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Elizabeth Burke wants to develop a model to more effec - tively plan production for the next year. Currently, PLE has a planned capacity of
Elizabeth Burke wants to develop a model to more effec tively plan production for the next year. Currently, PLE has a planned capacity of producing mowers each month, which is approximately the average monthly demand over the previous year. However, looking at the unit sales figures for the previous year, she observed that the demand for mowers has a seasonal fluctuation, so with this "level" production strategy, there is overproduction in some months, resulting in excess inventory buildup, and underproduction in others, which may result in lost sales during peak demand periods. Ms Burke explained that she could change the pro duction rate by using planned overtime or undertime pro ducing more or less than the average monthly demand but this incurs additional costs, although it may offset the cost of lost sales or of maintaining excess inventory. Con sequently, she believes that the company can save a signif icant amount of money by optimizing the production plan. Ms Burke saw a presentation at a conference about a similar model that another company used but didn't fully understand the approach. The PowerPoint notes didn't have all the details, but they did explain the variables and the types of constraints used in the model. She thought they would be helpful to you in implementing an optimiza tion model. Here are the highlights from the presentation: Variables: planned production in period inventory held at the end of period number of lost sales incurred in period amount of overtime scheduled in period amount of undertime scheduled in period increase in production rate from period to period decrease in production rate from period to period Material balance constraint: demand month Overtimeundertime constraint: normal production capacity Production ratechange constraint: Ms Burke also provided the following data and estimates for the next year: unit production cost $; inventoryholding cost $ per unit per month; lost sales cost $ per unit; overtime cost $ per unit; undertime cost $ per unit; and productionratechange cost $ per unit, which applies to any increase or decrease in the production rate from the previous month. Initially, units are expected to be in inventory at the beginning of January, and the pro duction rate for the past December was units. She believes that monthly demand will not change substan tially from last year, so the mower unit sales figures for the last year in the Performance Lawn Equipment Database should be used for the monthly demand forecasts. Your task is to design a spreadsheet that provides detailed information on monthly production, inventory, lost sales, and the different cost categories and solve a linear optimization model for minimizing the total cost of meeting demand over the next year. Compare your solution with the level production strategy of producing units each month. Interpret the Sensitivity Report and conduct an appropriate study of how the solution will be affected by changing the assumption of the lost sales costs. Summarize all your results in a report to Ms Burke.
Elizabeth Burke wants to develop a model to more effec
tively plan production for the next year. Currently, PLE
has a planned capacity of producing mowers each
month, which is approximately the average monthly
demand over the previous year. However, looking at the
unit sales figures for the previous year, she observed that
the demand for mowers has a seasonal fluctuation, so with
this "level" production strategy, there is overproduction in
some months, resulting in excess inventory buildup, and
underproduction in others, which may result in lost sales
during peak demand periods.
Ms Burke explained that she could change the pro
duction rate by using planned overtime or undertime pro
ducing more or less than the average monthly demand
but this incurs additional costs, although it may offset the
cost of lost sales or of maintaining excess inventory. Con
sequently, she believes that the company can save a signif
icant amount of money by optimizing the production plan.
Ms Burke saw a presentation at a conference about a
similar model that another company used but didn't fully
understand the approach. The PowerPoint notes didn't
have all the details, but they did explain the variables and
the types of constraints used in the model. She thought
they would be helpful to you in implementing an optimiza
tion model. Here are the highlights from the presentation:
Variables:
planned production in period
inventory held at the end of period
number of lost sales incurred in period
amount of overtime scheduled in period
amount of undertime scheduled in period
increase in production rate from period
to period
decrease in production rate from period
to period
Material balance constraint:
demand month
Overtimeundertime constraint:
normal production capacity
Production ratechange constraint:
Ms Burke also provided the following data
and estimates for the next year: unit production
cost $; inventoryholding cost $ per unit
per month; lost sales cost $ per unit; overtime
cost $ per unit; undertime cost $ per unit;
and productionratechange cost $ per unit, which
applies to any increase or decrease in the production rate
from the previous month. Initially, units are expected
to be in inventory at the beginning of January, and the pro
duction rate for the past December was units. She
believes that monthly demand will not change substan
tially from last year, so the mower unit sales figures for the
last year in the Performance Lawn Equipment Database
should be used for the monthly demand forecasts.
Your task is to design a spreadsheet that provides
detailed information on monthly production, inventory,
lost sales, and the different cost categories and solve a
linear optimization model for minimizing the total cost
of meeting demand over the next year. Compare your
solution with the level production strategy of producing
units each month. Interpret the Sensitivity Report
and conduct an appropriate study of how the solution will
be affected by changing the assumption of the lost sales
costs. Summarize all your results in a report to Ms Burke.
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