Outboard Boat Company

The Outboard Boat Company is in the business of manufacturing motorboats. The company needs a production plan for the year for its plant in Spring Valley, Tennessee. The Outboard Boat Company has four demands for the four different quarters of the year that need to be met. The company has to construct a minimum cost plan for the year that must incorporate the demand, inventory cost, carry over cost, regular workers, and overtime workers to meet its total production for the year. By using a minimum cost plan with standard variables the company can meet their demand and total production and only spending a cost of around $7 million for the year.

Table of Contents

1) INTRODUCTION

2) PROBLEM STATEMENT

3) MODEL FORMULATION

4) MODEL VERIFICATION

5) ASSUMPTIONS

6) RESULTS

7) SUMMARY

8) APPENDICES

Introduction

The Outboard Boat Company needs a minimum cost production plan for the year. The demand for boats is divided into four quarters of the year:

Jan.-Mar. 570 boats

Apr.-June 2165 boats

July-Sept. 3120 boats

Oct.-Dec. 735 boats

Total 6590 boats needed in the year.

The total production for the year must equal its total demand. However, a boat used to meet the demand for a particular quarter need not necessarily have been produced in that quarter. The boat could have been made in an earlier quarter and held in inventory. The inventory holding cost for a boat increases proportionately with the number of quarters it is kept in inventory. Company officials estimate constant of proportionality to be $180 per boat per quarter. Similarly, demand can be “carried over” from one quarter to the next at an estimated cost of $630 per boat per quarter. However, this carryover cannot occur at the end of the year.

A conversion factor between boats produced and workers employed on regular time obtained by dividing the number of boats produced by the number of regular-time workers required to produce them, equals 7.5 boats per employee-quarter. Unfortunately, the factor declines to 6.9 boats per employee-quarter for overtime.

The labor agreement requires overtime compensation for a person working more than 40 hours per week. The agreement allows the company to insist upon as much as ten overtime hours per employee per week. The company may request a person to work more than ten overtime hours in one week. However, the request may be accepted or rejected at the discretion of the worker. Accountants report that regular time compensation averages to $6900 per worker-quarter. A premium of 30% for overtime wages results in an “overtime only” cost of $8970 per worker-quarter. Accountants also report that the cost of hiring a worker averages to $1150, and the cost of laying off a worker averages to $2800. The workforce at the beginning of the year consists of 160 employees. There are initially 50 boats in inventory.

Problem Statement

The Outboard Boat Company is trying to minimize spending cost for the year while still meeting their demand and total production for the year. To minimize the cost for the year the company must consider the cost of hiring and firing of workers, the cost regular-time employees and “overtime only” employees, and finally the cost of inventory carry over and demand carry over.

Model Formulation

To construct this minimum cost model, we must first define all the variables used.

X = Regular-Time Workers (1, 2, 3, 4 for the different quarters) = $6900/quarter

Y = Overtime Only Workers (1, 2, 3, 4 for the different quarters) = $8970/quarter

H = New Hired Workers (1, 2, 3, 4 for the different quarters) = $1150/quarter

F = Fired Workers (1, 2, 3, 4 for the different quarters) = $2800/quarter

IM = Demand “Carry Over” Cost (1, 2, 3, 4 for the different quarters) = $630/quarter

IP = Inventory Hold over Cost (1, 2, 3, 4 for the different quarters) = $180/quarter

Then we must define a MIN Z and also some standard constraints.

Min Z = 6900X(1,2,3,4) + 8970Y(1,2,3,4) + 1150H(1,2,3,4) + 2800F(1,2,3,4) + 630IM(1,2,3,4) + 180IP(1,2,3,4)

Constraints:

7.5X(1,2,3,4) + 6.9Y(1,2,3,4) = 6590

7.5X1 + 6.9Y1 + IM1 вЂ" IP1 + 50 = 570

7.5X2 + 6.9Y2 + IP1 + IM2 вЂ" IP2 = 2165

7.5X3 + 6.9Y3 + IP2 + IM3 вЂ" IP3 = 3120

7.5X4 + 6.9Y4 + IP3 + IM4 вЂ" IP4 = 735

X1 + Y1 вЂ" H1 + F1 = 160

-X1 + X2 вЂ" Y1 вЂ" H2 + F2 + Y2 = 0

-X2 + X3 вЂ" Y2 вЂ" H3 + F3 + Y3 = 0

-X3 + X4 вЂ" Y3 вЂ" H4 + F4 + Y4 = 0

.25X1 вЂ" Y1 >= 0

.25X2 вЂ" Y2 >= 0

.25X3 вЂ" Y3 >= 0

.25X4 вЂ" Y4 >= 0

IM4 = 0

Model Verification

..title

Outboard Boat ID # 102

..objective min

+6900X1+6900X2+6900X3+6900X4+8970Y1+8970Y2+8970Y3+8970Y4+1150H1 +1150H2+1150H3+1150H4+2800F1+2800F2+2800F3+2800F4+630IM1+630IM2 +630IM3+630IM4+180IP1+180IP2+180IP3+180IP4+0.0000

...