ABC Company provides a service to its clients. Each client has a job with a processing time of severaldays. Once the process starts for a client's job, it must be carried out without any interruption. Eachclient's job requires a certain number of operators in each day of its process. ABC must create a planfor the 4 available clients' jobs for the next 5 days with minimum number of operators needed tosatisfy this demand. The processing time of the client's jobs and the number of operators each of themneeds in each day is given below. For instance, client 1 has a job that lasts for 2 days, and 2 and 3operators are needed for days 1 and 2 of its execution.Number of operators needed per dayClient1234Processing time indays21321221323333245(a) Formulate an integer linear programming model to minimise the total operators needed.Describe decision variables, objective function, and constraints properly.

With the help of linear programming, we can solve optimization cases, here, we will define the…

Answered: (a) Formulate an integer linear…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 59P

See similar textbooks

Similar questions

Joan has a small design and tailoring shop making custom outfits for women. She has two employees. Each employee only begins working on a dress when a customer order has been received and then she makes the dress from beginning to end. The average production time of a dress is 1.8 days, with a standard deviation of 2.1 days. Historically, Joan has been receiving orders with interarrival times of one day on average. The interarrival times of orders have a coefficient of variation of one. (Carry at least 4 decimal places in all intermediate calculations. Round your final answer to 2 decimal places.) What is the expected waiting time, in days, between when an order is received and when production begins on the dress? A. 9.12 days B. 6.50 days C. 1.23 days D.3.41 days
A manufacturing plant produces a product 'A' that requires one unit of 'B' and ½ unit of 'C'. Each unit of 'B' is comprised of one unit of 'D', two units of 'E', and one unit of 'F'. Each unit of 'C' requires ½ unit of 'G' and three units of 'H'. The manufacturing lead times for the components are as follows: 'A' - two weeks, 'B' - one week, 'C' - two weeks, 'D' - two weeks, 'E' - three weeks, 'F' - one week, 'G' - two weeks, 'H' - one week. There are 20 units in stock for each of these components. 100 units of 'A' are needed for delivery in seven weeks: a) Develop the product structure and indexed bill of materials for the product. b) Create a gross and net requirements plan for the manufacturer of the product.
bama pie company's assembly line operations (the assembly line operates for six hundred minutes per day) comprise of eleven tasks, with the longest task time being 2.4 minutes and the shortest task time being 0.4 minutes; the sum of the task times is eighteen minutes. the firm is working on balancing its assembly line operations. the firm needs to produce 200 pies per day; to achieve this, the firm calculates the required cycle time as ---- minutes?
A firm that produces wood shutters and bookcases has received two orders for shutters: onefor 100 shutters and one for 150 shutters. The 100-unit order is due for delivery at the startof week 4 of the current schedule, and the 150-unit order is due for delivery at the start ofweek 8. Each shutter consists of two frames and four slatted wood sections. The wood sections are made by the firm, and fabrication takes one week. The frames are ordered, and leadtime is two weeks. Assembly of the shutters requires one week. There is a scheduled receiptof 70 wood sections in (i.e., at the beginning of) week 1. Determine the size and timingof planned-order releases necessary to meet delivery requirements under each of theseconditions:1. Lot-for-lot ordering (i.e., planned-order release equal to net requirements).2. Lot-size ordering with a lot size of 320 units for frames and 70 units for woodsections.
A serial process has 5 steps – A (4), B(5), C(2), D(6), and E(3) – that have to be performed in this order. The numbers in parentheses are the times (in minutes) needed to process a unit. For each unit produced by this process, the process has a total idle time of: Group of answer choices 1 min 10 mins 6 mins 3 mins
Consider a two-step process that handles three types of customers. Each resourceis staffed by one employee. Type 1 customers spend 5 minutes at resource 1 and 2 minutesat resource 2. Type 2 customers also spend 5 minutes at resource 1, but spend 10 minutes atresource 2. Finally, type 3 customers spend no time at resource 1 and 8 minutes at resource2. Each hour, the demand is 10 customers of type 1, 4 customers of type 2, and 2 customers oftype 3. Where in the process is the bottleneck? What is the flow rate for each customer type?
The manager of a large group of employees must decideif she needs another photocopying machine. The cost of amachine is $40 per 8-hour day whether or not the machineis in use. An average of 4 people per hour need to use thecopying machine. Each person uses the copier for an averageof 10 minutes. Interarrival times and copying times areexponentially distributed. Employees are paid $8 per hour,and we assume that a waiting cost is incurred when a workeris waiting in line or is using the copying machine. Howmany copying machines should be rented?
JOHNSON’S RULE Five specialty jobs at a La Crosse, Wisconsin, tool and die shop must be processed through two workcenters (drill press and lathe). The time for processing each job follows:Work (processing) Time for Jobs (hours)JOBWORK CENTER 1(DRILL PRESS) WORK CENTER 2(LATHE)A5 2B3 6C8 4D 10 7E 7 12
The Hickory Company manufactures wooden desks. Manage-ment schedules overtime every weekend to reduce the backlogon the most popular models. The automatic routing machineis used to cut certain types of edges on the desktops. The fol-lowing orders need to be scheduled for the routing machine: The due dates reflect the need for the order to be at its nextoperation.a. Develop separate schedules by using the FCFS and EDDrules. Compare the schedules on the basis of average flowtime and average past due hours.b. Comment on the performance of the two rules relative tothese measures
The ABC Company is planning a new product line and a new plant to produce the parts for the line. The product line will include 8 different models. Annual production of each model is expected to be 900 units. Each product will be assembled of 180 components. All processing of parts will be accomplished in the new plant. On average, 6 processing operations are required to produce each component, and each operation takes an average of 1 min (including an allowance for setup time and part handling). All processing opera-tions are performed at workstations, each of which includes a production machine and a human worker. The plant operates one shift. Determine the number of (a) components, (b) processing operations, and (c) workers that will be needed to accomplish the processing operations if each worker works 2,000 hr/yr.
A machine tool company conducts a job-training programme at a ratio of one for everyten trainees. The training programme lasts for one month. From past experience it has been found thatout of 10 trainees hired, only seven complete the programme successfully. (The unsuccessful traineesare released). Trained machinists are also needed for machining. The company's requirement for thenext three months is as follows:January: 100 machinists, February: 150 machinists and March: 200 machinists.In addition, the company requires 250 trained machinists by April. There are 130 trained machinistsavailable at the beginning of the year. Pay roll cost per month is:Each trainee Rs. 400/- per month.Each trained machinist (machining or teaching): Rs. 700/- p.m.Each trained machinist who is idle: Rs.500/- p.m.(Labour union forbids ousting trained machinists). Build a l.p.p. for produce the minimum costhiring and training schedule and meet the company’s requirement.
The objectives of scheduling include all of the following except: A. Increased inventories in order to maximize profits. B. The ability to balance conflicting goals. C. Effective use of facilities, labor, and equipment. D. Costs are minimized by reducing waiting times, work-in-process, and other processing costs related to inventories

SEE MORE QUESTIONS

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

SEE MORE TEXTBOOKS

(a) Formulate an integer linear programming model to minimise the total operators needed. Describe decision variables, objective function, and constraints properly.