Develop an algebraic linear programming model, Advanced Statistics

Duck Lovers Unlimited (DLU) Inc. assembles specially configured light jet aircrafts for airborne duck hunting. The quarterly demand forecasts for the upcoming fiscal year are:

Quarter:                      1                        2                      3                  4               

Forecast (units):         11                       17                     8                  15

It takes an average of 2500 direct labor hours to assemble each aircraft. Currently, 48 full-time production workers are employed by DLU, working a single 8-hour shift each day. As of now, there is no inventory of completed or semi-finished units. Demand backlogging is possible, but 20% of backlogged demand eventually turns out to be lost sales, representing an opportunity loss of $80,000 per unit (aircraft). Under-time or overtime work may be resorted to, the latter being restricted to 4 hours per day for each worker. The average regular time labor wage rate is $10/hour, with a 50% premium for overtime work. Finished goods inventory holding costs are $16,000/unit/year and backordering costs are estimated to be $9,500/quarter for each aircraft. The inventory holding and backlogging costs, if any, are charged to end-of-quarter finished goods inventories and backorders, respectively. The workforce size can be varied through hires or layoffs (done at the beginning of any quarter) at $3,200 or $3,000, respectively, per worker. For simplicity, assume that there are about 500 regular-time hours in a typical quarter. Material and overhead costs per aircraft amount to $20,000. 

(a) Using the information given above, develop a minimum-cost, 4-quarter aggregate sales and operations plan (SOP) for DLU, such that the workforce size is constant throughout the year (after initial hires or layoffs, as necessary), allowing no overtime, backorders, lost sales or part-time employees. Summarize your SOP in a tabular format shown below and compute the resulting total relevant cost for the next fiscal year.

Demand          Production      Ending Inventory        Workforce

Quarter      (Units)                (Units)                (Units)                 (No. of Workers)

      1               11

      2               17

      3                8

      4               15                                                                                                   _

(b) In order to cope with demand uncertainty, DLU management has decided on a safety stock policy, requiring that at the end of each quarter, the planned finished goods inventory be at least 10% of that quarter's demand forecast. Repeat part (a) with this policy in effect.

(c) Removing all restrictions outlined in part (a), but with the safety stock policy (b) in effect, develop an algebraic linear programming model ( i.e. clearly define all decision variables used and formulate the objective function and all constraints) for determining the optimal SOP for DLU. Solve this model using Excel/Solver, showing the optimal aggregate plan and the resulting minimum total relevant cost for the next fiscal year.

Posted Date: 2/25/2013 12:06:46 AM | Location : United States







Related Discussions:- Develop an algebraic linear programming model, Assignment Help, Ask Question on Develop an algebraic linear programming model, Get Answer, Expert's Help, Develop an algebraic linear programming model Discussions

Write discussion on Develop an algebraic linear programming model
Your posts are moderated
Related Questions
Economic Interpretation of the Optimum Simplex solution

The distribution free or technique which is the analogue of the analysis of variance for the design with two factors. It can be applied to data sets which do not meet the assumptio

Described by the leading proponent as 'the conscientious, explicit, and judicious uses of present best evidence in making the decisions about the care of individual patients, and

Paul Jordan has just been hired as a management analyst at Digital Cell Phone Inc. Digital Cell manufactures a broad line of phones for the consumer market. Paul's boss, John Smith

Occam's razor  is an early statement of the parsimony principle, which was given by William of Occam (1280-1349) namely 'entia non sunt multiplicanda praeter necessitatem'; which m

Geo statistics: The body of methods useful for understanding and modelling spatial variability in a course of interest. Central to these techniques is the idea that measurements t

Hello! I am currently in graduate school earning a masters in mental health counseling. I am in a stats course at current and we are reviewing z-scores. I am a little lost because

A term commonly encountered in the analysis of the contingency tables. Such type of frequencies are the estimates of the values to be expected under hypothesis of interest. In a tw

a sequence of numbers consist of six 6''s seven 7''s eight 8''s nine 9''s ten 10''s what is the arithmetic mean?

Reasons for screening data     Garbage in-garbage out     Missing data          a. Amount of missing data is less crucial than the pattern of it. If randomly