एक बिक्री मैनेजर चार विक्रेताओं को बिक्री के लिए चार क्षेत्र नियत करना चाहता है। अलग- अलग विक्रेताओं की योग्यता और कौशल अलग-अलग हैं। अतः प्रत्येक क्षेत्र में प्रत्याशित बिक्री अलग-अलग होगी। अलग-अलग क्षेत्रों में प्रत्येक विक्रेता की प्रतिमाह बिक्री के आँकड़े नीचे दिये गये हैं :
| विक्रेता | आकलित मासिक बिक्री क्षेत्र | ||||||||
| I | II | III | IV | ||||||
| A | 20 | 40 | 45 | 30 | |||||
| B | 50 | 40 | 55 | 40 | |||||
| C | 45 | 40 | 42 | 50 | |||||
| D | 48 | 50 | 42 | 45 | |||||
चार विक्रेताओं का चार अलग-अलग क्षेत्रों में इष्टतम नियतन ज्ञात कीजिए और अधिकतम मासिक बिक्री भी बताइए।
यह समस्या आवंटन समस्या (Transportation Problem) के रूप में प्रस्तुत की गई है, जहाँ हमें विक्रेताओं को क्षेत्रों में आवंटित करना है ताकि अधिकतम मासिक बिक्री प्राप्त हो सके। इसे हल करने के लिए हम आवंटन तकनीक का उपयोग करेंगे, जो एक विशेष प्रकार की ऑप्टिमाइजेशन समस्या होती है। स्टेप 1: तालिका को ___ _______ _________ _______ ______ __________ ___ _____.
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इनमें से कौन-से हल सुसंगत हैं? स्पष्ट कीजिए।
In a factory, there are six jobs to perform each of which should go through two machines A and B in the order A B. The processing timings (in hours) for the jobs are given here. You are required to determine the sequence for performing the jobs that would minimize the total elapsed time T, what is the value of T?
A manufacturing company needs 2500 units of a particular item every year. The company buys it at the rate of ₹ 30 per unit. The order processing cost for this item is estimated at ₹ 15 and the cost of carrying a item in stock comes to about ₹ 4 per year. The company can manufacture this item internally. In that case it saves 20% of the price of the product. However, it estimates a set-up cost of ₹ 250 per production run. The annual production rate would be 4800 units. However, the inventory holding costs remain unchanged.
i) Determine the EOQ and the optimal number of orders placed in a year.
ii) Determine the optimum production lot size and the average duration of the production run.
Find the optimum solution to the following transportation problem:
Which of the following statements are true? Give reasons for your answers.
i) If an item is ordered frequently, then the risk of running out of stock is least.
ii) In deterministic queuing model, arrival rate must not exceed the service rate.
iii) The critical path of a project network represents the minimum time needed to complete the project.
iv) A necessary and sufficient condition for a basic feasible solution for a minimization LPP to be optimum is that all Zj - Cj 20.
v) If dual has an unbounded solution, primal has a feasible solution.
Use branch and bound method to solve the following LPP:
Minimize:
Z + 4x1 + 3x2
Subject to the constraints:
x1,x2 ≥ and are integers.
Use dual simplex method to solve the following LPP:
Minimize:
z = 3x1 + x2
Subject to the constraints:
