Montvelo is a manufacturer of luxury custom-order mountain bikes. The production

Question

Montvelo is a manufacturer of luxury custom-order mountain bikes. The production planning is to be done for the next four months, where the respective demands are d_1 = 10, d_2 = 24, d_3 = 16, and d_4 = 12 where d_i is the demand of bikes in the ith month. The setup cost is $10,000 and the unit production costs are $3,000 in the first two months and 2,500 in the third and the fourth month. The holding cost is $500 per bike per month. Using any method you like, find the optimal production schedule that minimizes the cost.

Explanation / Answer

In this problem, Montvelo is producing luxury car. In first four months demand are 10,24,16 and 12 respectively. Each time set up cost is $10,000. Holding cost of goods produced is $500 per unit per month. Production cost is $3,000 per bike for first two months. Then it will come down to $2,500 per month. You have to ascertain the production schedule that will optimize cost. Following points are considerd here.

1. Optimum production quantity per set up not mentioned. It is assumed that any quantity you can produce in a set up. So it is possible to produce full four months requirements in one set up.

2. second significant point is cost of production. Each unit will require extra $500 cost of production in first two months. So if you produce demanded items of month 3 or 4, then in addition to carry cost, you have to incur extra $500 per unit production cost. So it is not cost effective, if demand of third and 4th month is produced in 1st or 2nd month. So production judgement should be made in two parts. Consider first two months schedule and last two months schedule separately.

3. Suppose you want to produce first and second months quantity at a time. In that situation, you have to produce 10+24=34 units at a time in first month. From this quantity, only 10 units will be sold in first month. Rest 24 units will be carried for a month. So carry cost will be 24x$500=$12,000. It is higher than one extra set up cost of $10,000. So it is not ecoomical to produce first two months requiremerts at a time in first month. You must do two set up and produce exact demand of the month in the month itself. So in first month 10 units and in 2nd month, 24 units will be produced. Thus you can reduce carry cost of these two months to zero.

3. Now consider production of 3rd and 4th month. Total demand is 16+12=28. You can produce it in third month in full. Then only one set up cost will be required. From 28 units, 16 units will be sold in month 3. Balance 12 units will be carried for one month. It will require carry cost of 12x$500=$6,000. It is less than one extra set up cost of $10,000. Thus you have saved $10,000-$6,000=$4,000.

So optimal production schedule and minimized costs are shown below-

B. Cost data in $:

Answer: Optimum production schedule 10 units in month 1, 24 units in month 2 anf 28 units in month 3.

                   Minimized total cost $208,000

Details Month 1 Month 2 Month 3 Month 4 Total A.Quantities: 1. Demand (units) 10 24 16 12 62 2. Production (units) 10 24 28 0 62 3. Sold (units) 10 24 16 12 62 4. End stock carried (units)[2-3] 0 0 12 0 12 5. Begining stock 0 0 0 12 12

B. Cost data in $:

1. Production cost (per unit) 3,000 3,000 2,500 2,500 2. Total cost of goodssold [A3xB1] 30,000 72,000 40,000 30,000 172,000 3. Number of set up 1 1 1 0 3 4. Set up cost $10,00 each 10,000 10,000 10,000 0 30,000 5. Carry cost [A4x$500] 0 0 0 6,000 6,000 6. Total cost [B2+B4+B5] 40,000 82,000 50,000 36,000 208,000

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.