latest finish time. Slack is the amount of time that an activity can be delayed past its earliest start or earliest finish without delaying the project. The critical path is the path through the project network in which none of the activities have slack, that is, the path for which ES=LS and EF=LF for all activities in the path. A delay in the critical path delays the project. Similarly, to accelerate the project it is necessary to reduce the total time required for the activities in the critical path. 6. Update CPM Diagram As the project progresses, the actual task completion times will be known and the network diagram can be updated to include this information. A new critical path may emerge, and structural changes may be made in the network if project requirements change. CPM Limitations CPM was developed for complex but fairly routine projects with minimal uncertainty in the project completion times. For less routine projects there is more uncertainty in the completion times, and this uncertainty limits the usefulness of the deterministic CPM model. An alternative to CPM is the PERT project planning model, which allows a range of durations to be specified for each activity. Network Diagram Elements of Network:- A) Activity:- An individual operation which consumes resources and has a beginning and an end is called activity. An arrow ( ) is often used to represent an activity in the network diagram with its head indicating the direction of programme of the project. 1
  16. 16. B) Event:- Event represents a point in time signifying the completion of some activities and beginning of new ones. It is usually represent by a circle ( O ) in the network diagram and is also called as a mode or a connector. Types of Events:- 1) Start Event:- Is for which there is no preceding activity. Obviously, it will have no arrow entering into it but will have arrows emerging from it. 2) End Event:- Is for which there is no succeeding activity. Again this event won’t have any arrow emerging out but will have all arrows entering in. 3) First Event:- Is from which 2 or more activities emerge. ( O ) 4) Merge Event:- Is in which 2 or more activities merge. ( O) C) Dummy Activity:- is an activity with zero duration. Does not consume any resources but merely shows the technological dependencies. It is inserted in the network under following situation:- a. Created to make activities with common starting, finishing events distinguishable. b. To identify and maintain proper precedence relation between activities that are not connected by events. (They are represent by dotted lines in the network.) When all activities and events in a project are connected logically and sequentially they form a network. RULES FOR DRAWING A NETWORK:- 1
  17. 17. 1) Each activity will have two events. 2) Each activity should be represent by one and only one arrow in the network. 3) Length of an arrow is immaterial. 4) In beginning & end, there can be only 1 event, in between you can have multiple events. 5) No two activities can have same start and event. To avoid such situations a dummy activity can be introduced. A dummy line is a dotted line. It is drawn when there is no connection between the events. 6) The arrow should be drawn as straight lines from left to right and no arrows should cross each other. 7) One should take care that there are no loop formations in the network. 1
  18. 18. PERT Network Diagram of Shale Oil Co. & DU5. Cleaning, Repair & Maintenance of DU5 (Circle) Stands for Event (Arrow) stands for Activity 2 2 2 22 9 1 1 2 33 4 1 5 10 6 11 15 1 2 3 1 7 1 1 8 1 19 1
  19. 19. Time Estimates (In Days) Activity Optimistic Most likely Pessimistic Expected Time Variance (to) (tm) (tp) (te) σ² 1-2 1 2 2.5 1.9167 0.0625 2-3 1.5 2 2.5 2 0.0277 3-4 2 3 4 3 0.1111 3-5 1 2 3 2 - 3-6 1 2 4 2.1667 - 3-7 2 2.5 3 2.5 - 3-8 2 4 5 3.833 - 4-9 1 2 3 2 0.1111 5-10 1 1.5 2 1.5 - 5-11 1 1.5 2 1.5 - 6-12 2 2.5 3 2.5 - 6-17 15 20 30 20.833 - 7-13 1 1.5 2 1.5 - 7-18 3 5 8 5.1667 - 8-19 3 8 15 7 - 9-14 14 21 28 21 5.4444 10-16 1 5 10 5.1667 - 11-15 2 5 10 5.333 - 12-17 5 10 20 10.833 - 13-18 10 15 25 15.833 - 14-20 4 5 8 5.333 0.4444 15-16 1 2 3 2 - 16-20 1 2 2.5 1.9166 - 17-20 1 2 3 2 - 18-20 1 2 3 2 - 19-20 2 4 6 4 - 20-21 1.5 2 2.5 2 0.0277 21-22 1 3 5 3 0.4444 22-23 3 5 10 5.5 1.3611 Where, Expected time = ( Optimistic + 4 x Most likely + Pessimistic ) / 6 Variance = [ ( Pessimistic - Optimistic ) / 6 ]2 1
  20. 20. Σσ²=8.0344 Critical path = 1-2-3-4-9-14-20-21-22-23 Duration of the project= 45.7479 Days P (shutdown can be completed one week earlier) 45.7497-7= 38.7497 P (t<=38.7497) P (z<=38.7497-45.7497/2.83450) =0.00676 P (Finishes maintenance project one day earlier) P (z<=44.7497-45.7497/2.83450) =0.36212 P (Finishes maintenance project two days earlier) P (z<=43.7497-45.7497/2.83450) =0.24022 P (Finishes maintenance project three days earlier) P (z<=42.7497-45.7497/2.83450) =0.14494 P (Finishes maintenance project four days earlier) P (z<=41.7497-45.7497/2.83450) =0.0791 P (Finishes maintenance project five days earlier) P (z<=40.7497-45.7497/2.83450) =0.03887 P (Finishes maintenance project six days earlier) P (z<=39.7497-45.7497/2.83450) 1
  21. 21. = 0.01714 Shale oil is considering, increasing the budget to shorten the shutdown. How do you suggest the company proceed? As the company is ready to increase the budget to shorten the loss at the time of shutdown the company must employ a good amount of direct cost i.e. ,cost must be incurred on manpower loading, good equipments ,direct material etc. in respect of various productive activities. Also, proper planning of raw material should be done in order to maintain the flow of manufacturing activity. A good amount of finished product should be maintained so as to avoid the shortage during the length of shut down time. Also, skilled and efficient labor force should employed to increase the productive capacity. 1